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A MEMORIAL 



BY 



W SARTORIUS VON WALTERSHAUSEN 




S T A N F () U D I' N I V K R S I T Y L I B R A R I r S 



GAUSS 



A MEMORIAL 



by 



W. SARTORIUS VON WALTERSHAUSEN 



LEIPZIG 



Publisher: S. Hirzel 



1856 



GzSsis 



Translator's Note 

The translator, a great-granddaughter of the 
mathematician, wishes to call attention to the fact 
that the writer of this Memorial, Baron Wolfgang 
Sartorius von Walthershausen, Professor of Geology at 
the University of Gfottingen, wrote over one hundred 
years ago and immediately after the death of his 
long-cherished friend and colleague. This to some 
extent explains the extreme feeling and language 
of the Memorial. In the interests of clarity the 
somewhat archaic German has been given a very free 
rendering. 

In a personal letter to the translator, dated 
August 5, 1949, Dr. Albert Einstein wrote as 
follows : 

"The importance of C. F. Gauss for the 
development of modern physical theory 
and especially for the mathematical 
fundament of the theory of relativity 
is overwhelming indeed; also his 
achievement of the system of absolute 
measurement in the field of electro- 
magnetism. " 



Helen Worthington Gauss 



June 26, 1966 

Colorado Springs, Colorado 



-1- 



AUTHOR'S FOREWORD TO THE GERMAN EDITION 



Soon after the great man to whose memory these 
pages are dedicated had closed his searching blue eyes 
came the thought that a voice should be raised from 
this scene of his activity which extended from his early 
years through almost half a century. This voice should 
be that of one who loved him and would describe his life 
in a manner befitting his immortal name and also the 
honor of our "Georgia Augusta."* 

I know well that I can but incompletely meet the 
demands of this task that has been put upon me, yet I 
nay be allowed to sketch the life of this great spirit 
towering high over his century, not with the intention 
Df raising a monument to him (this he does not need) nor 
^ith a view of bringing into one wide compass his in- 
spiring discoveries. This is a task the full reach of 
^hich will presently be undertaken from another angle. I 
seek rather to acquit myself of a sacred obligation. At 
a time when our great loss is still a living sorrow I 
^ould sharply engrave upon our minds the memory of him 
^ho has left us. 

My desire is to give my readers a true picture of 
the man to whom no nation of today can present an equal, 
to grasp his forthright simple personality. With the 
lA/armth of my own feeling I would remind the oncoming 
generation of his Heaven-sent influence, for it is upon 
the foundation of his profound researches that they will 
be building. 



University of Goettingen ♦_.._ 



Also, since I am in possession of thoroughly reliable 
source material from which this sketch is drawn, I wish to 
correct certain erroneous rumors which have been given 
publicity. Now I give it to the public, hoping it may 
find a friendly reception among the many students and 
admirers of the great mathematician, and may also create 
a wider interest. 

From time to time in world history highly gifted, 
rarely endowed natures have stepped forth from the murk 
of their surroundings and through the creative force of 
their minds and the energy of their achievements have 
exercised a surpassing influence upon the spiritual 
development of nations. They stand like boundary stones 
between different centuries. From them new trends have 
come into Man's civilization. 

As such pioneer spirits we have in the history of 
mathematics and the natural sciences Archimedes of 
Syracuse for ancient times, Newton after the close of 
the Middle Ages, and for our day Gauss, whose life was 
ended this year, 1855, on the 23rd day of February. 

During his life we saw in him an extraordinary 
spirit, mightily striving, richly endowed by nature with 
very great gifts. To his profound power of thought was 
added an amazing memory. He had moreover a strength of 
will which carried him through seemingly impossible 
tasks. 

From such a mind, uniting varied and rarely com- 
bined talents and sustained by a strong body, have come 
in the past sixty years creations of genius which have 
moved to reverence the most profound thinkers of our 
time, an honor to our century. 



-iii- 



Gauss' life was dedicated to that free science 
which refuses to be narrowed to practical applications 
and which is placed of its own right with the stars 
above, to proclaim the immortal in the soul of Man. 
This loftiness of thought guided Gauss throughout life 
and is now left as a sacred legacy to our University, 
that far into the future pure science may live on in 
our midst, vigorous and vivifying. 



-IV- 



Carl Friedrich Gauss was born April 30, 1111 ^ in a 
small poor house on the Wendengraben in Braunschweig, of 
parents in humble circumstances. His father's father 
lived in the country and about 1740 moved to Braunschweig 
to settle there and support himself chiefly with garden- 
ing. He had three sons of whom Gauss' father, born in 
1744, was the second. The other two, of whom no descen- 
dents are known, died much earlier than he. 

Gauss' father held the title of Master of Water- 
works and followed a variety of occupations. In time 
these brought him a kind of prosperity and he gave up 
most of them. For the last fifteen years of his life - 
up to his death in 1808 - he retained only a little 
gardening business. Also he assisted a merchant in the 
Braunschweiger and Leipsiger Fair and since he wrote and 
reckoned well managed a small office for a large Burial 
Insurance Society, recording and collecting payments. 
He was a completely upright, estimable, well respected 
man. But at home he was dictatorial and harsh. It was 
natural that Gauss as a child could not turn to him for 
understanding. Yet there was no discord between them, 
for Gauss early became wholly independent. 

Gauss' father was married twice. By the first 
marriage he had a son George, born in 1768, who left 
his father's home early to learn a trade, moved about 
to different places, and in 1794 returned to Braun- 
schweig because of serious eye trouble which had 
forced him to give up his trade. But the father 
tolerated no idleness, and the son turned soldier 
since it was too late to learn a new trade. On the 
side he helped his father in all his business. In 
1806 he withdrew from military service, and on his 
father's death two years later became manager of the 
Burial Society, holding this office up to the day of 
his death, August 7, 1854. 



-1- 



Gauss* grandfather on his mother *s side, Christopher 
Benze, was a stonemason in the village of Velpke, five 
miles from Braunschweig. Through his work he contracted 
consumption and died in his thirtieth year, leaving a 
daughter Dorothea and a younger son Friedrich, The son 
learned weaving and soon, without instruction from others, 
was doing artistic damask weaving, showing in general an 
intelligent, keen brain. Gauss as a child found great 
pleasure in his clever uncle and in later years found 
still more, leading him into talk on stimulating j chal- 
lenging subjects. He saw in him unusual gifts and always 
regretted his early death, saying: "A born genius was 
lo^st in him." 

The daughter Dorothea, born in 1742, came to 
Braunschweig about the year 1769 and married Gauss' father 
in 1776. She had a naturally clever mind, a straight- 
forward, humorously gay disposition and a strong character 
Her great son was her only child, her pride and joy. She 
clung to him, as he to her, with warm devotion up to her 
last hour. She was of strong constitution, but completely 
blind from cataract the last four years of her life. She 
died in April, 1839, at the age of ninety-seven, at our 
Goettingen Observatory, where she had lived with her son 
for the last twenty-two years of her life. 

As long as he lived Gauss cherished memories of the 
narrow little homecircle of his childhood. In old age he 
liked to recall characteristic little episodes which 
reflected the outwardly restricted, modest homelife, but 
in which one detected the sparks of genius which later 
rose to such heights. He remembered these incidents 
accurately and in recounting them he never varied the 
details o His amused and cheerful telling gave them a 
delightful charm which would be lost were they to be 
repeated in print. 



-2- 



When very small, he recalled, he was once near 
death • The Wendengraben on which his parents lived was 
in those days an open canal connected with the Ocker 
river, and in the spring was full of water. The little 
fellow was playing by it one day, when he fell in, to be 
saved just as he was sinking, as if preserved by Provi- 
dence for his high achievements in the world of Science. 

While still very young Gauss showed rare mental 
gifts • He leajrned to read by asking one or another in 
the home the sound of the letters. His marked aptitude 
for numbers and his ease and accuracy in mental arith- 
metic soon attracted the attention of his parents and 
their friends. He used to say jestingly that he 
learned to count before he could talk. 

Gauss' father carried on in the summer a masonry 
business. On Saturday evenings it was his habit to pay 
his workmen their past week's wages, paying those who 
had worked overtime according to the extra hours they 
had put in. On one such occasion he had finished the 
reckoning and was about to pay out the money when there 
came a childish voice from a small bed in the corner 
of the room. Unnoticed the three-year old child had 
been following his father's transactions. Now he 
said, "Father, the reckoning is wrong. It is so much," 
naming a certain figure. The reckoning was gone over 
again and was found to be what the child had said. 

In 1784 after his seventh birthday the little fellow 
entered the public school where elementary subjects were 
taught and which was then under a man named Btlttner. It 
was a drab, low school-room with a worn, uneven floor. 
On one side one looked out on the two slender Gothic 
towers of the Catharinen Church, on the other side were 
stables and poor back-yard dwellings.* Here among some 
hundred pupils Btlttner went back and forth, in his hand 



-3- 



the switch which was then accepted by everyone as the 
final argument of the teacher. As occasion warranted 
he used it. In this school — which seems to have followed 
very much the pattern of the Middle Ages — the young Gauss 
remained two years without special incident. By that 
time he had reached the arithmetic class in which most 
boys remained up to their fifteenth year. 

Here occurred an incident which he often related in 
old age with amusement and relish. In this class the 
pupil who first finished his example in arithmetic was to 
place his slate in the middle of a large table. On top of 
this the second placed his slate and so on. The young 
Gauss had just entered the class when Btlttner gave out for 
a problem the adding of a series of numbers from 1 to 100. 
The problem was barely stated before Gauss threw his slate 
on the table with the words (in the low Braunschweig dia- 
lect): "There it lies." While the other pupils continued 
busily adding, Bflttner, with conscious dignity, walked 
back and forth, occasionally throwing an ironical, pitying 
glance toward this the youngest of the pupils. The boy 
sat quietly with his task ended, as fully aware as he 
always was on finishing a task that the problem had been 
correctly solved and that there could be no other result. 

At the end df the hour the slates were turned bottom 
jp« That of the young Gauss with one solitary figure lay 
Dn,top. When Btlttner read out the answer, to the surprise 
Df "all present that of young Gauss was found to be correct, 
vhereas many of the others were wrong. Btlttner now decid- 
ed to write to Hamburg for a new book on arithmetic which 
vould be better suited to the young lad's exceptional mind. 
3ut before long he is said to have had enough insight to 
ieclare that Gauss could learn nothing more in his school. 



\ 

-4- 



Assisting Btlttner at the time was a young man by the 
name of Bartels whose task it was to assist the younger 
boys with the cutting of their quill pens and with their 
writing. Since he also was interested in mathematics a 
close friendship developed between him and the 10-year old 
Gauss which later had importance for the life work of 
both. Bartels was able to procure some useful books on 
mathematics which the two young people studied together. 
Gauss thus became fully acquainted with the Binomial 
Theorem in complete generality and soon thereafter with 
the Theory of Infinite Numbers which opened the way for 
him into Higher Analysis. 

To Bartels also is due the special credit that he 
drew the attention of several prominent people in 
Braunschweig to the genius of the young Gauss. Among 
these was the State Privy Councillor von Zimmerman, a 
man of unusual insight and lovable character, who soon 
perceived the extraordinary mental ability of the 
young lad and developed a warmly affectionate interest 
in him. Out of this there grew with the years an even 
closer personal friendship — Gauss never spoke of him 
without expressions of deep gratitude and affection. 

Besides Zimmerman we should recall Privy Councillor 
von Feronce who helped Gauss in like manner. Through 
these two men the attention of the Duke Carl Wilhelm 
Ferdinand was first called to the young mathematician. 

Bartels remained throughout his life in the most 
friendly relationship with Gauss. At Michaelmas, 1788, 
he left the Btlttner school to study at the Collegium 
Carolinum, went from there to Switzerland, next filled a 
position in Casan, and was finally honored by being called 
to be professor of mathematics at the University of Dorpat 



-5- 



Here he died at the age of 68 years. Gauss gratefully 
honored him to the last as an old friend, put a high 
value on his noble and generous mind and respected him 
as a ipathematician. 

In 1788 after four years in the Btlttner school Gauss 
entered the Gymnasium, almost against the will of his 
father. Through private study and the help of some older 
friends he was already well grounded in the classical 
languages and was immediately taken into the second class. 
Here he mastered the classical languages with such rapid- 
ity (it was only to these languages that any attention 
was paid at the time) that he amazed both teachers and 
fellow pupils. After two years he went into the first 
class. It was then that the Duke Carl Wilhelm Ferdinand 
had his attention called to the young genius. He expressed 
his desire to become acquainted with him and in 1791 Gauss 
was presented at Court. 

While all the company enjoyed the arithmetical 
prowess of the shy 14-year old boy it was the Duke whose 
fine tact won his confidence. It was he who also could 
provide for the further development of such remarkable 
talent. Gauss left the distinguished gathering with many 
gifts; from Feronce his first logarithmic tables. In 1792 
provided for by the Duke, he entered the Collegium 
Carolinum. 

• . Here'hecpferfebtedchfmself .in'.the classic languages 
and studied the modern. We know that he also busied him- 
self in those years with deep mathematical problems, and 
that through the works of Euler and Lagrange he widely 
extended the range of his studies. From Newton's 
Prlncipia he seems to have absorbed both the divine 
spirit and the method of that immortal mathematician. 



-6- 



From the Collegium Carolinum Gauss went on to the 
University of Goettingen. On October 11, he left 
Braunschweig for Goettingen, not yet fully decided 
whether to devote himself to philology or mathematics. 
At first he attended philology lectures at the home of 
Heyne and found them of great interest. KSstner's 
lectures on mathematics appealed to him less. He 
busied himself the more zealously therefore with 
researches of his own, and in the next two years made 
several of his most important and celebrated discoveries. 

In 1795 he discovered the method of least squares 
and in the following year, 1796, on March 30* he dis- 
covered the theory of the division of the circle, in- 
volving the construction of the 17-angled polygon. This 
discovery he highly prized to the end of his life. It 
determined the course of his career, for from that day 
forth he was firmly resolved to devote his life to 
mathematics. 

Gauss seems to have formed very few friendships dur- 
ing his student days at Goettingen; of those known to us 
only two are living today. The younger is Regierungs- 
President Eschenburg at Detmold, with whom Gauss* friend- 
ship began in 1789 when they were boys at school together 
Eschenburg entered the University two years later than 
Gauss, but through the year 1797 and part of 1798 was 
closely associated with him. Somewhat older and now a 
hoary old man of eighty years was Wolfgang Bolyai, of 
Maros Vasarhely in Siebenbtlrgen, a man of outstanding 
powers. Of him Gauss is said to have remarked in his 



Noted in his own handwriting in his copy of the 
Disquisitiones, p. 662. 



-7- 



earlier years that Bolyai was the only one who could 
anderstand his metaphysical view of mathematics. To 
judge by the few things we have from Bolyai 's pen (in a 
style which reminds us of Jean Paul's writings) he is a 
man of great depth and sincerity of character. He 
lives in a remote part of his country, separated from 
kindred souls and now in his old age surrounded by tur- 
bulent revolution, by murder and the horrors of civil 
war. Through the tears and suffering we have brought 
upon ourselves he looks out over the ruins of his pro- 
perty toward Eternity, with noble calm and serene 
assurance. He deplores only that he was not granted 
the privilege of making his own way, for with but few 
exceptions life has been made easy for him. "Anyway," 
he says, "here I am on the earth with my fellow-worms, 
each of us busy with his own web. Presently I shall 
come to rest in a nameless grave, reconciled with destiny." 

A close University friend of both men was a young 
Ide of Braunschweig. Like Bolyai he remained in 
Goettingen a year longer than Gauss and kept in touch 
with him through correspondence. In a letter to Gauss 
dated May 23, 1799, he recalls their mutual friend's 
unusual personality in these words: "Bolyai will attend 
the coming shooting-fete, but only as a philosopher who 
finds material in such things for expounding his views on 
Man's foolishness. So far as I can figure it out, this 
is his principle; to forego no such occasions, not that 
they give him pleasure, but that they confirm his own 
peace of soul." 

Connected with Bolyai also was a correspondence 
between Gauss and Benzenberg which lasted over many 
years. 



-8- 



Benzenberg's first letter asks Gauss a question, recalls 
meeting him, and adds: "Bolyai is one of the rarest men 
I have ever seen." 

These are the student friends of Gauss who are till 
now spared by death. In the youth of these men came the 
fullest blossoming of our German literature, the purest 
scientific aspiration, the profoundest zeal for an exalte^ 
ideal. Whereas now in our highly enlightened time throug] 
uninspired teaching and the deplorable urge to turn scien* 
only to practical uses, there is spreading throughout our 
nation an endless bare field of mediocrity where evidence: 
of originality can only too easily be stunted. 

By Michaelmas of 1798 Gauss had completed his studies 
in Goettingen. From him had already come works of high 
genius. Now he returned to Braunschweig to oversee the 
publishing of his Disquisitiones arithmeticae . 

