In 1927 Max Schneidewin, then an old man of eighty-four years, the son of a Göttingen professor of classical philology, at his home in Hamlin gave his reminiscences of Gauss in the Revolution of 1848. In his parents’ home he and his brothers and sisters always heard the name “Gauss” mentioned with a certain amount of awe. During the Revolution, professors who were physically fit were chosen by the state or municipal authorities to patrol and preserve order. As a small boy of six, he was astonished to see his father wearing a light-weight black coat, similar to a uniform, with a large belt. He saw a lance leaning against the bookcase. One day at noon his father related that he had to stand guard with other professors at the Geismar Tor. Suddenly it was announced that Gauss, who lived only five minutes’ walk from the Geismar Tor, was coming. At once the whole guard of professors lined up in order to “present arms.” Schneidewin said that could have happened only for Gauss. After that, the boy always felt a special admiration for Gauss whenever he saw him.
In a letter to Encke, dated December 14, 1848, Gauss expressed himself thus concerning the Revolution:
I read your speech of October 18 with so much more pleasure, since in the sad period from March 18 to December 6 one so rarely got to hear the voice of calm reason from Berlin. In this time I was able to think of your king72 only with a painful feeling. I do not know whether there was ever another prince who in all his steps so sincerely meant well, and in return was always rewarded with such shameful ingratitude. May his newest experiment now be more successful. It made the same impression on me which is reflected between the lines in an utterance attributed to a French diplomat in the newspapers, that this constitution gives more than the need of an enlightened nation demands, and that one will have to admire the Prussian people if they prove able to bear this one.
The direction of Jacobi’s political views had long been known to me from the newspapers; even Steiner and Erman are mentioned in them, sometimes in a similar though not quite so blunt manner, but that even Dirichlet joins this tendency was to me quite unexpected. In Göttingen we are happier to the extent that in the faculty (now) only a very small number who worship such idols can be pointed out.
Gauss had a very low opinion of the intelligence and ethics of “the people”; he frequently expressed this view with reference to political, religious, and scientific matters. He used to say mundus vult decipi and pursued agitators and rabble rousers with the eye of mistrust, with the steadfast gaze of a falcon. He had a low opinion of constitutional systems of government and was unremitting in his efforts to demonstrate either logical errors or lack of expert knowledge on the part of politicians. His friends, although differing with him occasionally, felt that he often succeeded. As an old man he loved above all quiet and peace in the land, and to him the thought of a civil war’s breaking out in Germany was equivalent to thinking of his own death. Yet he did not cling to the traditional merely because it was traditional. If there was some really demonstrable progress involved, whether in the intellectual or the material area, he was just as much in favor of reform as his contemporaries. However, he did not like change in his home, preferring the simplicity to which he was accustomed in his youth.
Gauss’ home was his castle, and he demanded the same independence for the state. He deplored the political behavior of Germany in his day, her lack of harmony, and longed for national unity.73 Like so many Germans, he would gladly have entrusted the fate of his nation to the hand of a strong ruler, and did not wish to adhere to a reed swayed by every passing wind or a ship without a pilot. He was definitely opposed to foreign rule or occupation of one nation by another.
Apparently Gauss attached peculiar significance to the fact that he discovered the division of the circle into seventeen equal parts on the same day that Napoleon left Paris to journey to the Italian army. He used to mention the fact to his friends. Napoleon reached the Italian army at Nice on March 26, 1796. In the Hamburger Correspondent for March 29, 1796, there is a note dated March 17, “General Bonaparte has left here (Paris) for the Italian army.” Of course his actual departure could have occurred one or two days earlier.
On April 20, 1848, Gauss wrote to Bolyai, the intimate friend of his youth:
The violent political and social earthquake, which in ever increasing extent is upsetting almost all European conditions, has not yet touched your fatherland in the narrow sense (I mean Transylvania). Indeed I cherish the confidence that in the end enjoyable fruits will proceed from it; but the transition period will first bring manifold oppressions, and (quod tamen deus avertat) can last a long time. At our age it is always very doubtful whether we shall experience the golden age just ahead.
Through the present devaluation of Austrian bonds, in which the greatest part74 of my 40 years’ savings is invested, I am threatened with being able to leave little or nothing to my children at my death.