In September of this year he went to Helmstedt, not 
to study at the University, but to use the Library there 
in connection with the publication of the above-named 
work. The librarian Bruno he found very cordial and 
obliging. He also became acquainted with Pfaff and spent 
an hour or two with him. But only in the next year when 
he returned to Helmstedt to continue his work was there 
any closer acquaintance between the two mathematicians. 
Gauss now went to live in Pfaff 's house, in one room 
which he furnished himself. He worked so strenuously 
and continuously however that he seldom saw his housemate 
till evening when they often went for walks together, to 
the Spring or to Harpke, discussing mathematical subjects 
at length as they walked. In this exchange of thought 
Gauss believed he gave more than he received. 

We feel called upon to go somewhat at length into 
the relationship of these two mathematicians since 



-9- 



several times recently, first in a published biography 
of Pfaff , and in several articles published since, it 
has been said that Gauss went to Helmstedt to study under 
Pfaff and weis led by him into his mathematical research. 

Gauss has indeed very generously recognized and 
honored Pfaff 's mathematical talent and his thorough 
scientific research, but he himself possessed such a 
completely original mind that he did not need to be led 
by another to those discoveries so inspired by genius, 
so revered by all mathematicians, at a time moreover 
when his Disquisitiones arithmeticae was in all essen- 
tials complete, was in fact already in proof. All his 
splendid research came from the profound depths of his 
own genius, developed with such originality and perfec- 
tion of form that it carried no trace of other influence. 
This noteworthy quality we see in the work of his 
earliest youth as well as in that of his last days, as his 
scientific legacy will presently reveal more clearly. 

The Disquisitiones arithmeticae had its inception 
in the fall of 1795. After various interruptions had 
dragged the printing through four years, it was finally 
published in 1801 with the help of the Duke of Braun- 
schweig. Only the most eminent minds in this field are 
qualified to give a complete and adequate evaluation of 
this work, so renowned and epoch-making in the history 
of science. Gauss' own judgment of it, given in the 
late evening of his life, has interest for the pene- 
trating mind of the scientist as well as for a wider 
circle of friends. 

"The Disquisitiones arithmeticae belong to history. 
In a new edition, to which I am not disinclined but for 
which I now have no leisure, I would change nothing but 
the misprints. I would only like to add the eighth 
section which was worked out in essentials at the time 
of the first printing, but did not appear at that time 
in order not to increase the costs." 



-10- 



Gauss once said in a letter to Bolyai that he hoped 
in time to furnish so many additions to this work that 
they would make up a second volume of the Disquisitiones . 
These investigations to which Gauss referred were later 
set down in part in the "Commentationen" of the Royal 
Scientific Society. Some smaller treatises, such as a 
contribution to the theory of imaginary numbers are to be 
found in the Goettingen "Scientific Anzeigen." Higher 
mathematics remained the favorite study of the great 
mathematician to the end of his life. In his old age he 
lamented that for these tasks demanding so much sustained 
exertion he had never been granted the necessary leisure. 

The Disquisitiones arithmeticae its author gratefully 
dedicated to Duke Carl Wilhelm Ferdinand of Braunschweig. 
This work assured him fame, for with its appearance there 
begins a new epoch for the theory of numbers in" mathema- 
tics. Material advantages did not come to Gauss from this 
work, for a great part of the commissions due him from a 
book-dealer in Paris were lost through the latter 's 
bankruptcy. 

In this connection it should be mentioned that the 
Disquisitiones have long been out of print and that the 
gifted young Eisenstein (his career cut short by an 
early death) was never able to own an original. Like- 
wise other pupils of Gauss copied this work from begin- 
ning to end because of the lack of printed copies. 
Learned mathematicians of this century may be seen on 
their travels carrying thoroughly thumbed copies like 
priests going about with their prayer-books. 

One would think a work of such compass and profundity 
would have demanded all of its author's time and interest 
fram the time of its beginning to its completion. It is 
therefore amazing that besides this great work Gauss was 
carrying on other important investigations reaching into 



-11- 



widely varied aspects of mathematics and of theoretical 
and practical astronomy, each in its own way breaking 
new paths • In that period of his life such an extra- 
ordinary richness of thought sprang day and night from 
the mind of this youthful genius, that one discovery 
tumbled over another almost too fast to be set down even 
in outline. Thus some of his greatest discoveries lay 
to one side — most of them for more than a decade, some 
for even half a century — before they were made known to 
the scientific public. 

To cite one instance. Gauss arrived at the theory 
of least squares in 1795. Not till 1799 did his "Dis- 
quisitiones" appear, for which he received his doctoral 
degree "in absentia" while in Helmstedt. The thesis 
was entitled "Demonstratio nova theorematis omnem func- 
tionem algebraicam, rationalem integram unius variabilis 
in factores reales primi vel secundi gradus resolvi 
posse." It may be this treatise known as "Disquisitiones 
arithmeticae" which gave rise to the erroneous impression 
that Gauss was a student in Helmstedt and there received 
his degree. 

Again in 1797 Gauss found a new, thoroughly rigor- 
ous and simple proof of Lagrange's Theorem, which by a 
mischance was never given publicity. Gauss sent this to 
Pfaff, and Pfaff forwarded it to Hindenburg who died soon 
afterwards. The enclosed manuscript was never seen again 
Gauss never published his proof, of which there is still 
a copy, since he found later that Laplace had hit upon 
a similar solution for this problem. Among other things 
Gauss further found a new method for reckoning Easter. 

In 1801 the wide-spreading fame of his notable 
achievements brought him his first public tribute, of 
a kind which later poured in on him in such numbers. 
The St. Petersburg Academy of Science on January 31 



-12- 



elected him a corresponding member. The official an- 
nouncement of this he received through State Chancellor 
von Fuss who from then on always remained in correspon- 
dence and close touch with him. With keen interest von 
Fuss conducted the negotiations which soon afterwards 
were initiated, and later several times renewed, through 
which the Russian Government sought to win Gauss for the 
Petersburg observatory. Fuss* last letter, like his 
first, brought word of the conferring of an honor. In 
1824 he announced that on March 24th Gauss was named a 
Foreign Member of the Academy. On the 24th of January, 
1826, Fuss died in Petersburg in his seventy-first year. 

While Gauss even before his twentieth year was on 
the one hand reforming the various branches of higher 
mathematics, he was active on the other hand and with 
equally great success so far as equipment permitted, 
as a practical astronomer. The observation of comets, 
eclipses, latitudes and longitudes, etc., was his 
great joy. His discoveries in the field of pure mathe- 
matics, profound as they were, were naturally confined 
for some time and even up to the present, to a very 
narrow circle of thinkers. Another discovery had to be 
recorded — in astronomy — before Gauss' name became 
known to the larger public as one of the most cele- 
brated in Europe. 

On January 24th, 1801, Piazzi in Palermo wrote to 
Bode in Berlin that he had discovered on the first day 
of the new century a small comet, like a star of the 
8th magnitude without nebula, at 51** 47 • right ascen- 
sion and 16** 8' north declination. Some days later 
Zach* , already informed of Piazzi's discovery, 
received a letter from Oriani in Milan with the same 
news and with the comment that Piazzi took the new 
star, which he had observed on several different 
days in January, to be a planet. Oriani tried 
immediately and eagerly to find this newcomer in 
the skies. But neither Oriani nor any of our German 



♦ Publisher of Zach*s monthly Correspondenz 

-13- 



astronomers who scanned the heavens with such care could 
find it, since Piazzi's letter from Palermo to Milan 
was seventy-one days on the way during which time the 
star had gone down in the twilight. 

Meanwhile Olbers also had received the noteworthy 
news and had immediately calculated a circular orbit 
from two positions, at the same time expressing the 
fear that even with the help of his elements the planet 
could not again be located after its course passed the 
sun* After much delay Piazzi's observations of the new 
star finally reached Paris and were next discussed by 
Burkhardt. He also soon found as had Olbers that no 
parabolic orbit would conform to the course of the new 
star. He therefore calculated a circular orbit which 
deviated somewhat from the approximately circular orbit 
hit upon by Olbers, and somewhat later he calculated an 
elliptical orbit, the elements of which were immediately 
made known through Zach's monthly Correspondenz . 

Toward the end of the summer of 1801 astronomers 
everywhere were turning their attention to Piazzi's new 
planet which he had meanwhile named "Ceres Ferdinandea". 
But even the most careful investigations were without 
result. In early December with all efforts still 
fruitless Zach made the following important announcement. 

"Great hope of help comes to us from the investiga- 
tions and calculations of Dr. Gauss in Braunschweig, just 
received. They give us new and highly probable grounds 
for believing that the star discovered by Piazzi is 
truly a planetary body moving according to Kepler's laws 
between the orbits of Mars and Jupiter. We hasten to 
make this announcement of his calculations since his new 
elliptical orbit differs considerably from the ellipse 
of Dr. Burkhardt and from the two circular orbits of 



-14- 



of Olbers and Piazzi announced in our previous issues, and 
since moreover their deviations from the Gauss positions 
may amount this present month to as much as six to seven 
degrees in geocentric longitudes. It is therefore impor- 
tant to make this known as soon as possible to practical 
astronomers, that they may understand the need of extend- 
ing six to seven degrees further to the east the section 
of the heavens in which this new and elusive star is to 
be looked for. 

"Dr. Gauss was led into these calculations by some 
investigations into physical astronomy which led him to 
some rather significant additions to the theory of 
motion of heavenly bodies in conic sections of every 
kind and which he was so kind as to communicate to us. 
We hope to bring this to our astronomical readers 
another time, since to deal with it now in any detail 
would lead us too far from the present subject. We 
confine ourselves therefore to what directly concerns 
the course of Ceres Ferdinandea . " 

There follow next the elliptical elements of Ceres 
reckoned by Gauss* theory from Piazzi 's observations of 
January 2nd, 22nd and February 11th, 1801. Immediately 
afterwards there was given out a second series only 
slightly different from the first, which placed all 
nineteen observations most favorably within the announced 
limits. Shortly thereafter came two new systems of 
elements for this plarft: based on more refined observa- 
tions taken from Piazzi 's own hand-written communications, 
together with an Ephemeris reckoned up to the year's end, 
for facilitating the search. 

At last, as Zach relates it, the united and untiring 
efforts and zeal of all Europe's astronomers succeeded in 
finding again this significant planet of our system, dis- 
covered first a year before and now re-discovered like a 



-15- 



grain of semd on the shore of the sea. The discovery 
was made by Zach on December 7, 1801, and by Olbers on 
January 1, 1802, on the anniversary of the first dis- 
covery. Concerning this extension of knowledge so 
important to astronomy Zach wrote further: 

"Ceres is now easy to find and can never again be 
lost, since the ellipse of Dr. Gauss agrees so exactly 
with its location.* Only those who know from theory how 
difficult it is to close an orbit of 360** from the 
scanty data available from Piazzi's forty-day observa- 
tions covering an arc of only 9^ can adequately evaluate 
and appreciate the ability and powers of penetration 
possessed by Dr. Gauss." 

Olbeirfe writeSwConcertiingGthe damecdisfovery^ "You 
will have noted with pleasure how exactly Dr. Gauss' 
ellipse agrees with the observations. To show my very 
special esteem please say this to the worthy scholar: 
without his laborious investigations of the elliptical 
elements of this planet we should perhaps never have 
found it again. At least I would never have looked for 
it so far to the east." 

Piazzi expressed himself in similar strain. Uni- 
versal admiration was accorded Gauss at that time, and 
will continue to be accorded him by men of science, for 
the energy and devotion with which he gave himself to the 
gradual correction of the Ceres orbit. With every letter 
to Zach he sent newly determined reckonings. It is hard 
to credit the ease with which in such a short time he was 
able to produce such weighty investigations and extensive 
calculations. Just twenty-four years old, he had already 
developed these highly original methods while also 
pursuing much deeper research. 

In connection with the discovery and rediscovery of 
Ceres, Zach tells of a letter which he received in April, 



-16- 



1801, from another country, in which the writer makes 
a jest of the efforts of astronomers everywhere and 
suggests that there is a point at which it is well to 
refrain from building air-castles. Zach comments: "In 
this connection we can't refrain from quoting part of a 
letter from Dr. Gauss which reveals the outstanding 
characteristics and manner of thinking of this great 
scholar: 'It is hardly conceivable' writes Gauss, 
'that men of honor, priests of science, can show them- 
selves in such a light. As for me, I look on all such 
opportunities as tests of whether I am working for my- 
self or for Science!" Zach continues: "These then are 
the burdens of Fame, and Gauss will meet many more of 
them now that he is beginning to write. But to such a 
mind as his, full of conviction and of aspiration, 
working only for science, such burdens will never be 
oppressive. Neither will they put him out of tune 
with his own age, nor embitter him. We urged him 
indeed to stand firm on those noble principles on which 
we likewise would wish to stand, and to recall the 
following moral-political-mathematical formula of our 
ever gay, happy and honored old Patriarch and Teacher, 
Citizen Lalande, Dean of Astronomers: 

"Result of a calculation mathematical, political 
and moral 

There are a thousand million people living on 

this earth. 
Of these thousand million heads 
How many are wicked, foolish, bestial 
But we cannot cure, we can only pity and serve 

them." 



-17- 



Perhaps this is the place to quote part of a letter 
Dm Privy Councillor v«tn Zimmerman of Braunschweig 
Lch Zimmerman wrote to Zach: "Incidentally it may not 

unpleasant for you to know that Dr. Gauss is indeed 
\rerY high-minded, un-self seeking young man (he is only 
snty-four). When I informed him that our excellent 
ce was voluntarily granting him a stipend of 400 
Lchsthaler, he said, 'But I have not earned it. I 
/en*t yet done anything for the nation.' Accordingly 

planned to buy a sextant to put to use on surveys." 



thor*s note: 

I would scarcely have included the above quotation 
in these pages had I not come upon it only yesterday 
(March 24) in a way to arrest my attention. It is 
now more than a half-century since the Ceres inves- 
tigations of Gauss were given out. Perhaps no man 
living has seen the original of this work. Yester- 
day evening for the first time since February 23rd 
(day of Gauss' death) I entered the deserted, quiet 
little work-room of the man now gone from us. A 
cabinet was kindly opened for me where were note- 
books containing unsuspected treasures for his 
scientific legacy. A small book, one of the first I 
took up, bore the inscription "Cereri Ferdinandea 
Sacrum," and below stood the verse (in French) taken 
from the monthly "Correspondenz, " evidence that 
Gauss in all good humor recalled those individuals 
who once felt qualified to make sport of his scien- 
tific performance. In the book set down most 
precisely in thousands of figures, are the calcula- 
tions of the different orbits worked out for Ceres 
and comparisons with the calculations of Olbers, 
Zach and others. 



-18- 



Through the linexpected rediscovery of Ceres the 
astronomers of that time were inspired with fresh zeal. 
New discoveries followed fast on the heels of one 
another. 

On March 28, 1802, Olbers found another grain of 
sand in space, the planet Pallas. Its orbit was immed- 
iately calculated by Gauss, and presently this planet 
came to be Gauss' "favorite", inasmuch as he devoted 
years of investigation and voluminous calculations to 
its deviations. Once in 1832 we saw and handled a manu- 
script dealing with this subject and labelled "ready for 
the press". But since then almost a quarter-century has 
slipped by without astronomers having had further word 
of it. Without doubt these pioneer calculations are 
now lying by, put to one side with those of Ceres. 

In 1810 Gauss received from the Institute of 
France a new distinction, the medal established by M. 
Lalande for the best work or the most novel astronomical 
observation. This came to him for his work on Pallas. 
He chose however to have a watch sent him from Paris in 
place of the more costly medal, and in arranging this 
was aided by the Secretary of the Institue and by Mile. 
Sophie Germain.* Many creative hours of the richest 
period of his life and many hours of pain in his last 
illness he counted off on this time-piece, from that 
time till it stopped at the hour of his death a month 
ago. 

Early in the new century the government of 
Hannover had intended to build for Goettingen a new 
Observatory provided with the best possible equipment 
and to entrust its direction to Professor Seyffer. 
Now suddenly Gauss* name was heard as one of the most 
eminent in astronomy. The kind and alert Olbers is 
perhaps the one .chiefly to be thanked that a few years 
later Gauss was called to our University, to its 
glory and fame. 



Gauss had carried on a scientific correspondence with 
her since 1804, knowing her only as LeBlanc. Not till 
ISO 7, thru' Denon. did he learn her real name. 

-19- 



I 



Olbers had learned in confidence that Gauss had 
received from the Russian government a call to Peters- 
burg under very advantageous conditions. Gauss had 
sought Olbers' advice on this. Olbers was therefore 
moved both by the fear of losing Gauss for Germany and 
IdY his wish to win for him a suitable sphere of activity 
In the Fatherland. 

Gauss had never intimated to Olbers any desire to 
come to Goettingen, nor was there any mention in the 
letters that passed between them of the building of the 
Observatory. But Olbers saw in Gauss so lofty a mind 
and so completely the right personality for directing 
the future Observatory that he immediately thought to 
avail himself of the existing situation to secure Gauss 
for Goettingen. He therefore asked Gauss' permission, 
vithout explaining his reasons, to tell a friend under 
promise of strictest secrecy of the Petersburg call. He 
then wrote to Heeren in Goettingen as follows, warmly 
xecommending Gauss: 

"Pardon me, my respected friend, that I trespass on 
your limited time. Only love of science and patriotism 
(if I may call it that) for Goettingen move me to this 
importunity. Yet it may be pardoned since you asked me 
when you were here in Bremen to give you my thoughts on 
the choice of a director for the Observatory soon to be 
built in Goettingen. 

"I assume that it is still the intention not to 
entrust this position to Professor Seyffer who will 
always be merely a professor of astronomy, also that no 
definite choice has yet been made, a choice which I said 
as we talked together was not an easy one. But just now 
I see a possibility of presently filling this position in 
a very exceptional way, and if my idea is to be considered 
it must be presented without delay. 



-20- 



"You know, my dear friend, although mathematics and 
astronomy are not your field, of the great fame which has 
come to Dr. Gauss of Braunschweig. The fame is fully 
merited, for this young man of twenty-five years is 
already ahead of all his mathematical contemporaries. I 
consider myself in some measure qualified to express this 
judgment since I have not only read all he has written, 
but have been in confidential correspondence with him 
since the first of the year. I have been moved to high- 
est admiration by his knowledge, his extraordinary prow- 
ess in ainalytical and astronomical calculation, his 
unwearying activity and industry, his quite incomparable 
genius. And in our correspondence the further he has 
gone in communicating his thought, the higher my admira- 
tion has risen. Moreover the science of astronomy, and 
preferably practical astronomy, is particularly close 
to his heart, though thus far he has had little oppor- 
tunity for the latter because of lack of instruments. 
He is wholly averse to any position as teacher of math- 
ematics* His heart's desire is to be astronomer in 
some observatory where he could divide his time between 
observation and close, profound research for the 
advancement of science. 

"Is not this just the man who would fit into the 
future opening at Goettingen in any capacity? I can 
testify on my honor that never has there been even any 
mention of the observatory at Goettingen. 

"I give you now the picture and immediate cause for 
this letter. Germany is in danger of losing this distin- 
guished scientist. Under date of October 12 Dr. Gauss 
informed me in strictest confidence that he had received 
from Petersburg the offer of the position of astronomer 
and director of the observatory there, but .was undecided 
as to whether he should accept this call, which in many 
respects is very pleasing to him. He asked my advice on 
thia matter. In my reply I asked him to postpone any 



-21- 



acceptance and meanwhile to permit me to communicate the 
offer to a friend on whose discretion he could rely. 
Yesterday I received his permission, and I make immediate 
use of it to inform you of the circumstances. If it 
should be desired, or if it is possible to give consider- 
ation to Dr. Gauss, quick action must be taken. 

"I trust wholly to your judgment and discernment as 
to how valuable this would be for Goettingen. Only I 
ask you in any case to consider this letter and its con--- 
tents as matters brought to you as a friend and in 
strictest confidence . 

"Yet I must repeat that I see it as important for 
the glory of • Georgia Augusta' to secure a man who is 
already admired by all Europe. 

"It will be a great favor, dear friend, if you can 
let me have some word on this matter as soon as possible. 
Pardon this very unorganized, perhaps hardly intelligi- 
ble letter, which has been written in great haste and 
with constant interruptions. 

"With — as you know — feelings of sincerest attachment and 
respect, 

I am ever yours 

W. Olbers" 
Bremen, November 3, 1802 

The answer showed that the proposal mef a most 
favorable reception, though there would still be some 
unavoidable delay with the matter. Olbers communicated 
this to Gauss who up to this time was in complete 
ignorance of the steps taken. 



-22- 

1 



Gauss now decided to await further developments and 
to decline the Petersburg offer. Moreover he felt him- 
self obligated by sincere gratitude to his noble benefac- 
tor Duke Carl Wilhelm Ferdinand, who had just approved a 
salary increase for his scientific work in Braunschweig, 
where also the building of an observatory was in 
prospect. 

Now that the discussions with Petersburg were at an 
end and the University Senate had had its attention 
directed to Gauss, there would have been an immediate 
call to Goettingen had not the close relationship of 
Gauss to the Duke of Braunschweig made this impractical. 
The University Regents kept Gauss in sight however and 
seized the first opportunity to appoint him. 

The mutual desire of Gauss and Olbers to know each 
other personally came as a natural result of their 
close correspondence, begun with a letter from Gauss 
dated January 18, 1801. On June 22, 1802, Gauss took 
his first trip to Bremen. Here he spent three weeks in 
Olbers' home, during which time they went to Lilienthal 
to spend two days of rare enjoyment with SchrOter. 

An excellent portrait painter, Schwartz, who was 
then in Bremen^ did a pastel portrait of Gauss at this 
time, the only youthful one in existence. This was 
said to be a speaking likeness and has remained in 
possession of the Olbers family. Soon afterwards Gauss 
received an equally successful portrait of Olbers, 
executed by the same artist, and dear to him as long 
as he lived. After his death it passed into the hands 
of Gauss' trusted physician and Olbers' great admirer. 
Professor Baum. 

It was at this time that Olbers first mentioned to 
Gauss a young man by the name of Bessel, with whom he 
had become acquainted at the Kulenkamp counting-house. 



-23- 



and who zealously spent his free time and even his nights 
on astronomy, showing a marked gift for it. 

Gauss did not meet Bessel personally during this 
first visit to Bremen, but soon there developed between 
the two astronomers a close association brought about by 
Olbers and by Gauss' investigations of the Pallas devia- 
tions. This continued for forty-two years and worked an 
infinite blessing to the development of astronomy. 

On July 15th, just returned from Bremen to Braun- 
schweig, Gauss was met with another invitation. Zach 
invited him, that they might become better acquainted, ". 
to join him on the Brocken — a short, delightful trip — 
where Zach was to spend fourteen days , to give powder 
Signals from there. On August 28th Gauss joined him and 
some days later went with him to Gotha, where Gauss re- 
mained till December 7th, part of the time staying with 
Zach at the Seeberger Observatory. 

The following year he saw his good friend Olbers 
again at Bad Rehburg near Hannover. Olbers wrote him 
on July 6th, 1804: "The first of August I go to Rehburg 
for fourteen days. In one day you could get there from 
Braunschweig. What a delight for me if your good angel 
were to inspire you to seek refreshment in this romanti- 
cally lovely place at just that time!" 

The deep enjoyment Gauss experienced in these three 
short trips stood out to the end of his life as among 
the happiest memories of his youth. The more, since 
those years covered the particularly rich period in which 
not only his great mental achievements were crowned with 
fame, but in which also his sensitive spirit received its 
richest inspiration. 



-24- 



From 1803 Gauss and Johanna Osthof of Braunschweig 
had come to know each other better and better, and on 
November 22, 1804, they became engaged. Three days later- 
a letter Gauss wrote to his friend Bolyai contained the 
happy words: "Life stands before me like eternal spring, 
in new and shining colors." 

On October 9, 1805, they were married and experience^ 
in their marriage the fullest, most unmarred happiness. 
Of this marriage three children were born: the oldest 
son Joseph (Ober-Baurath in Hannover), born in Braun- 
schweig August 21, 1806; Minna (later married to Prof. 
Ewald) born in Goettingen February 29, 1808, died at 
TUbingen August 12, 1840; Louis, born at Goettingen 
September 10, 1809, died March 1, 1810. Following this 
last birth Gauss lost his beloved wife on October 11, 180S 

While Gauss was living a quiet family life in 
Braunschweig and was hastening from one great achieve- 
ment to another, inspired by the creative forces of 
youth, there was drawing closer that disastrous time 
which subjected our Fatherland to a bitter fate. 

Napoleon's power had already fastened itself upon 
western Germany. And though the worst was to be feared 
from the encroachments of the enemy, still no defense 
agreement could be reached between Prussia and Austria. 
In the face of an ever more confused and threatening sit- 
uation, ^ on January 30, 1806, the Duke of Braunschweig 
was entrusted by the Court at Berlin with a diplomatic 
mission to St. Petersburg which seems to have achieved 
no results. In Petersburg however he was approached 
several times on the subject of the gifted young astrono- 
mer, and to use his own words, "they dropped a word" in 
his ear to approve Gauss' call to the Petersburg Academy. 



-25- 



The Duke, definitely turning down this suggestion, 
was again in Braunschweig by March 24, when he bettered 
Gauss' position by an increase in salary announced to him 
on his birthday, April 30th. It was on this occasion 
that both men saw each other for the last time. Soon 
death had dissolved the relationship which had lasted 
for fourteen years of mutual respect and esteem. 

The battle of Austerlitz was fought. Prussia 
stood deserted and was forced to take up alone the 
unequal struggle against the Emperor of France. Napo- 
leon's army early in October, 1806, rolled on through 
the Frankland towards the river Saale: the battles of 
Auerstedt and Jena were fought by Duke Carl Wilhelm 
Ferdinand and were lost, and the Duke himself was 
fatally wounded and brought back to Braunschweig. 

It was decided immediately to send a deputation to 
Napoleon who was then in Halle, to ask mercy for the 
sorely wounded commander, with permission for the 
unhappy old Duke to die by his own fireside. The depu- 
tation was rudely repulsed, with derision for the Duke's 
poor military leadership. With nothing accomplished the 
deputation then turned back and took steps to save the 
unhappy commander from disgraceful captivity. 

On a morning late in the fall Gauss, then living on 
the Steinweg, saw a big ambulance drawn by a pair of 
horses pass out the gate of the Castle garden and move 
towards Braunschweig's Wenden Gate. In the ambulance 
lay the sorely wounded Duke on his flight to Altona. 
Gauss watched with deep emotion the departure of this 
friend who had done for him what a father might well have 
done. He said little but was deeply moved. After some 
days of travel the dying Duke reached Altona, and here 
in a small house in Ottensen he died, not far from that 
linden tree which shaded the grave of a great German 
poet. 



-26- 



So ended the life of this noble prince, doomed to 
go down in German history as one of those blamed for the 
defeats of Jena and Auerstedt, responsible for the most 
disastrous years of our Fatherland's history. But his 
noble heart which considered always the good of his coun- 
try and the well-being of his subjects, had been rewarded. 
For in future millennia in which Napoleon's victories 
will be as good as forgotten a net of telegraph wires will 
encircle the globe, man will build a new civilization on 
the basis of mathematics, astronomy and the natural 
sciences, and close to the name of Gauss who celebrated 
Germany's victories of the Spirit will stand the name of 
his patron, Duke Carl Wilhelm Ferdinand, filling an 
honorable place in the history of Science. Zach wrote 
Gauss in a letter dated January 27, 1803: "You will see 
to it that his great name is inscribed on the Heavens." 

In that gloomy year when the enemy poured over 
Germany from the Rhine to the Niemen, Gauss lived on for 
SGjne months with his little family in the city of his 
birth, criticized by many and perhaps even envied for his 
independent attitude. Then at last there came to him the 
call to Goettingen which was the turning point in his 
life. Discussion of it had never been v/holly dropped, 
had been often resumed, but the right moment for a 
definite decision had never been found. How much they 
had counted however on securing Gauss for Goettingen 
comes out in a letter from Heyne to Olbers, dated Sept. 
26, 1804. We quote the following excerpt: 

"I am infinitely grateful to youX for your inter- 
est in helping Georgia Augusta and for your kind media- 
tion in the matter so close to our hearts, of securing 
Dr. Gauss. Thought has been given to an adequate 
salary and this should present no difficulties. 
Greater difficulties are to be met in Gauss' relations 
with his Duke. Likewise the building of the observa- 
tory is halted, though a start will presently be 
made. So at the moment in fact there would be 
only labor in vain for Gauss. I can give you assurance 
from Hannover, however, that the position stands open for 
Gauss and will remain so. What you say of our Gauss as a 



-27- 



man is precisely what enhances his greatness as mathe- 
matician and astronomer • " 

After the unfortunate results of the battle at Jena 
all conditions in Braunschweig were so completely changed 
that fresh attempts were made by Petersburg to reopen 
negotiations • These were reason for Hannover's taking 
prompt steps to prevent the loss of Gauss to Germany. 
Several men of vision, among them Brandes, former 
Curator, again exerted themselves to secure Gauss as 
Director of the Observatory, and this time they met with 
success. 

Gauss received the call in 180 7 while on a visit to 
Olbers and accepted it, first counseling with his old 
friend. On his return journey from Bremen he visited 
Brandes in Hannover and there made Rehburg's acquaint- 
ance. On November 21st of the same year he came to 
Goettingen to assume his position. 

As matters stood our country was then occupied by 
the enemy, although there were certain authorities which 
kept in touch with the London Chancellory. Gauss was 
installed by the Hannoverian government. By the time he 
entered upon his work however, this was in complete 
dissolution and the new Westphalian government was not 
yet organized. In this confusion the matter of swearing 
Gauss into office was forgotten and he remained all his 
life exempt from this formality. 

The first years of Gauss' residence in Goettingen 
were troubled ones in a number of ways. He was in 
material need, was oppressed by many unhappy events. Yet 
held himself only the more closely to his science. It 
was at this time that he lost his father, and two years 
later, on October 11, 1809, death took from him the be- 
loved wife with whom he had had such complete happiness. 



-28- 



Also there were many annoyances connected with his 
position. He had hardly more than settled here and had 
as yet drawn no salary when Napoleon's order was issued 
for a huge contribution to the war, a forced levy for the 
new Kingdom of Westphalia. For our University this bur- 
den was divided according to position and Gauss' share 
was set at two thousand francs. 

For Gauss it was all but impossible to meet this 
oppressive levy. Then one day he received the full sum 
from Olbers, with a kind letter expressing regret that 
men of learning should be subject to such shameful exac- 
tions. But Gauss could not bring himself to accept the 
money and returned it forthwith, though deeply grateful 
for his friend's high-minded generosity. Shortly after- 
wards he received another letter from Laplace, telling 
him that Laplace had already paid in for him in Paris 
the two thousand francs demanded. Again Gauss felt 
obliged to decline this kind offer and presently returned 
to the great French mathematician the full sum of the 
obligation with interest for the time elapsed. We would 
not go into the matter in such detail but for the light 
it sheds on Gauss' character and for the fact that some 
incorrect reports of the matter received wide circulation 

Nevertheless it seemed meant that his difficult 
situation was not to be ignored* Soon after declining 
the help of all. friends he received from Frankfort an 
anonymous gift of one thousand guilders which he later 
learned was a gift from the Crown Prince. Also Friedrich 
Perthes, who of course had other connections with Gauss, ■ 
proved during these hard times to be so thoughtful that I 
Gauss commemorated him with warm gratitude when Perthes' | 
biography was published by his son some years ago. 
Towards the expense of this Gauss had been able to make | 
"a friendly contribution," to use his* own words. I 



-29- 



1 

I 



1 



Gauss was occupied during the first part of his 
residence in Goettingen with the publication of his 
immortal work: "Theoria motus corporum coelestium in 
sectionibus conicis solem ambientium." This was at first 
written in German, but Perthes (the publisher), wishing 
to reach a wider public, wanted it published in French. 
Gauss' political feelings would not permit this, but he 
decided, in order so far as possible to satisfy Perthes, 
to publish the work in Latin. In this language it 
appeared therefore in 1809, with an introduction written 
on March 28th; as it happened, just two hundred years 
later, almost to the day, than Kepler's Praefatio de 
Stella Martis . 

On the foundation of Newton's Law of Gravitation or 
of Kepler's Laws inductively arrived at and known to be 
implicit in that general law. Gauss develops in his 
Theoria methods by which the orbit of every heavenly 
body of our solar system may be determined in the surest 
and simplest way from the necessary observations, and 
without any further hypothesis as to their nature. 

This new theory, as has already been said, found 
its confirmation in 1801 when it was applied with amaz- 
ing success to the planet Ceres discovered by Piazzi. 
This led to its largely supplanting all other methods 
in use since Newton's time for calculating the orbits 
of the heavenly bodies. 

It is known that the calculation of the paths of 
comets presented the earlier astronomers with much 
greater difficulties than the calculations of the five 
major planets of our solar system as investigated by 
Kepler. 

Remarkably enough Gauss already in 1795, at the end 
of his eighteenth year was using the method of least 



-30- 



squares • We cannot doubt that practical need as well 
as the study of nature led him to this epoch-making 
discovery. He has often said to us that the solution 
of this problem was very plain since the question be- 
fore him was that of combining a system of observa- 
tions according to the most logical principle. He had 
supposed that others, and certainly Tobias Mayer, were 
in possession of this method. He had therefore gone 
through the great astronomer's handwritten manuscripts 
in the Goettingen Library, but unfortunately his search 
revealed nothing. 

It is known that in 1806 Legendre had likewise 
been led to the method of least squares in his work 
Nouvelles Mfithodes pour la determination des orbites 
des cometes and that for this reason French claims 
to priority were raised, for the Theoria Motus 
appeared almost three years later. Since Gauss had 
communicated this important discovery which he made 
in 1795 in the following year to his friend Bolyai, 
Bolyai is the only man now living who ceui give both 
scientific and contemporary testimony. In the begin- 
ning of the century Gauss acquainted Olbers and also 
a friend in South Germany with the method of least 
squares, though only in the Theoria Motus was it 
given to the public. In mentioning the dispute he 
once said to us: "The method of least squares is not 
the greatest of my discoveries". Another time in the 
presence of other listeners he said only: "They 
should have felt they could believe me." 

The appearance of the Theoria Motus arrested 
universal attention among scientists, receiving the 
recognition and admiration it merited. The Crown 
Prince who had so warmly interested himself in Gauss 
sent him a gold medal. Another was sent him by the 
Royal Society of London. Honors from learned 
societies in all parts of the world came to 
him. Even the enemy who occupied our country sent 



-31- 



his token of high esteem. It is typical of Gauss that 
in this time of Germany's humiliation he proved himself 
so loyal a German, opposing the foreign conqueror and 
guarding the treasures of our literature and science with 
the full force of his giant spirit. With Napoleon's 
predilection for mathematics, with the admiration 
Laplace expressed for him, how easy it would have been 
for him to attain to high place, high distinctions and 
material advantages! But he sought no such harvests. 
The fulfilment of his scientific calling provided him 
his happiness and his goal in life. 

The French had meanwhile settled down in Germany 
and so comfortably that they seemed indeed to have little 
desire to turn their backs on us in any near future. It 
was therefore to their interest not to slight the govern- 
ment's University in the Kingdom of Westphalia. For this 
reason Gauss was subjected to no further annoyances. 

Before Gauss came to Goettingen but little was 
accomplished in the field of practical astronomy. This 
in common with theoretical astronomy was entering a new 
phase with the coming of the new century. Of the new 
Observatory there were only the foundations and there 
was little prospect under existing conditions that the 
building would go forward quickly. 

For the time being therefore Gauss continued his 
observations at the old Observatory where Tobias Mayer 
had been so active and had accomplished so much. It 
was located in an old slate-roofed tower which had served 
in the Middle Ages to protect the inner city wall. It is 
now in ruins and can be recognized only by its foundations 



-32- 



Finally in 1810, after long interruption, construc- 
tion of the new Observatory was resumed by the Wesphalian 
Government and there was set aside for the completion of 
the building the sum of 200,000 francs, to be spread over 
five years. Various architects worked on the plans under 
the direction of the church-architect Mtlller, and at last 
it was erected in Doric style, in essentials according to 
the ideas of the astronomers* 

The painful loneliness which the death of his first 
wife in October of 1809 brought Gauss proved a desolating 
experience. He was a sensitive man, of warm and deep 
feeling, a man who turned to the small, simple pleasures 
in his hours of leisure, just as at other times he was 
absorbed by his mental labors. Anxiety over his small 
motherless children oppressed him. He saw their need of 
a mother and the conviction grew in him that in such a 
second marriage the choice involved would be guided by 
his dead wife's judgment. Soon his decision was made to 
take the step. 

On April 1, 1810, he became engaged to Minna 
Waldeck, daughter of Hofrath Waldeck* and beloved friend 
of his first wife. On August 4th of the same year they 
were married. His two younger sons and his youngest 
daughter, ail still living, were the issue of this 
marriage. 

This happy re-establishment of his home in Goettin- 
gen served to tie him here more definitely and confirmed 
his resolve to decline a call to the Royal Academy 
of Science in Berlin which had come to him in April 

♦ Professor of Law at Goettingen University. 



-33- 



through Wilhelm von Humboldt. At first Gauss had hesi- 
tated to decline, since in Berlin he would have been free 
of the teaching involved in a professorship. This was 
always a burden to him, as much then as in later years, 
since he was reluctant to give it the time which was so 
precious to him. Nevertheless he performed as teacher 
a service as richly rewarding to science as was every- 
thing else he undertook. In a higher sense also this 
labor was richly repaid by the many close bonds of 
friendship now cemented for life. For soon there 
gathered around him, though he had not lived long in 
Goettingen, a circle of scholars who ever afterward 
treasured his memory in their hearts. In the earliest 
years, as early as 1808, we call to mind first of all 
the now deceased Schumacher, publisher for so many years 
of the Astronomical News and later Director of the Altona 
Observatory. Up to his death in 1850 he remained in 
close touch with Gauss and in active and uninterrupted 
correspondence. In this was doubtless much news of 
scientific as well as of biographical importance. 

Then in 1810, came Gerling, and soon thereafter 
Nicolai, MObius, Struve and Encke, subsequently the 
Directors of the Observatories of Mannheim, Leipzig, 
Pulkowa and Berlin. Several of these were still study- 
ing here in the year 1813, and only in that troubled 
time did they leave their studies, Hanbury to prove him- 
self on the battlefield. 

Gauss was soon in touch, either by correspondence or 
in person, with a wider circle of the most distinguished 
European scholars; with Olbers and Zach, both close friends 
from the time of the discovery of Ceres; with Piazzi, 
who was god-father to his oldest son Joseph, and with 
whom he was in active correspondence. With Lindenau, 



-34- 



Laplace, Alexander v* K^jniboldt, Herschel and others a 
closer relationship developed later. 

Meanwhile 10 the joy and surprise of the astronomers 
the great corret of 1811 had unexpectedly appeaired in the 
Heavens • It was seen by Gauss for the first time in the 

' because 

., .^ ,^-.„ atory was 

too restricted by city buildings :r But already, early in 
August when Zach*s observations first arrived Gauss had 
calculated from partial data the parabolic elements of 
the comet and had thus pre-determined its course in a way 
fully verified by the appeareuice of the comet itself. 
Likewise he predicted its much more brilliant appearance 
as it moved away from the sun. The nations of Europe 
saw in it only a divine rod of wrath, a prelude to the 
burning of Moscow, a sign of the overthrow of Napoleon 
whoso great army soon lay buried in the ice-fields of 
Smolensk and on the Beresina*, 

At once Germany leaped to arms, and our friends the 
Cossacks, for whom one could not but feel great sympathy, 
were close behind • One of their officers was naive 
enough, after he had been shcv;n the Observatory by Gauss, 
to ask for its only chronometer, one presented to it as 
a souvenir by King Jerome. 

With Napoleon's power overthrown and former condi- 
tions restored. Gauss enjoyed the continuous good-will 
of our Kings and of the University Senate. The new 
Observatory which the new Westphalian government had 
begun was soon finished so far as essentials went, and 
in the fall of 1816 the Director moved in. 



-35- 



For instruments there were those in use in the old 
Observatory, including the big Bird'sche wallquadrant 
(now obsolete), and also, coming from Lilienthal, a 
number of mostly useless telescopes with which little 
could be done. First of all then, at Gerling*s insti- 
gation a new meridian-circle was procured from the senior 
Repsold. 

Soon afterwards, in April of 1816, Gauss with his 
ten-year old son and Dr. Tittels as companions undertook 
a journey to Mtlnchen and Benedictbeuern in order to be- 
come better acquainted with the firm of Reichenbachs and 
Frauenhof ers , Utzschneiders and Ertels. From these 
unexcelled makers Gauss meant to order two new meridian 
instruments of the best design, after discussing the 
details of their construction. 

Gauss went by way of Gotha, where he stopped over 
some days to visit Lindenau at the Seeberg Observatory. 
The heaviness of the Goettingen coach in which they were 
travelling had annoyed him, and he gladly accepted 
Lindenau' s friendly offer of his own comfortable coach 
for continuing the journey. We take a short report of 
the journey from a letter home which he wrote in Mtlnich 
on Friday, April 26th. 

"Yesterday evening about 8 o'clock we arrived here 
in good shape ... .Now first of all a little account 
of the trip. On Sunday, early, we left Seeberg in 
Lindenau 's coach and with horses we hired, to drive 
through the Thuringian Forest where the roads were still 
completely covered with ice. In summer this region must 
be romantically beautiful. These horses brought us the 
seven miles to Meinungen, where we immediately took post- 
horses for the all night drive over the fine Bavarian 
highway. The horses flew swift as birds and we 



-36- 



reached Wtirzburg next morning. We were rather weary, but 
were refreshed by a mid-day meal. As night approached 
we continued on our way, again to drive all night and 
into the next day as far as Augsburg, where we spent the 
night. Thursday morning we looked around a little and 
by mid-day were again on our way. These last eight and a 
half miles over an indescribable road took seven and a 
half hours. And so we came yesterday to beautiful Munich 

I was myself rather exhausted by the journey, but 
rest has set all right again and today I feel as well as 
in Goettingen. We are lodged in a very good inn. 

Early this morning Reichenbach came to see me, hav- 
ing already learned of my arrival. I have spent the 
greater part of the day with him and have accepted his 
very friendly and urgent invitation to stay in his home. 

Tomorrow we will move there, also Tittels Utz- 

schneider too I have become acquainted with, and on 
Tuesday we will go with him to his estate in Benedict- 
beuern on the Tyrolean border. Reichenbach is a very 
gracious man who overwhelms me with kindness; his home 
is in the suburbs, has an extremely pleasant location 
and bears the stamp of great affluence." 

A second letter, headed: "Reichenhall , 36 hours 
beyond Munich. Sunday evening. May 11, 1816" contains 
the account of the return journey: 

"At last I am on my way home. After twelve very 
pleasant days in Munich, in which I include the trip to 
Benedictbeuern, I have come this far with Reichenbach 
who had to come here on business. After seeing something 
of this vicinity and the nearby Berchtesgaden, as well as 



-37- 



II 



the extremely interesting salt-mines and the incomparably 
beautiful region, tomorrow will find me on my way back to 
Goettingen. We do not return to Munich, but take the 
nearer way to Regensburg and Ntlrnberg, then Gotha for a 

couple of days I write this at midnight with my 

eyes almost closing, since today we made the excursion 
to Berchtesgaden, and there in the underground salt- 
mines we were constantly on the move • • • ." 

The new meridian instruments which arrived here in 
1819 and 1821, also an excellent clock from Hardy in 
London, a gift from the Earl of Sussex, were put to 
efficient use under Gauss' skilled hand and have since 
given valued service. 

During this period Gauss gave himself chiefly to 
theoretical and practical astronomy. He gave himself 
no rest, day or night. No exertion of mind or body 
seemed too great for him in carrying through a series of 
tasks. This labor was destined to reorient 19th Century 
science and to broaden its foundations in ways the 
soundness of which will be recognized and evaluated only 
by future generations. 

Gauss linked astronomy very closely with geodesy 
a science which till now had been scarcely more than 
land-surveying. He soon felt the call to work in this 
new field, and in a short time had carried it forward to 
an original and illustrious eminence which puts it 
today in the group of the loftiest of the sciences. 

It was in the summer of 1819 that Schumacher and 
Gauss met in Lauenburg to begin observations with the 
Ramsden zenith-sector which the English government had 
put at their disposal. The Danish government had al- 
ready commissioned Schumacher to make a base measurement 



and a triangulation of the Duchy of Schleswig-Hol stein, 
to which were to be attached longitudinal measurements 
to the south. This zenith-sector, brought to Goettingen 
in 182 7, later was destroyed by fire in the Tower of 
London, in 1845 if we remember correctly. 

During Gauss* stay in Lauenburg there appeared again 
a brilliant comet which he stated was one of the most 
remarkable on record, for in the summer of 1819 the earth 
found itself within its tail. Gauss thought it probable 
that it exercised a certain influence on our atmosphere, 
for after very sultry and oppressive air conditions there 
followed a thunderstorm of greater violence than any 
other he could recall in his lifetime. 

Through the influence and the strong scientific 
bent of the Count of Mtlnster the necessary means were 
readily provided for the geodetic survey of Hauinover, to 
be executed by Gauss between Goettingen and Altona. This 
work was accomplished between 1821 and 1824 and is in 
theory as well as in practical execution to be ranked with 
Gauss • most memorable achievements. 

A geodetic survey we know falls into two parts. On 
the astronomical side is the ascertaining of the geograph- 
ical measurement between the two extremities, and on the 
geodetic side is the joining of these by a trigonometrical 
network. In this undertaking the astronomical observa- 
tions present comparatively few difficulties. With the 
help of the zenith-sector mentioned above and the two 
Reichenbach meridian circles for control, these were 
announced by Gauss in 1828. 

Very much more complicated are the geodetic operation; 
worked out between the two end-points. For this Gauss 



-39- 



devised new and original methods. Working from the prin- 
ciple of choosing for the uniting triangle sides as long 
as possible, he soon discovered that with ordinary means 
in a distance from five to fifteen miles the end-points 
of the triangle sides either could not be seen at all, 
or could be made visible only with great difficulty and 
with none of the needed distinctness. In the great 
French geodetic survey between Dunkirk and Formentera 
argand lamps had therefore been used, provided with 
reflectors similar to those used on light-houses. These 
had however soon proved unsuitable and impractical for 
the purpose. First, one was obliged to work at night, 
which involved many inconveniences. Next, it was generally 
extremely difficult to discern such a light from a great 
distance. For this reason there are recorded some very 
astonishing data. In short the whole arrangement proved 
to be inexact and extremely costly. 

Gauss quickly recognized all these faults and re- 
placed the artificial night-light with his simple, cheap, 
infinitely more powerful and efficient heliotrope, an 
instrument consisting of a telescope and two small plane- 
mirrors mounted at right angles to each other. With this 
it is possible with great accuracy to direct sunlight, 
reflected by one mirror, to a point many miles away. 
Across the miles this light resembles a brilliant star 
fixed on top of a mountain or a tower. This simple but 
very ingenious instrument, variously altered in the course 
of time partly by Gauss, partly by others, has proved so 
useful for all triangulations that it is in universal use 
today. In the field of experiment the heliotrope was 
Gauss' "pet" discovery, arrived at by straight thinking 
he said, and not — as some claimed — by a happy accident. 
It might well be that he saw a window-pane on the Michae- 
lis tower in Ltlneburg illuminated by a pane on a Hamburg 
tower, but long before that he had his invention clecirly 
in mind. 



-40- 



Following this discovery Gauss threw out the ques- 
tion, half in earnest, half in jest, of whether the 
moon might be inhabited by a more intelligent race. 
Admitting this was not very probable in view of his 
observations of our nearer planets, he suggested that 
the heliotrope might help to establish safe telegraphic 
communication between the two worlds, and without 
exorbitant cost. He is said even to have calculated the 
size of the mirrors needed and to have reached a very 
satisfactory result. "This would be a discovery even 
greater than that of America"., he said, "if we ^could get 
in touch with our neighbors on the moon." ' 

With the help of the heliotrope this great Hannover 
triajigle between the Brocken, the Inselsberg and the 
Hohenhagen^ — perhaps the greatest yet measured — was meas- 
ured so exactly that the sum of the three angles differed 
by only about two-tenths of a second from the two right- 
angles. It is indeed not only the quite unprecedented 
accuracy (for that day) of the observations which distin- 
guished this triangulation, but the insight with which 
Gauss assembled the measurements into a completely inte- 
grated result. We may therefore say in conclusion that 
Gauss simultaneously devised new methods for (1) project- 
ing on a plane the points of the surface of the elliptic 
spheroid of our earth; (2) comparing widely separated 
systems of triangles according to the laws of probability 
which were set forth in his Supplementum Theoriae Combin- 
ationis Observationum . 

Not seldom in these investigations one stumbles on 
tasks of such magnitude and difficulty that only a mind 
such as his could penetrate and solve them. Intimations 
of the methods he used but never published are to be 
found now and again amidst other material in Paragraph 
22 of the writing just named. 



-41- 



In the years following the completion of this survey 
and triangulation it was Gauss' intention to publish a 
comprehensive volume on geodesy, in which these surveys 
would be included as examples to clarify his theory. 
He said as much to us and also wrote to this effect to 
Pfaff , but unfortunately this plan was never carried 
through. Instead there appeared later, in 1847 and 1848, 
when the great man saw the compass of his life growing 
narrower and narrower, two articles in the publication 
of the Royal Academy of Science: "Investigations into 
Problems of Higher Geodesy". All remaining material, 
namely the detail of the Hannoverian Survey, is preserved 
with his scientific legacy, awaiting future publication. 

It is not possible to give to a wide circle any idea 
of the profundity of these geodetic investigations nor of 
the scope of both the practical execution and the numer- 
ical calculations involved. Only those who, like the 
author of these pages, have themselves experimented in 
such matters, can fully evaluate such prodigious achieve- 
ments. In fact even the initiated stand amazed that a 
single head, a single hand, could have mastered alone and 
unaided and in such comparatively short time, such a 
gigantic piece of calculation. 

As the keystone of this geodetic task there stands 
a determination of co-ordinates for some 3000 points of 
the Hannoverian countryside, in which every pair of num- 
bers is the result of an extended calculation resting on 
the method of least squares. For the carrying out of 
each of these a less practised calculator would have 
needed perhaps several days. 

At this point in our task it seems proper to throw a 
clearer light on the proposed calling of Gauss to Berlin 
by the Prussian government, concerning which none too fair 



-42- 



reports were circulated. These showed Gauss' sincere, 
scrupulously upright character in a most unfavorable 
light. This proposed call to Berlin which never 
definitely materialized was promoted by General von 
Mtlffling with Herr von Lindenau serving as friendly 
go-between. The situation is completely revealed in 
a series of letters from von Mtlffling and Lindenau to 
Gauss which we have in our possession; and also in 
the reports of the Royal University Senate at 
Hannover, which are put at our disposal. 

We give here brief excerpts from these documents. 
In the first letter from von Mtlffling, headed Berlin, 
April 14, 1821, there is expressed merely the wish to 
secure Gauss for Berlin. On November 15 of the same 
year Mtlffling in Berlin writes to Lindenau, and the 
latter communicates to Gauss the following from 
Mtlffling • s letter : 

"The Minister von Altenstein has informed me that 
the business concerning Gauss has prospered so far 
that he needs to know Gauss' terms in order to report 
to the King on the matter. Gauss does not want the 
position of ordinary University Professor, and 
Altenstein is agreed to that. He shall not be bothered 
with daily routines, provided that he does not refuse 
to give to very promising young men the final polish- 
ing and opportunity for development. Altenstein has 
especially in mind that Gauss should work to brighten 
again the dimming lustre of a once glorious Academy, 
something Gauss of all men could do. Altenstein wished 
to report to the King by New Year's at latest, and the 
affair will meet with no difficulties if Gauss asks not 
over 2000 thaler. Gauss could then enter on his new 
position here towards Easter." 

Lindenau then recommends to Gauss the new position ii 
Berlin, asks him to take it under consideration and to 



-43- 



commiinicate his decision either to him or to Mtlf fling. 
At the end of a letter from Lindenau written from Gotha 
July 18, 1822, we find only this: "From Berlin nothing 
more has reached me concerning the business in hand." 

In Lindenau 's next letter to G^uss dated Gotha, 
Januciry 6, 1823, he expresses regret that the Survey was 
taking so much time from Gauss' scientific investigations 
and continues: "This bring5 me to the business begun 
with Berlin. In Berlin I believe you would be completely 
master of your own time, as the interests of science 
require. A few weeks ago I spoke with General MUf fling 
on this matter. He felt not a moment's doubt of the 
King's compliance with your terms and only wanted me to 
give him early information as to whether the transfer to 
Berlin still was in your plans and when you could go. 
Through Tralles' death every obstacle which might have 
arisen is removed." 

There follows then a letter from Mtlffling dated 
April 1, 1823, saying: "Gauss is now proposed by the 
Academy of Science to the King for Tralles' position, 
in addition to two others, Pfaff, and Bessel. But the 
salary, covering also the secretaryship, is a matter of 
only about 1200 thaler. Minister Altenstein, with whom 
everything moves slowly, has asked me to support him 
with the King in asking for the balance. Quite briefly 
but most urgently I represented the need, thus coming 
back to my old project of a Polytechnic School which 
Alexander von Humboldt has also been urging. Incident- 
ally I have learned definitely that our German philolo- 
gists are just as intolerant as are the Jesuits, and 
that a real conspiracy exists to keep down the mathemati- 
cians. I hope the Gauss business now at last comes off, 
and when he is once here that I find in him a pillar for 
raising aloft the mathematics of our country." 



This letter was forwarded by Llndenau to Gauss on 
April 29, 1823, with a note from which we take the fol- 
lowing: "The enclosed letter from MUf fling I wanted to 
bring to you personally in order to speak further with 
you about it. But circumstances have made that impossi- 
ble. It is the prescribed procedure that you were pro- 
posed not alone, but with Pfaff and Bessel. But that you 
will be preferred and also probably all your conditions 
agreed to, is reasonably to be expected, though at this 
time we cannot be sure. That there is beginning to be 
talk about it in public is not surprising, since in Berlin 
no secret is made of anything proposed to the King. I 
am writing Mtlffling today in order to hasten a definite 
decision, and if an official offer follows, it remains 
for you to decide whether to accept it or the improved 
conditions in Hannover. It is hard to advise since the 
choice depends on one's individual situation, and in 
recent years I have been too unacquainted with your home 
and personal life to judge understandingly between the 
advantages of life for you in Berlin or in Goettingen. 
For your intellectual labors Berlin would seem to me 
more favorable. 

"If it is possible it would be better for you to 
defer your visit to Hannover until you have Mtlffling 's 
next letter, since out of it may come more perplexities. 
But if you should be obliged to go to Hannover sooner, 
and should be asked by the authorities there if you have 
received a call to Berlin, it would in my opinion be 
completely truthful as well as wise to reply that you 
have indeed been informed by friends of the intention 
of the Royal Prussian Government to offer you a place 
in the Academy, without yet having received any pro- 
posal yourself. This would perhaps give you an 
opportunity to learn Hannover's inclination as to your 
advancement, and thus enable you to decide which life 
offers more advantages." 



-45- 



Then came two letters from Lindenau dated July 2 and 
October 21, 1823, in which only brief mention is made of 
the expected call. In the first we find: "MUf fling is 
beside himself over the long delay of the business which 
should have been settled long since, but definitely hopes 
that surely within a few weeks the matter will be 
settled." In the second we find: "That no further news 
comes from Berlin is to me incredible, since General 
Mflf fling way back in June considered the matter settled." 

After more than a year had again elapsed and nothing 
further had come from Berlin, Gauss — with his Survey 
finished — went in the end of October, 1824, to Hannover, 
visited the Privy Councillor of the Cabinet, Hoppenstedt, 
and told him of the Prussian Government's proposal to 
call him. A month later Hoppenstedt brought the matter 
before the University Senate, having requested Gauss to 
put his terms in writing, which he did in a letter dated 
November 4. By December 11th Gauss received the announce- 
ment from Hoppenstedt that all his conditions were 
accepted, and on December 17th he received the final 
papers from London. 

In the meantime, between Nov. 4 and Dec. 11, Lindenau 
forwarded to Gauss a note of Mtlffling's (of Nov. 28) in 
which the latter set down in detail the conditions which 
it was thought Gauss mad^ for Berlin. These however were 
completely different from those which Gauss himself had 
made, for Gauss had put first the securing of free time 
for his scientific investigations. Gauss' request for 
free residence was ignored, besides which there was re- 
quired the taking over of the Academy's secretaryship as 
well as the business of its administration, conditions 
quite exceeding Gauss' terms. Mtlf fling writes in this 
letter: "Now the question is: is Gauss of a mind to 
accept the position, and on the terms here set forth?" 



-46- 



Lindenau noted further: "As for the forms to be 
observed, I suppose that once you have definitely and 
irrevocably made up your mind to leave Goettingen, you 
would need to request an official call from Berlin and 
then ask for release from Hannover." 

Gauss now turned down the call to Berlin, since the 
obligations involved would have worked a disadvantage to 
his scientific work, and the Hannoverian government 
immediately met all his wishes. 

The presentation of these facts makes it definitely 
clear that Gauss had in no way obligated himself to the 
Prussian government, and that no definite call ever came 
to him. He was therefore free to accept or decline as 
seemed best. He had moreover promised Hannover to accept 
Berlin's call only after Hannover's last efforts had 
failed. Our University may thank the vision and the 
quick and business-like methods of our Council and 
above all the scientific and enlightened mind of the 
Earl of Mtlnster, that Gauss' great name has gone beyond 
her own. 

Some months later a last attempt was made by 
Bessel to secure Gauss for Berlin. "As for Gauss," 
writes Bessel to Olbers March 6, 1825, "I have made still 
a last effort, though with no hope of succeeding. I 
can't penetrate the mystery which lies over this affair, 
but I believe a tricky negotiator has spoiled it. If 
this is the case, perhaps it could still be straightened 
out if one went at it openly. I have asked Gauss if he 
will not authorize me to arrange matters with Berlin by 
word of mouth. I fear it is too late, but I await his 
reply with impatience." 

Gauss decided not to sever his connection with 
Goettingen, and writes Pfaff : "I am now bound for life 



A. 



-47- 



to Goettingen, unforeseen circumstances excepted. Not 
by formal promises, to be sure, but by the bonds of very 
sincere gratitude for our Government Is* very liberal 
attitude. My affair might well have taken another turn 
but for several fortuitous occurrences." 

In the fall of 1828 Gauss decided to accept the 
friendly invitation of Alexander von Humboldt to spend 
some days with him in Berlin during the Berlin Exhibi- 
tion of Natural Sciences. Here he became acquainted 
with Wilhelm Weber, an acquaintance which led to Weber *s 
call to Goettingen when the chair of physics was vacated 
by the death of Tobias Mayer. 

Now that the survey and triangulation were completed, 
work which had claimed Gauss' time for so long, there 
appeared almost yearly one or more treatises in the 
Goettingen Society's publication, some arithmetical in 
content, some geodetic, some physical. In 1831 he was 
suddenly seized by a great fancy for crystallography and 
in a few weeks had so mastered the subject that he went 
beyond what was known of this science up to that time. 
He measured the crystals with a 12-inch Reichenbach 
theodolite, then calculated and drew their most intricate 
forms. His method of distinguishing crystals was essen- 
tially that announced later by Miller of Cambridge. Soon 
however Gauss laid aside all papers, observations, calcu- 
lations and drawings, and with nothing published there 
was no further talk of crystallography. 

With Weber's call in the fall of 1831 work on ques- 
tions of pure physics' quite suddenly took first place. The 
close and friendly, untroubled living and working together 
of the two men Gauss once characterized by saying, "The 
steel strikes sparks." Through it there came in a few years 



-48- 



1 



those memorable, epoch-making 19th century achievements 
in physics which later found expression chiefly in the 
field of magnetism. 

One day in the winter of 1832 I happened in at the 
Observatory. Always ready to teach and share his 
thoughts, Gauss picked up a small box-compass and showed 
me how the iron rods which closed the windows were them- 
selves turned into magnets through the influence of the 
earth •s magnetism. Like a landslide suddenly set in 
motion by a small falling stone on a mountain-side and 
swelling to a size powerful enough to block valleys and 
force glaciers to a new course, there grew from these 
smallest beginnings, through the impact of Gauss' 
creative force, those remarkable investigations which 
opened an infinite perspective into the future. They 
had unexpectedly left the road travelled by man for 
centuries and opened a new road for a reinvigorated 
Science. The magnetometer in its present form was soon 
in use, and in the fall of 1833 Gauss gave to the 
Society his treatise on the Determination of the 
Absolute Intensities of Terrestrial Magnetism . 

The following spring observations were begun on the 
variations of the Declination, on the basis of the 44-houJ 
periods previously determined by the great natural scien- 
tist von Humboldt. Later such observations were begun 
all over the world after Gauss and Alexander von Humboldt 
had encouraged the organization of a magnetic I 

association. I 

Observations set up to use everywhere instruments of I 
the same construction were soon pouring in from north and | 
from south. This led to the discovery that the daily 
course of the magnet's needle was everywhere simultane- »• 
ously affected by disturbing forces, a result already i 
suspected but in its universality and precision highly ^ 
surprising to all physicists. 



-49- 



I 

I 
I 



With the development of the magrgbometer and with 
the observations carried out almost daily on the abso- 
lute Declination and its variations, as also on the 
Intensity, the discovery of the electro-magnetic tele- 
graph is most intimately connected. Different magr$:o- 
meters were immediately equipped with amplifiers and a 
double wire connection which at first reached only from 
the Observatory to the little magnetic house built in 
1833 some hundred meters west of it. Hydrogalvanic 
action of a single pair of plates was to be seen passing 
from one end to the other of the magnetometer. But in 
this same year, 1834, induction replaced hydrogalvanism, 
and thus was the electromagnetic telegraph discovered, now 
— with various mechanical modifications — in universal use. 
Single words, then sentences, were telegraphed between 
the two substations with complete assurance; once in the 
presence of his Highness the Duke of Cambridge who showed 
special interest in the new discovery. 

Following the entirely successful efforts in Goettin- 
gen. Professor Ernst Heinrich Weber of Leipzig reported 
them at the suggestion of Minister of State Lindenau to 
the Directorate of the Leipzig-Dresden Railroad and pro- 
posed the construction of an electromagnetic telegraph 
between Dresden and Leipzig. According to an estimate of 
Wilhelm Weber a double line of copper wire between the 
two places would need to be of 1.6 mm diameter and 60 
cent, weight. Iron wire would need to be 3.8 mm thick 
and 330 Centner weight. 

Ernst Heinrich Weber had grasped the full signifi- 
cance of the great discovery and he closed his report 
with these words: "If once the earth is covered with a 
net of railways and telegraph lines, this net will per- 
form a service similar to that of the nervous system in 
the human body, communicating motion and transmitting 
perceptions and ideas at lightning speed." 



-50- 



In 1835 therefore Dr. HUlsse of the Railway Direct- 
orate was sent here to acquaint himself more fully with 
the set-up of the Goettingen telegraph. After his return 
to Leipzig in Sept., 1835, Wilhelm Weber wrote him semi- 
officially, enclosing a plan by Gauss. From the two 
documents (which it is hoped will later be published) 
one gets a clear idea of the construction and peculi- 
arities of the electromagnetic telegraph of that day. 
Gauss says in this paper: "Our way of telegraphing 
dispenses with all hydrogalvanic current and depends 
on a particular application of induction. We transmit 
8 letters a minute." By a slightly altered arrangement 
which will be described in more detail in Gauss* docu- 
ments, it would even be possible to send 20 letters a 
minute. 

The Directorate of the Railway now approved its 
committee's decision of July 15, 1836, at the second 
general meeting of the Leipzig-Dresden RR., to move for 
the building of an electro-magnetic telegraph between 
the two chief cities of Saxony. Unfortunately railroad 
shares just then fell considerably in value and the 
Directorate shrank from every avoidable large expendi- 
ture. Thus the decision to unite Leipzig and Dresden 
by telegraph at that time failed of execution. 

It should be noted that in 183 7 Herr von Steinheil 
in Munich, relying on the Gauss-Weber invention, re- 
duced the mechanism of the telegraph to a greatly 
simplified form (since then entirely altered) by means 
of which one could use it for speaking as well as for 
writing. 

The conducting wires of the first Goettingen tele- 
graph after ten years of use were largely destroyed on 
December 16, 1845, by a fierce bolt of lightening. But 
a .short length of wire is still preserved today. 



-51- 



On September 19, 1837, at a session of the Academy 
of Science during the celebration of the University's 
100th anniversary. Gauss put into the hands of Alexander 
V. Humboldt his treatise on the Bif ilarmaqnetometer , In 
this treatise are set forth the methods for using this 
instrument (now everywhere employed in magnetic fields) 
to determine variations of intensity with the same 
accuracy obtained by the magnetometer when observing 
variations of declination. 

In 1840 there next appeared, to the joy of physi- 
cists, the long awaited General Theory of Terrestrial 
Magnetism which placed a new foundation under physics. 
For two centuries men had been giving close attention to 
observations of the magnetic declination and inclination, 
and now in our own times to the observation of intensity, 
and had been laboring to put these phenomena on charts 
and globes. Now it was for the physicists to attain a 
loftier point of view from which to look out over the 
confused labyrinth of data piling up higher and higher, 
and to be led toward a general law, away from the ground 
of apparent chance to the ground of the inevitable. 

The assembling of observations on our magnetic 
charts may be likened, said Gauss, to the visible course 
of a comet across the sky. Man has only the cornerstone; 
he can erect no scientific structure so long as these 
manifestations come under no known scientific law. 
There was no dearth of attempts to decipher the great 
riddle, but the^e only serve to recall the time when 
astronomers tried to explain the course of the planets 
through accumulating epicycles, before Kepler's Laws 
and Newton's Law of Gravitation lifted us to the highest 
plane of Science, moving like bright sunlight over the 
dull background of human knowledge. 



-52- 



Thus Newton's creative mind led astronomy to the 
final principle which controls all science, and Gauss 
solved the hitherto veiled problem of terrestrial 
magnetism. This problem might well have had to wait 
another two hundred years for solution, with its 
mysterious phenomena and inadequate methods of observa- 
tion. So in these investigations of our illustrious 
mathematician the way was indicated which science was to 
follow in the future, and through them all was scattered 
a rich sowing of seeds for future generations to harvest. 
Yet as we read of such intimations we feel deep sorrow 
that through the loss of this incomparable man our 
world is the poorer by a whole worldful of thought, and 
our spiritual course has fallen short of reaching its 
highest peak. 

Besides many small undertakings which are included 
in Gauss' magnetic findings, we should mention one 
investigation which he valued as one of his most impor- 
tant, namely the general principle of the operation of 
forces under the law of inverse squares. With this the 
findings of the Magnetic Society were in large part 
closed o From this time on Gauss had still approxi- 
mately ten working years before him. These, however, 
slipped by even more quickly than we had anticipated. 

Gauss published next an important treatise on 
Dioptrics, and then two larger ones on Geodesy, which 
have already been mentioned and which are to be viewed 
as part of that work so long contemplated but never 
put through. 

In addition to this scientific work he put much time 
into his academic teaching. His lectures on practical 
astronomy and on different aspects of mathematics, espe- 
cially en the method of least squares, seemed to give him 
more pleasure in his later than in his earlier years. 



-53- 



Though he groaned over the burden he faced at the begin- 
ning of each semester, he was soon in the heart of the 
subject with great zest and energy of mind. Also he 
felt the stimulation of a larger circle of students than 
he had formerly gathered about him. At the Senate's 
request he took over also a reorganization of the Univer- 
sity's Widows' Fund, a task he performed with great 
unselfishness, demonstrating anew his extraordinary 
versatility and genius with figures. In this his practi- 
cal talent for organizing large financial operations, 
his kindness, his sense of justice, his objective 
approach to all situations were clearly in evidence. 
His exact studies of nature and the careful uniformity of 
his methods doubtless helped. 

So Gauss cleaned out the Augean stable, bringing a 
blessing to our widows and orphans (which will last as 
long as the affairs of men run peacefully) by re-estab- 
lishing an institution which was on the brink of ruin 
and which — through mismanagement — would otherwise cer- 
tainly have gone into eclipse. On this matter a care- 
fully drawn report was laid before the University Coun- 
cil and Senate, embodying the principles to be considered 
in managing such funds. This was unanimously endorsed. 
It would be well if this report with its many new ideas 
could now be made available to more such institutions. 

On July 16, 1849, we attended the 50th anniversary 
of the noble old scholar's Doctorate. A numerous circle 
of friends, admirers and grateful pupils gathered round 
him, coming from near and far to express once again 
their profound admiration and respect. Also there came 
many tokens of homage, renewed degrees, the keys to the 
cities of Goettingen and Braunschweig, and various orders 
of decoration, distinctions accorded even small men. 

At a meeting of the Society of Science held in cele- 
bration of the day in a flower-bedecked hall. Gauss pre- 
sented his last treatise: Contribution to the Theory of 



-54- 



Algebraic Equations , in which he treated the same subject 
with which he had entered on his scholar's career fifty 
years before, but this time from a general point of view. 
At the banquet he spoke with emotion of the continuously 
active, earnest efforts in behalf of science which had 
ever been the blessing of our University. "Banale 
phrases had never been accepted in Goettingen," he said. 
Then he pointed to the helpful attitude of the Council 
under whose far-sighted leadership the representatives of 
science were shielded from misfortune and enabled almost 
undisturbed to devote themselves to research, not seldom 
reaching notable heights. 

On July 26, of the same year, in times otherwise so 
troubled, we recall still another happy event, the visit 
of the Minister von Lindenau, last of the old friends 
from the beginning of the century to see Gauss here. 

From then on Gauss seemed to rest on his laurels. H( 
said often to his nearer friends that he did not wish to 
drive himself and that his working hours were much shorte: 
than in his earlier years. Again he deplored the burden 
of lectures which took him from weightier investigations. 
Yet there were few days on which he did not carry on with 
his research and calculations. For example he worked on 
the theory of the convergence of lines , on a second re- 
vision and balancing of the University Widows' Fund, and 
still again on mechanical problems connected with the 
earth's rotation, following Foucault's effort and the 
theories put out by Lagrange, Plana, Hansen and Clausen. 

Practical astronomy and natural science continued to 
delight and interest him even though he could put into 
them less time and strength than formerly. Thus he had 
the Reichenbach meridian-circle provided with new micro- 
scopes, observed at such times as he comfortably could 
several of the newly discovered planets, and ordered from. 



-55- 



the Berlin firm of Oertling an optical apparatus, that 
he might go more deeply into the new theories of light, 
in which he felt great interest. In fact shortly before 
his death he designed and made a pendulum apparatus of 
large dimensions to show the rotation of the earth by 
striking. 

Almost the only physical relaxation Gauss took in 
his old age was a daily walk from the Observatory to the 
Library. Here he was regularly to be found between 
eleven and one o'clock, rapidly going through all the 
political, literary and scientific journals, culling from 
each that which was of interest to him. This he would 
sometimes jot down or he would store it away in his 
powerful memory. 

At home we would find him occupied with lighter 
reading than formerly. He tired more easily and needed 
more rest. No small part of his time still went into 
hi-s extensive correspondence with friends and scientific 
associates all over the world, though many of the old 
bonds had been broken by death. Already laid aside for 
several years were the pens of Olbers and Bessel. With 
Schumacher in Altona he exchanged weekly letters as long 
as the latter lived. Also with Alexander v. Humboldt he 
was in close, though not such regular touch. Several 
months before this great scientist would have reached the 
age of Newton he marked the day on his calendar, and when 
the day came round expressed to him his heartiest good 
wishes^ 

In February of 1851 death took from us our friend 
Professor Goldschmidt. The previous night he had been 
observing in the Observatory and had shown some friends 
the Pleiades in a telescope. Next mo^ng he was found 
dead in bed. The sudden passing of a man so highly 
valued by us all for his kindly character and his sound 
scholarship and so closely associated with Gauss, and 
for whom Gauss felt such deep admiration, was for all of 
us a deep blow. 



In the two following winters Gauss complained 
repeatedly of his health* He suffered from sleeplessness 
and shortness of breath, also from congestion which he 
thought was the main trouble. He had adopted the simple 
remedy which seemed to help him of getting up every night 
about three o'clock for a drink of Selters water and warm 
milk.. In all his long life he had till now allowed him- 
self to be given only two prescriptions and those by 
Olbers forty years earlier. He had scant confidence in 
medical science and now in his failing health was for a 
long time opposed to calling in a physician. 

At length the repeated pleas of those close to him 
persuaded him to call in our common friend and col- 
league Dr. Baum. This v;as on the 21st of last January. 
An examination which continued over several days showed 
the trouble to be enlargement of the heart, an illness 
which would probably be fatal and of short duration. 
The trouble seemed to be an old one, though grown 
conspicuously worse in old age. Olbers many years 
before had recognized or suspected it and advised 
caution. The use now of specific remedies combined 
with the coming of warmer weather worked such improve- 
ment that in the course of the spring and summer Gauss 
was again seen almost daily at the Library between the 
hours of eleven and one. He could also take short 
walks here and there in the neighborhood. 

He took great interest in the building and manage- 
ment of railroads, though for over twenty years he had 
not spent a night away from Goettingen and had therefore 
seen nothing of the new developments. But this interest 
led him on June 16th last to visit the railroad under 
construction between here and Cassel. Unfortunately a 
passing locomotive frightened the horses of the carriage 
in which Gauss was riding with his daughter, the carriage 
Was overturned and the driver seriously injured. The aged 



-57- 



man and his daughter miraculously escaped all injury and 
both returned unscathed to the Observatory, 

On May 21st the newspapers announced the death of 
Bernard von Lindenau* The news appeared to touch Gauss 
so deeply that we avoided speaking of it. But he kept 
coming back to it and the memories of their old friend- 
ship, dwelling on Lindenau's disinterested, noble char- 
acter, to which he ascribed the success of his diplomatic 
career. No thought of his own approaching end seemed to 
touch him, whether because he was shutting it away or 
more likely because he did not believe his end was so 
near. 

After some weeks, on July 31, the official opening 
of the railroad between Goettingen and Hannover took 
place. It was a fine summer day and Gauss was well 
enough to go downtown and view the celebration from 
various places. It was however the last day we saw him 
in tolerable health. 

With the coming of fall the disease took fresh hold 
on him and as the weeks passed we did not hide from our- 
selves our friend^s increasingly serious condition. A 
swelling of the feet which in lesser degree had for a 
long time been observed but which he seemed to view as of 
little consequence, now forced him to remain housed and 
to give up his walks to the Library; even the few steps 
in his own house became difficult for him as the short- 
ness of breath increased. 

On December 7th very disquieting symptoms developed 
and Baum did not expect him to survive the night. But once 
again the strong spirit kept the weakening body together. 
After a quiet night Gauss was definitely better the next 
day and wanted to return to his accustomed routine as soon 
as possible. Though he could not work continuously toward 
the end he was still always mentally occupied. He read 



-58- 



much and often for very long periods. Also he wrote 
each day although with much greater labor. He still 
noted down various memoranda and wrote letters. The 
last letter of all, a keepsake to be honored by him 
who possesses it, went to Sir David Brewster on the 
subject of the discovery of the electric telegraph. " 

The last evening of the departing year I visited 
the great man as usual. I saw him but briefly, find- 
ing him in comparatively good spirits, but left him 
knowing that we two would never celebrate another New 
Year together* In the early part of January Gauss was 
very miserable and saw hardly any visitors, yet hoped 
confidently to be better presently and wrote on 
January 5th to Architect Prflel concerning repairs to 
his dwelling planned for early spring. Only now did 
his beautiful handwriting become faltering, something 
which had not been the case before. 

With the ups and downs of his illness I did not 
see Gauss again till January 14th. At that time the 
Sculptor Hesemann of Hannover had just arrived on 
commission of his Majesty the King to make a medal- 
lion of the great mathematician. He planned to 
begin work the following morning. I found Gauss 
weaker but cheerful. He related some incident out 
of his earlier life; his blue eyes sparkled, the 
last time I saw them so. 

On February 21st I saw him for only a few minutes 
soon after mid-day. He was still fully conscious, as 
he was up to his last hour. But he was strikingly 
altered, for Death hovered close. I pressed his hand 
once more and left the room. I did not again see 
him alive. 

February 22nd soon after mid-day he passed through 
his last hard struggle. Then toward evening it seemed 
to be better with him, and though his eyes were already 



-59- 



closed on this world, consciousness had not left him; 
he heard everything that went on about him, inquired 
about those present in the room and asked for a drink. 
Then came the need for rest, the balm of eternal sleep. 
We sat in the next room and hoped for a better night. 
His heart continued beating, but the breath grew 
shorter, ceasing altogether at times, then beginning 
again. Then the intervals became longer, and on 
February 23rd at five minutes after one in the morning 
he drew his last breath. Also at a few minutes after 
one his watch stopped, the watch which had gone with him 
through the best part of his life and which is something 
an astronomer does not easily forget to wind. 

It was over. The noble soul had breathed its last, 
called home for completion of the work it had begun. It 
had entered that realm washed by the peaceful waves of 
Eternity, in which live only great thoughts, great feel- 
ings, and in which there is no pain, no sound of earthly 
mourning, where are left behind the sad scenes of decay. 

Next morning the great man still sat in the arm- 
chair in which he had gone to sleep. His noble head with 
its silver hair was bent forward almost to his breast , 
his tired eyes were closed. The last sunset glow of his 
earthly world of thought seemed to envelop his high, 
nobly thoughtful brow, and the mildness of the spring 
rested like a benediction on his kindly features. 
Earthly pain was overcome and there remained for us only 
the tears, the sorrow, and the hope of another meeting.. 
It was for me a touching, deeply moving, and unforget- 
table picture to see now before the dead man the faithful 
daughter and nurse of his old age, her task performed with 
such high devotion and filial love. She knelt at his 
feet, smoothed his silvery hair, kissed and caressed his 
face as if she would call him back to life. It was so 
still every breath was audible, only not his. 



-60- 



The night of February 25th was the last Gauss spent 
in his room. With a simple black casket made ready, only 
those closest to him performed the last duties; no unde- 
dicated hand touched him. We made ready his quiet couch, 
placed him on it, and wreathed his noble head and peace- 
ful face with fresh laurel and spring flowers. 

Next morning by nine o'clock the casket stood open 
in the rotunda of the Observatory, crowned with cypress 
and surrounded by lighted candles. It seemed as if for 
the ceremonies of these grave hours the countenance of 
the dead man had taken on another expression. The 
grandeur of his features had supplanted the earlier 
mildness; the high forehead surrounded by laurel, the 
eyebrows with their characteristic and slightly irregular 
modelling, the aquiline nose and still mouth combined to 
give an impression of consecrated solemnity and impres- 
sive dignity. It seemed as if he would say: "My great 
life course is run. I can look back on my life serene- 
ly and look forward with hope." 

There had meantime gathered the Fellows of the 
University, the Mayor of the city and numerous friends 
and admirers of the deceased. The casket was placed on 
the terrace by Students of mathematics and of natural 
science. Then followed the chorale, "Eine feste Burg ist 
unser Gott." Words of farewell were spoken by two close 
friends, after which a long procession accompanied the 
dead man to his last resting-place. There the pastor 
pronounced the blessing and the casket was lowered into 
the earth, covered with palms and laurel. Nature's 
frosty shroud soon enveloped the quiet grave, which we 
hope will be marked with a.*.t[tanite shaft for the benefit 
of coming centuries. 

The great man's features and still more his inner 
nature and powerful work are imprinted deep in our 



-61- 



memories. That his likeness should be preserved also for 
coming generations is therefore a matter that concerns us 
First, there is a bust modelled from life when he was in 
his 34th year. In this the face and forehead are excel- 
lently reproduced, but the back of the head is poor. 
Then we have also an excellent, very life-like oil 
portrait done by Janssen of Copenhagen. The original is 
in the Royal Russian Observatory of Pulkowa near St. 
Petersburg. Three copies of this are in Goettingen. 
From one of them was made the well-known steel engraving 
with the motto from King Lear , Also we have the success^ 
ful medallion by Hesemann, made this past January, and a 
death-mask which we hope will serve as a guide for an 
excellent bust. And last of all Herr Petri here in 
Goettingen, skilled in making daguerreotypes, has made 
several pictures, two showing only the head, two the 
whole figure in death. In these we see the great mathe- 
matician as he rested in quiet peace in his room that 
last night before his burial, robed in his scholar's 
gown. Unfortunately there exists no photograph from life 



Adequately to describe the character and the manner 
of mind of this man is a task which I well know is be- 
yond my powers, - a man towering high over our Age, to 
whom aspiring mankind and above all the better part of 
the German' nation can raise justly proud eyes, a man who 
in his own inspired life reaped as rich a harvest as he 
sowed for future generations. Yet if in concluding 
these pages I attempt in some measure to do this, I hope 
for kind indulgence from those who are convinced of my 
aim and deepest desire to fulfil a sacred duty. 



-62- 



The son of poor but upright parents. Gauss was from 
his youth accustomed neither to the luxury nor the refine- 
ments of our day. The very scanty means which provided 
for his early years were enough for his small needs. From 
childhood on he knew how to spend carefully the little ^ 
that he had, so that there was always a little left for I 
the unexpected, enough to prevent his needing to turn to ■ 
others for material aid. A high sense of personal pride 
as well as his inborn independence of spirit doubtless 
held him to this, - an attitude from which he never 
swerved . 



So it was that in mature years he felt it impossible 
to accept assistance from private sources, even from his 
closest friend Olbers, as likewise from Laplace, when 
they wished to supply the sum needed for the French war- 
levy at a time when Gauss was in real need. He accepted 
the support of the Duke of Braunschweig because this had 
to do with his work and not with him as a person. 

The restricted circumstances under which Gauss grew 
up left on his spirit no trace of depression. He was 
cheerful, gay, forward-looking. The goods of this world 
which Fate denied him seemed to him superfluous, almost 
disturbing. In the years of his early development he 
remained rather apart from the world, since after 
Bartel's departure no one in Braunschweig was able to 
follow his studies. 



I 
I 
1 
I 



1 






At various times Gauss remaxked to me that only for 
himself, that is from the deep urge of his own soul, was 
he pursuing his scientific investigations, and that it was 
to him of secondary interest that his work should later I 
appear in print in order to reach a wider circle. Another" 
time he said that in his youth his thoughts streamed forth 
in such an unbroken flood that he could hardly control therl 

I 
I 

-63- 

1 



and was able to record them only in part. This explairfe 
the fact that often his greatest discoveries lay for 
decades in his writing-desk without being made public un- 
til later the same things were discovered by other mathe- 
maticians. In part also the manner of presentation and 
the final editing of his works, of which we will speak 
below, had something to do with their delayed publication. 

When a task which had perhaps occupied him a long 
time was completed he was accustomed frequently to enter 
only the end-result on a slip of paper or in a small note- 
book, in the neatest of figures. It was then put aside 
and years might pass before it was again called forth. 
How many thoughts may have risen up in this powerful brain 
with its incredible productivity, to be again submerged! 
lost to science! — at least for the time being. 

Gauss said of himself that he was wholly a mathemati- 
cian. To be anything else at the expense of mathematics 
was an idea he repudiated. Yet the natural sciences also 
drew him. On the occasion when he copied the motto from 
King Lear , * lines he treasured and loved, I heard him say 
it was a fitting motto for a natural scientist :- 

Thou, nature, art my goddess, to thji^y laws my 
services are bound. 

To use Gauss' own words, mathematics was for him 
"the Queen of sciences, and arithmetic the Queen of 
mathematics." It may often stoop to do a service for 



♦ Note: From Shakespear's King Lear , Act I, Scene II, 

where however it has a different meaning. 

Gauss wrote Laws in place of Law , a small 

change essential for its application to the 

natural sciences. 

-64- 



astronomy and other natural sciences, but under all 
circumstances it must take first place. Gauss saw 
mathematics as the prime building-stuff for the human 
spirit, yet gave full recognition to the study of 
classical literature, and said occasionally he had 
not ignored the latter, though he had chosen to 
follow the former. 

In all mathematical research he placed at the top 
rigorous analysis. This was strongly emphasized in 
the congratulatory message of the Berlin Academy on the 
day of the anniversary celebration. This pointed out 
that Gauss was the mathematician of modern times who 
had brought the long-lost austerity of the Greek geom- 
eters again into acceptance and had introduced it into 
the higher branches of mathematics. 

Through the study of Euclid and Archimedes he 
could only be confirmed in this attitude which so 
accorded with the bent of his own genius. Moreover 
to young and promising mathematicians he always 
urgently recommended the study of the ancients. 

Although Gauss was better acquainted than was 
perhaps anyone else living with analytical calculus, 
he was strongly opposed to every mechanical handling 
of it and tried to restrict his own use of it so far 
as possible. He often said that he never started a 
calculation until the problem was fully solved in 
his own mind. Thus for him calculus was only a tool 
for carrying through a task. 

In discussing these things he once remarked that 
many of the most distinguished mathematicians, Euler 
very often, and even Lagrange occasionally, trusted 
so much to calculus that they were unable to account 
for their investigations at every step of the way. 
Of himself he could say that with every step he took 



-65- 



he always had definitely and undeviatingly before his 
eyes the end and aim of his task. The same was true of 
Newton* 

For greater certainty and control of calculations 
Gauss tried so far as was practical to support his compu- 
tations with geometrical principles. He further demon- 
strated his general theories by applying them to practi- 
cal examples. In early youth geometry inspired little 
interest in him. Only later did this develop in high 
degree. 

It was especially noteworthy and illuminating to see 
the principles on which mathematics is based laid bare by 
Gauss, and to see them sharply distinguished from meta- 
physics • Although Gauss never published anything on 
these questions, we may well suspect that something may 
yet come to light in his scientific estate. In earlier 
years when his course in life was not yet determined and 
he had to think of the possibility of somewhere being a 
teacher of mathematics, he worked with this in mind on a 
paper which is said to have come to hand in these last 
years and in which he treated the rudiments of mathema- 
tics philosophical "ly. It is doubtful if this is still 
in existence. 

Geometry was for Gauss a consistent structure, with \ 
the theorem of Parallels standing as an axiom at its 
peak. He was convinced nevertheless that this proposition 
could not be proved, though shown by experience with the 
angles of the triangle Brocken, Hohenhagen, Inselsberg to 
be approximately correct. If however people were not 
willing to accept the axiom named above, there would then 
follow another quite independent geometry which he had 
once briefly pursued and had called Anti -Euclidean 
Geometry. 

According to his frequently expressed convictions 
Gauss regarded the three dimensions of space as a specific 



-66- 



i 



characteristic of human beings. People who could not 
understand this he humorously called Boeotians. "We can 
think of creatures who are conscious of themselves in 
only two dimensions," he said. "Higher above us in like 
manner would stand those who look down on us. Certain 
problems pertaining to this", he continued jestingly, he 
had "put aside to deal with later through geometry, in a 
higher state of existence." 

Gauss* aim was always to give his investigations 
the form of perfect works of art. He would not rest 
sooner and never gave a piece of work to the public 
until he had given it the perfection of form he desired 
for it. A good building should not show its scaffold- 
ing when completed, he used to say. In his demonstra- 
tions he used almost entirely the synthetic method, 
which he had come to prize through his studies of 
Archimedes and Newton. It is distinguished from the 
analytic method by its brevity and comprehensiveness. 
But the road leading to the discovery remains veiled; 
and indeed it often seems that Gaijss frequently and 
intentionally turned aside from the road that led to 
mere instruction. 

It is not to be denied, he often said, that this 
ingenious method of demonstration, which made the 
reading of his treatises much more difficult for those 
less versed in mathematics, also cost him much time. 
But having chosen this path in his youth he was 
unwilling to desert it later. It is explained in the 
motto on his seal: "Pauca sed mature." (Few, but 
ripe. ) 

Some eminent mathematicians of recent times have 
expressed the opinion in connection with Gauss" discov- 
eries that it would have been better for the advance- 
ment of science if he had attached less importance to 
this perfection of form and had instead given out more 
of his inexhaustible ideas, which are lost to us 
insofar as they are not noted down. 



-67- 



Gauss* writings delved into the most varied branches 
of mathematics, astronomy and physics. Through their 
wealth of material as well as through their unimpeachable 
correctness they won the universal admiration of all the 
initiated. It is indeed remarkable that in so many deep- 
plunging investigations no man has been able to find any 
error other than a misprint. 

Mathematical research had value for Gauss only when 
it was the culmination of long mental effort. He never 
rested until he had solved the problem before him. Were 
other people but willing, he said, to ponder mathematical 
truths as deeply and continuously as he did, they too 
could have arrived at his discoveries. Often for days he 
had pondered in vain over one or another piece of investi- 
gation without reaching the answer, when all at once — per- 
haps on a sleepless night — this would come clear to him. 
In talks with others he would often become suddenly 
silent, especially in his younger years. Staring into 
space he would seem to be intently following some new 
thought. Conversation would cease, to be resumed some 
days later after ripe consideration. 

Gauss' extensive knowledge was amazingly at his 
command. His unexcelled memory for figures especially 
excited our wonder. If a question was put to him which 
he did not wish to answer immediately, or could not, one 
might be sure that there would shortly follow a discussion 
of the subject, either orally or in writing, which would 
leave nothing to be desired. During his active years he 
enjoyed sharing such matters with his pupils or young 
friends. 

Gauss had a remarkable combination of rare endowments, 
a combination perhaps never in such high degree equalled. 
To his striking ability to work out abstract questions in 



-68- 



every field and from varied standpoints was added the 
amazing gift for numerical calculation, the peculiar 
gift for a quick grasp of the most involved relations of 
numbers, and finally special delight in the exact 
observation of nature. 

Archimedes, with his inborn logic in addition to 
his mechanical gifts, seems to have been a nature 
closely related to Gauss, But under the conditions of 
his time his gift for combinations of numbers could not 
be developed. Gauss often said to us that Archimedes 
was the man of antiquity he most revered. He pictured 
him as completely noble in appearance, old and digni- 
fied. But he could not forgive him that in his 
reckonings in the sand he had not hit upon the decimal 
system. "How could he have missed it!" he exclaimed. 
"And on what heights science would find itself today 
if only Archimedes had made that discovery I" 

Still closer was the spiritual kinship of Newton 
and Gauss. Indeed Gauss cherished for the great English 
scientist an unbounded admiration and in his writings 
usually referred to him as "summus Newton", a term he 
applied to no other mortal. Indeed Newton's exalted 
genius was revered by Gauss as by few others in like 
degree. Gauss expressed indignation that the great 
discovery of the law of gravitation was said to be 
attributed to petty chance. 

"The story of the apple is too simple," he said. 
"Whether the apple fell or remained where it was, how 
can one believe that through it such a discovery was 
hastened or delayed. The circumstances were probably 
like this. There came to Newton sometime, somewhere, 
a stupid bore of a man who asked Newton how he happened 
on his great discovery. Newton, seeing clearly what 
kind of an ignoramus he had before him, and wishing to 
be rid of him, probably answered it was an apple which 
fell and hit him on the nose. Whereat the man went 
contentedly away, fully enlightened." 



-69- 



The two outstanding personalities of the 17th 
century, Newton and Leibnitz, have often been compared. 
Gauss likewise did this. He recognized indeed the high 
genius of Leibnitz whenever he spoke of him and did not 
underrate his services in the discovery of differential 
calculus, but he censured him for having occupied himself 
with everything under the sun and at the cost of mathema- 
tics. Therefore the achievements of Leibnitz could not 
be remotely compared with those of Newton. 

The mind for experiment as well a.s for numerical 
calculation was peculiar to both of these great mathema- 
ticians, though in calculation Gauss far excelled all 
others, living or dead. We were constantly overwhelmed 
by his complete mastery of the world of numbers as we 
saw it on every side yield to his genius. For example 
he could name off— hand or at least after very brief re- 
flection, the characteristics of every one of the first 
couple of thousand numbers, and with these still keep in 
mind the later ones. In mental reckoning he was unexcel- 
led, though he placed no special value on this gift^ 
"since up to a certain point it was a necessity." We saw 
daily astonishing instances of this gift. Likewise the 
first digits of all logarithms were always stored in his 
mind, to be used for rough mental calculation. Often a 
many-sided closely-packed calculation continuing over 
days and weeks, with number crowding on number, calcula- 
tions which to others less expert presented insuperable 
difficulties, seemed to him neither baffling nor exhaus- 
ting, but all in the day's work. It is possible that 
some skilled calculators can resolve long and involved 
calculations just as quickly by using accepted shortcuts. 
The remarkable thing with Gauss was that in all tasks of 
this kind on which he embarked for the first time he was 
always finding new paths, new methods, new devices 
through which he could always enliven a tedious task 
with fresh interest. 



-70- 



In larger tasks where it was a matter of obtaining 
an important result he rarely made an error, for he 
knew how to weave into these computations so many expert 
controls that an error was almost impossible. In all 
extended computations he observed a standard pattern. 
Every figure was most neatly written, each stood in its 
right place, row under row with unvarying precision. 
Gauss* aim was always to carry out the task as exactly 
as the means at hand permitted. Thus the last decimal 
in the 7 or 10-cipher logarithms must be carried out as 
far as possible. And in this connection he pursued 
extensive investigations of his own as to how far in the 
different tables the last decimal was reliable. Reckon- 
ing with incorrect tables gave him a special pleasure, 
since then, on the side, he had the agreeable opportun- 
ity of correcting what errors of printing or reckoning 
might appear. But his greatest pleasure was to simplify 
as far as 'possible interminable analytical or numerical 
calculations, finally to condense them into small 
compass, and sometimes to present on one side of an 
octavo sheet the results of a task which had taken 
weeks, making all clear to the initiated. Also where 

he had to make excerpts from the works of others, the 
contents of a volume or the di^gest of a whole pile of 
reports was so concisely put together as to require 
little space. 

The peculiar combination of Gauss' gifts, the 
acuteness of his mathematical powers and the ease with 
which he mastered computations were in essence the 
explanation of his success with astronomy. As long as 
he lived he found both pleasure and exhilaration in 
astronomy. 

In the letter we have already quoted Olbers wrote 
that Gauss "loved" astronomy, and most particularly 
practical astronomy, wherefore he desired to divide his 
time between this and his profoundly deep mathematical 



-71- 



inve3tigations. Some great mathematicians have regretted 
that Gauss did not confine himself entirely to the field 
of mathematics, and it is true that this science suffered 
for the sake of astronomy and geodesy. As we have already 
noted Gauss himself ranked mathematics as Queen of the 
sciences. But he obviously felt the need at times to rest 
from exhausting investigations and it was in the study of 
nature — in astronomy and physics — that he found recrea- 
tion. His profoundest joy was to listen to Nature in her 
deeper moods. The exact observations he always made at 
such times then served as starting-points for new investi- 
gations, new theories. To all observations in either 
astronomy or physics he sought to give all the precision 
which observer and instruments could supply, just as he 
executed numerical calculations with all the exactness 
the means at hand permitted. 

The construction of instruments he grasped intuitive- 
ly. Once their purpose was defined he was able to produce 
a geometrical drawing of them which showed their function 
clearly and graphically. All errors to which observations 
by a given instrument were subject were then investigated 
and the manner of their correction indicated. This ex"-^ 
pertness in understanding and criticizing the performance 
of an instrument was increased by his natural taste for 
it, especially in his younger years, by his restless 
axdor, his great skill and marked success. In the latter 
half of his strenuous life he was glad to turn over to 
his pupils those daily recurring observations which he 
had himself previously conducted. His eyes, nearsighted 
from youth on, were sharp and his ears acute for time- 
intervals. Every phase of physical astronomy was of keen 
interest to him even when there were no exact aspects to 
observe and even though he might consider it quite beyond 
the bounds of pure science. However, when the applica- 
tion of mathematics seemed to promise any reward he put 
into the task just that much more zeal. 



^72- 



We recall the time when the moon-chart of Bear and 
Mfldler appeared and Gauss stood at the telescope almost 
every clear evening to observe the surface of our nearest 
neighbor from different angles and under differing condi- 
tions. Again we were surprised by the short time it took 
him to orient himself in this new field. 

Likewise other phenomena of the heavens kept him 
pondering and observing. Variable stars, double-stars^ 
nebulae, the nature of the surfaces of sun and planets, 
the appearance of comets, shooting-stars, zodiacal light 
and many other phenomena all claimed his attention* 
From time to time he let fall a few comments on these 
matters, but attached no weight to them. Prevailing 
views on one or another such matter he now and then 
rejected without communicating more at length his own 
thinking. Among other things he held order and 
conscious life on the sun and planets to be very 
probable and occasionally called attention to the action 
of gravity on the surface of heavenly bodies as bearing 
preeminently on this question. Considering the univer- 
sal nature of matter, there could exist on the sun with 
its 28-fold greater gravity only very tiny creatures 
somewhat like cock-chafers, whereas our bodies would be 
crushed and our limbs broken to bits; then he added 
whimsically: "Yes, on the sun there is room for us all; 
only each one of us to be sure would need his own 
valet." 

When in the mood Gauss took pleasure in looking to 
the future of Man's development and especially to that 
of his beloved science. He seemed to expect most from 
the further development of mathematics and the theory of 
numbers. He placed extraordinary weight on the develop- 
ment of topology, in which wide and wholly unexplored 
fields lie op^B^, completely beyond the range of our 
present-day calculations • 



-73- 



It accorded with his character, with his investiga- 
tions of pure mathematics and his studies of the natural 
sciences that he carried over to all other situations 
in life his methods of close observation. Wherever pos- 
sible he sought to base his experience on numbers. 
Beyond all else he was concerned to turn a new page for 
the application of mathematics. He therefore kept the 
most varied register of numbers, entered most neatly and 
precisely in small books. For example he had reckoned 
in days the life-spans of important men, including his 
deceased friends. Also he registered the monthly re- 
ceipts of the Hannover Railroad; again the steps from 
the Observatory to those places he was accustomed to 
visit; the dates and the number of thunder-storms in 
different years, and so on. 

In life's manifold situations he saw a broad and 
open field for the application of mathematical theories. 
The answering of questions on national economics, finance 
and statistics gave him rich material for such investiga- 
tions. To mortality tables and the exploring of laws un- 
der which life spins itself away, he attached special 
importance, in part for the purely scientific side, in 
part to study their application to life-insurance annu- 
ities, widows' funds, etc. Gauss' careful investigation 
of our University Widows' Fund I have already described 
in some detail. It is only another example of his thor- 
oughness and exactness applied to specific situations. 

In mortality tables Gauss was especially interested 
in the two extremes of man's life, where a far greater 
uniformity of law is to be seen than in the intervening 
years affected by so many strange and incalculable influ- 
ences. He told us once that he had "started studies of 
his children's developmental stages in their first year 
and a half, and these showed such an amazing uniformity 
that they were scarcely inferior to astronomical observa- 
tions." In like manner he believed that in advanced 



-74- 



I 



age the average life-expectancy followed strict law. 
For answering these questions there were unfortunately 
too few observations, a lack that could be corrected 
by granting rewards to those reaching a proven age of 
90 or 100. If he were rich he would set aside money 
for this, he said. 

State finance, revenue and outlay, bank and rail- 
road management, the ratio between coin and paper money, 
amortizations etc. were all among his special hobbies. 
There was seldom a day when he did not follow the market 
on government bonds , shares and money-exchange in the 
many different newspapers he rapidly perused for amazing- 
ly quick comparison. All paper money he considered a 
menace to the State, since in times of need governments 
could easily be led .into overestimating their strength. 
He felt the nation could be congratulated on having thus 
far avoided it. He was a resolute enemy of small 
financial operations which burdened the people without 
appreciable results. He labelled these penny-wise and 
ascribed to their authors little sense or judgment. 

Without question Gauss would have made an outstand-zr 
ing minister of Finance, operating with consistent skill, 
prudence and integrity. We must indeed thank Providence 
that these gifts did not become known to a wider circle, 
for innumerable demands would without doubt have kept 
him from his purely scientific occupations. Thus, 
preeminently occupied with mathematics though he was, 
wishing to be known only as a mathematician, he was far 
from having mind and inclination for this science alone. 
Indeed all that moves the mind and heart of man stirred 
his sympathy and kept him pondering. 

After mathematics is to be noted first his talent for 
widely different languages. With the classic languages 
he was familiar from his youth on, and most of the modern 



-75- 



] 



languages of Europe he could read. The more important 
ones he spoke and wrote with complete correctness. His 
mother tongue he used with a freedom, a force, dignity 
and precision suiting the subject. In his advanced age 
(his 62nd year) he decided that in addition to his regu- 
lar studies in mathematics he must find a new means of 
keeping his mind alert and active and receptive to new 
impressions. He gave passing consideration to botany, 
but since this would involve considerable physical strain 
he turned tentatively to Sanskrit. This too did not sat- 
isfy him. So he took up Russian with such zeal that in 
two years he had mastered it to the point of reading 
easily all books of prose or poetry and at times carry- 
ing on his correspondence with St. Petersburg in 
Russian. When visited one day by a Russian state coun- 
cillor he conversed with the latter in Russian and with a 
wholly Russian accent, reported the official. 

Gauss valued languages in general according to their 
logical exactness and richness of the concepts which they 
were able to convey. Often he lamented their inadequacies, 
particularly when it was a matter of precise description 
of strictly scientific phenomena. At such times — though 
cautiously and only when strictly necessary — he tried to 
introduce for new concepts new expressions, which indeed 
soon received general acceptance. 



Almost the only recreation which he allowed himself 
1 as a change from his mathematical studies was extensive 
■^ reading in the most varied fields of human knowledge. 
The fine literature of Germany and England chiefly 

! attracted him. In later years he spoke also with great 
esteem of the Russian. 






Among our German poets he placed Jean Paul definitely 
in the front rank because of his richness of thought, his 
deep kindliness and his inexhaustible humor. The Campan- 
erthal he highly esteemed, though the grounds which Jean 



-76- 



Paul gave for the immortality of the soul he considered 
to be of but a negative nature. He often deplored the 
blind alley to which the poet had brought himself by his 
belief in animal magnetism, and through which the fine 
effect of what went before was sadly weakened. Dr. 
Katzenberqer ' s Badereise he pronounced a successful book 
and he always laughed over the struggle of the doctor and 
the apothecary for the 8-legged hare and over the art of 
making the ducats look like gold with ear-wax. Gauss and 
Jean Paul had a mutual respect for each other, but never 
met. 

The great mathematician could not enter so readily 
into Goethe's writing and thinking. Though he undoubted- 
ly knew the poet's works well he was only incompletely 
satisfied with them. For him they were poor in thought, 
Goethe's lyrical poems he appreciated and valued for their 
finished form, yet he did not rate them highly. Still 
less did Schiller mean to him, - his own philosophy com- 
pletely at odds with Schiller's. Schiller's Resignation 
he called blasphemous and morally decadent. In the mar- 
gin of his copy he had carefully printed the word 
"Mephistopheles ! " with an exclamation point. Among the ':: 
dramas he valued Wallenstein ' s Lager . The Piccolomini 
and Wallenstein ' s Death left him completely cold; the hero 
excited no interest in him, a view others indeed have 
shared. Schiller's little poem Archimedes he inscribed 
"admired", though criticizing the unfortunate handling 
of the couplets. 

Gauss did not enjoy tragedy. Misanthropic, life- 
weary, pessimistic tendencies were all uncongenial to * 
him, tendencies resounding too often in Byron and 
through him entering German literature. The young 
Englishman's type of mind seemed to him unwholesome and 
decadent, quite alien to his own. 



-77- 



I seldom heard him speak of Shakespeare, but he was 
a warm admirer of Sir Walter Scott and knew his works 
thoroughly. Yet the tragedy of Kenil worth made so pain- 
ful an impression on him he would rather not have read 
it. Scott's Life of Napoleon , a work on which opinion 
is divided, he read with close attention, commenting 
that he was satisfied and agreed with the author. One 
day he noticed in Scott a passage which greatly amused 
him and set him to comparing all editions which were at 
hand. The words were: "The moon rises broad in the 
northwest," a shocking sentence to an astronomer. He 
laughed heartily and marked the spot. 

The English historians he read also with attention. 
Some years before his death he read with interest 
Gibbon's Decline and Fall of the Roman Empire and 
Macaulay's History of England . He took a deep interest 
in the political development of nations and particularly 
in that of our Fatherland. This interest showed itself 
in his daily visits to our Library to peruse the news- 
papers of different countries, from the English Times to 
the German Wochenblatt . 

His political views often differed considerably from 
oiors, but one could never deny their character and con- 
sistency. By nature an aristocrat Gauss was thoroughly a 
conservative and would have preferred above every other an 
absolute rule, but one directed by a higher intelligence. 
The rule of the rabble with its deeds of violence, and 
especially the Bloody Blouses of Paris in 1848, filled' him 
with unspeakable horror. He had but a low opinion of the 
intelligence and morals of the masses and often gave ex- 
pression to it in connection with political, religious 
and scientific matters. "Mundus vult decipi" (the world 
wants to be deceived) he would say. He followed agitarr 
tors and insurgents with the mistrustful eye of a falcon. 



-78- 



He had slight regard for our constitutional form of 
government and was constantly at pains to point out the 
faulty reasoning or the ignorance of our parliamentary 
leaders, and often all too successfully. In his old age 
he wanted quiet and peace for his country, and the thought 
of seeing civil war break out in Germany was like the 
thought of laying himself down forthwith in his grave. 

Our readers would form a false picture of Gauss if 
they thought him capable of clinging obstinately to the 
old and traditional merely because it was traditional. 
When it concerned progress that could be demonstrated, 
whether in material or spiritual things, he was as 
eagerly alert and ready for change as were any of his 
contemporaries. Yet in his home surroundings he liked 
no innovations. For more than thirty years everything 
remained practically unchanged. He clung to the sim- 
plicity he had known in his youth; many of the 
conveniences of modern life were unknown to him; indeed 
he seemed to scorn them as hindrances to his aims. 

The independence he wanted in his own household he 
wanted also for the State. Foreign domination of his 
Fatherland was abhorrent to him. Just recently he 
called attention to the words of a new writer which he 
said he completely endorsed: even if the political 
conditions following the Peace of Paris had become 
still more deplorable than they already were, our first 
need was to resist foreign domination. Our political 
trend, our lack of vision distressed him, and one day, 
more than a year before the great catastrophe, standing 
with me on the terrace of the Observatory, he gave 
vigorous expression to this feeling: - A firmly unified 
Germany was what was essential. To this end he would 
willingly have entrusted our fate to the strong hand of 
one ruler; he had no mind for a weak reed bending 
before every breath of wind, nor for a ship driven 
hither and thither without a helmsman. 



-79- 



Gauss was a man of iron character who respected only 
strong characters. All unsteady, irresolute tendencies, 
all half -men (of whom there were many) were odious to him. 
His own unswerving life-purpose was embodied in his large 
scientific aims and constant striving to lead the exact 
sciences of the 19th century to new heights, new consum- 
mations. This aim of paramount importance he pursued 
with indescribable energy, inspired with a strength of 
will and a capacity for work seldom equalled. In a 
comparatively short time he could accomplish Herculean 
tasks. The combination of these special gifts with his 
great genius and almost perfect health — up to his last 
years — brought forth those great discoveries which we 
revere today and which posterity will ever hold in 
grateful honor. 

Gauss was a born academician with an innate compre- 
hension of science. To exchange thoughts with spiritually 
congenial souls was his greatest delight, a joy denied 
him in his youth when he is said to have had almost no 
associates with whom he could discuss his deep arithme- 
tical investigations. Applied science was for him of 
secondary importance, though he did not underrate it. 
Likewise all routine teaching at the University was un- 
congenial to him. How often have we heard him lament 
the fact that this prevented him from executing many an 
important task he would gladly have undertaken! Once he 
had set himself to lecture to a small group, however, he 
revealed himself in full stature, - his presentation 
clear, original, in high degree stimulating. In the 
course of time he thus prepared a widening circle of 
younger men, partly orally, partly by his writings, who 
have striven to carry on in the direction he pointed 
out. 

For us Gauss was the lofty image of a completely 
true nature, both intellectually and emotionally. All 
pretense was repugnant to him. All charlatanism (espe- 
cially scientific) he treated with sovereign contempt or 



-80- 



sharp irony • "That man is most contemptible who sees his 
mistakes and still clings to them" he once said to me. 
This thirst for truth, joined with a holy urge toward 
righteousness, were his preeminent characteristics. Both 
passions were rooted in the depths of his being, coincidinc 
closely with his philosophic and religious views and 
unquestionably further developed by his lofty studies of 
nature. The principle of the least force was in fact the 
embodiment in mathematics of the ethical principle which 
he recognized as binding for the Universe. 

All philosophical investigations had a great fascin- 
ation for him, though he often took exception to the 
course followed in reaching them. He once said: "There 
are questions calling for answers on which I would place 
an infinitely higher value than on mathematical questions. 
For example :i ethics, our relation to God, our destiny, 
our future. But their solution lies beyond our reach, 
and quite outside the realm of science." 

Under science he understood that logical, strictly 
unique structure of which the foundations rest on certain 
truths universally recognized by the human mind. This 
once admitted provides an immeasurably wide field for the 
most complicated investigations strung together on an 
iron chain of thought. He therefore, as already noted, 
gave to mathematics the topmost place, and when it came 
to questions which could not be scientifically resolved 
he used to say "God arithmetizes , " thus acknowledging 
those fields into which our minds are not permitted to 
penetrate. 

Nevertheless Gauss himself never ceased turning over 
such questions in his own mind and was constantly at 
pains to bring his scientific experience into harmony with 
his world philosophy. Yet he held all philosophic concepts 



-81- 



to be subjective and alien to science insofar as they 
lacked scientific proof. We attribute to this the fact 
that he never wrote on philosophic questions and only 
seldom spoke of them. 

It is therefore easy to understand that Gauss did 
not favor the application of mathematics to psychology, 
as attempted by Herbart and some other philosophers. On 
this subject he expressed himself only this last year as 
follows: "In earlier years I thought I would have to 
teach mathematics and with this in view I prepared a 
paper which I ran across some years back but which per- 
haps no longer exists. In this I had set down my 
thoughts on the foundations of mathematics and in one 
place I said this: "Extensive magnitudes I understand as 
those which by reason of homogeneous parts can be put 
together; these form the material of mathematics. Inten- 
sive magnitudes can be included only so far as they can 
be made extensive and a scale provided by which they can 
be measured and compared. It would be to the credit of a 
metaphysician to state the starting-points for a tolerably 
exact investigation. And crude though the first results 
proved to be, one could still hope to get further in time." 

A vast and lofty cosmic outlook penetrated Gauss' 
inmost being. And inseparably bound up with it was that 
exalted religious conviction which illumined his great 
spirit with a holy sense of calm, confidence and peace. 

It was natural for him to scatter before him like 
leaves in the wind isolated thoughts on forever unsolved 
questions, thoughts that moved him deeply. Yet before 
there could be further development of them, they were 
blown away as quickly as they had come. A humorous turn 
or a sudden shift of the conversation to ordinary affairs 
left them behind in a veil of mystery. One day he said 
to me: "It is all the same to me if Saturn has five or 



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seven moons. There is something higher in the world." 
Then he was silent and we sat for several minutes facing 
each other without speaking. The light in his eyes 
revealed the flood of thought surging over him. 

Our readers will doubtless wish — and expect — to 
have a closer description of the religious life and re- 
ligious views of this immortal scientist. Through the 
long and friendly association which by great good fortune 
was my lot there was no lack of opportunity to get many 
deep glimpses into this side of his life, a side usually 
concealed by his scientific investigations. But however 
I might wish to attempt a true presentation according to 
my best knowledge and convictions of the astronomer's 
religious views, I would inevitably be charged with hav- 
ing confused my own with his. I could too easily be 
misunderstood. Moreover I doubt if it would be in accord 
with the spirit of the departed so soon after he has left 
the scene of his activities immediately to spread out for 
thousands what all his life he kept in the stillness of 
his own heart or shared in intimate talk with only a very 
close circle. 

Nevertheless I venture to express the hope that for 
the distant future when we here are gone Gauss' lofty 
religious outlook will not be lost, for we know that notes 
in his own hand have been found. These may well prove to 
be the best means of refuting incorrect assumptions on 
this subject. 

Without going further into the particulars of Gauss* 
religious attitudes I would like to touch on those aspects 
which are apart from all questions of faith and which more 
clearly depict the character of the man. First I cite the 
religious tolerance which he extended to every faith 
sprung from man's heart and which should not be mis- 
construed as religious indifference. On the contrary Gaus: 
took the deepest interest in the religious evolution of ma. 



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and particularly in that of our century. As for the 
manifold varieties of religious faith with which his own 
views frequently differed, he ever stressed the fact that 
no man was justified in disturbing in any way the faith 
of others who found in it comfort in earthly afflictions 
and a certain refuge in time of trouble. But this same 
tolerance which he readily accorded to every religious 
creed he also claimed in full measure for himself. I 
suspect that anyone who made so bold as to dispute his 
religious views would have met with very lively 
opposition* 

The foundation for Gauss' religious convictions 
was his insatiable thirst for Truth and his sense of 
righteousness extending to matters both material and 
spiritual. These two complementary tendencies clearly 
revealed his true character and were revealed conspicu- 
ously many times over in even the smallest situations. 
Each and everything he did must be done with utmost 
exactness, utmost conscientiousness. In dealing with 
observations for example he strove to wrest from them 
all they had to give. When carrying out a scientific 
calculation, however large or small, he gave it all the 
exactness the means at hand permitted. In money trans- 
actions with anyone he was accurate to the splitting of 
a penny. He was the basic type of an upright man: 
strictly to fulfil his obligations was for him a funda- 
mental principle. But from others he also demanded the 
same uprightness he practised himself. Anyone who might 
have ventured to deceive him in even small matters or to 
deviate from strict honesty in dealings with him would 
assuredly have forfeited once and for all his respect 
and confidence. He was on guard however not to let him- 
self be deceived, presumably taught by experience; his 
penetrating knowledge of men enabled him quickly to 
separate the wheat from the chaff. 



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To repeat, the search for Truth and the feeling for 
righteousness were the basis of his religious views. Thus 
he conceived of spiritual life throughout the Universe as 
a state of Righteousness penetrated by eternal Truth. 
From this he drew the trust, the confidence that our life- 
course is not ended by death. 

"There is for the soul a satisfaction of a higher 
kind," he said once, "for which the material is wholly 
unnecessary. Whether I apply mathematics to a couple of 
lumps of dirt which we call planets, or to problems of 
pure mathematics, makes no difference. Only for me the 
latter holds a higher charm." 

These words reveal his thoughts on the final destiny 
of man's soul and the deep religious conviction which was 
tied so closely to his outlook on science. Science was 
for him the instrument for revving the immortal source 
of the human spirit. In the years of his full powers as 
also in later years when he saw life's limits drawing 
closer and the goal of existence almost within reach, its 
wide vistas gave him comfort and confidence. 

Gauss' character was an odd mixture of virile force, 
of lofty self-confidence and of quiet childlike modesty. 
He was well aware on the one hand of the mighty forces he 
could set in motion with his intellectual levers; and in 
truth we have never seen a man with a more striking pre- 
sence. While others appeared as of our own kind he stood 
among us like a superman. Yet on the other hand he was 
the plain, simple man, deeply humble before that all- 
penetrating Intelligence re-echoing from one sun-system 
to another throughout the Universe. 



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If ambitious plans had entered Gauss' life his genius 
and intellectual powers would have made them easy of 
attainment. But all the honors paid him had to be carried 
to him; never did he reach out a hand for them. In youth 
and in old age, up to the end he remained the same simple 
scholar. A small study, a small work-table with green 
cover, a high desk painted white, a narrow sofa and after 
his 70th year an arm-chair, a single dim light, a bedroom 
that could not be heated, simple food, a dressing-gown 
and velvet cap, these were apparently all his needs. 

In such wholly unadorned surroundings his powerful 
spirit worked on, charming forth from their divine source 
new inventions, new concepts, ever moving toward that 
consummation which he sought here and has now found there. 

His unwavering conviction of personal life after 
death, his firm faith in an ultimate Order, in an eternal, 
just, all-wise, all-powerful God were the basis of his 
religious life, merging with his scientific achievements 
into full harmony. He said one day: "There is in this 
world a joy of the mind which finds its satisfaction in 
science, and a joy of the heart which expresses itself 
chiefly in men's efforts to lighten one another's cares 
and burdens. But if it is the plan of the Supreme Being 
to create beings on separate planets and for their enjoy- 
ment to grant them but eighty or ninety years of existence, 
it would truly be a cruel plan." ("A pitiable solution 
of the problem", he called it another time.) "Whether 
the soul lives eighty years or eighty million years, if 
it must someday perish then is this life-span a mere 
respite from the gallows. Eventually it would count for 
nothing. 

"One is therefore forced to the conclusion, for 
which without any strictly scientific proof so much else 



-ftf.- 



speaks, that in addition to this material world there 
exists still another, a second purely spiritual world- 
order, as diversified as this in which we live. And in 
this we are meant to share." 

This divine conviction was food and drink to his 
spirit till that quiet midnight when his eyes were for- 
ever closed. The time has now come when he belongs to 
the world of the Spirit, that world of which the aged 
Bolyai said in a letter, having compared this life on 
earth to a mining operation: "On and up go the precious 
mine-lights, leading the soul thirsting for Truth and 
Love from the ever widening endless level of mystery on 
to its source; from the Ocean of Tears from which we can 
remove but a few drops, on to that shore where no more 
fall." 

This was Gauss whom we have been privileged to call 
ours. His spirit is gone hence. Like a comet leaving 
a trail of sparks behind he streaked through the twi- 
light of this earth-life. He is gone and we will see 
no other like him. 

Only love and profoundest reverence have enabled me 
to write these pages. I would consider myself more than 
repaid if in any degree they could meet the wishes of hii 
who is gone. As a devout tribute to the departed I plac« 
this Memorial on that green mound on the very day when 
seventy-nine years ago the great man first looked on the 
light of this world. *' 



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