A wave of “table rapping” swept over Europe and America at the mid-century. German newspapers were full of it, and Gauss’ friend Rudolf Wagner became interested and published on the subject. This table movement or table turning was supposed to be a form of psychic phenomena. Many believed that spirits from the other world were “rapping for admission to our world.” A group of people would sit around a table with arched hands resting upon it, and wait to see what happened. Gerling became interested and performed many experiments in this “field.” He reported at great length to Gauss about it, and asked his advice. The reply, dated April 21, 1853, is last letter Gauss wrote to Gerling:
I had intended to answer you this afternoon and to explain my own view of the matter. Since this could not occur without some prolixity, I was very glad this morning among so much nonsense which the newspapers offer us on the subject to find an essay in a journal, whereby I am spared that effort. The journal is the one that arrived here this morning, I have forgotten whether it was the Didaskalia or Konversationsblatt, and the essay had two signatures, the first one I have forgotten, the other was Poppe. I would have had to write you exactly the same thing that is in this essay. I have made an experiment on our round, rather massive (perhaps 50 pounds) dining-room table75 with Therese, in order to check how much pressure is necessary for the four hands lying flat (not touching one another) to set the table in rotating motion, of course with a pressure purposely not perpendicular, but acting simultaneously tangentially, and I found to my own amazement, that only a very slight pressure was necessary. Moreover, the three-foot table was on a rug. If I now consider that of that pressure I myself exerted by far the greatest part, then I believe that in the case of the tiny, light weight table described by you that each of the eight hands has such a slight share that after a half hour’s wait the hands become insensitive to it.
I myself shall certainly make no experiment after the manner of Andreas. My patience would not suffice to hold my hands one half hour or longer in an unchanged position on the table top: but if I did it, then I, am certain in advance that my hands, even if they did not get cramped, would get into such a condition, that I would no longer be master of them as in the normal condition, I mean, that I would no longer remain certain whether I was not pressing or whether I was pressing perpendicularly or at an angle. Therefore, in so far as only movements are produced by the experiment, to my mind it proves nothing. It would be different if the objective effects claimed in the newspaper articles, and similar to the galvanic, were corroborated: sparks, decomposition of water, paralysis, or great augmentations of a horseshoe magnet. But all these claims are without a guarantor, and in dubio I would give them the signature Münchhausen.
In almost all experiments I find something of which I must disapprove. As soon as a movement is noted, the people jump up, push back their chairs with their feet and run after the moving table. I would demand most strictly that each one remain seated on his chair. Since by regulation the hands are to lie only very loosely on it, why doesn’t one allow the table to glide away under the hands, without lifting the contact? Tables whose oblong fo
rm do not permit that, should be excluded. If you say that it will then stand still, then this proves that just a not-too-slight pressure is essentially necessary, and this [pressure] in the running after the table will certainly become a pushing after it, even though the people forced by the long martyrdom are not definitely conscious of it. In this connection I was especially amused by the pittoresque description of the Heidelberg experiment, where the whole law faculty, including two young women, ran after the table like mad, so that poor Zöpflein, who, as I hear, is said to be a true Falstaff in figure, finally couldn’t keep up with the others.
Table rapping was alleged to be connected with animal magnetism in some occult manner. The following lines in a letter of May 10, 1853, show that Gauss was unimpressed by all that he heard and read on the subject. The letter is addressed to Humboldt:
I have been able to observe the present-day tomfooleries rather calmly, indeed to laugh heartily about several genre pictures like the experiments of the Heidelberg law faculty with table rapping. I have long been accustomed to have a low opinion of the sterling quality of the higher culture which the so-called upper classes believe they can acquire by reading popular writings or attending popular lectures. I am rather of the opinion that in scientific areas genuine insight can be gotten only by use of a certain measure of one’s own effort and of one’s own processing of that offered by others.
This was a mild criticism of Humboldt, who spent considerable time in delivering popular lectures and publishing popular works. At least. Gauss let him know that he doubted the efficacy of the results.
XIX
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Monarch of Mathematics in Europe
Augustus De Morgan in his Budget of Paradoxes (p. 187) relates the following story. Francis Baily76 wrote a singular book, Account of the Rev. John Flamsteed, the first Astronomer-Royal. It was published by the Admiralty for distribution, and the author drew up the distribution list. Certain rumors led to a run upon the Admiralty for copies. The Lords were in a difficulty; but on looking at the list they saw names, as they thought, which were so obscure that they had a right to assume Mr. Baily had included persons who had no claim to such a compliment as presentation from the Admiralty. The secretary requested Mr. Baily to call upon him.
“Mr. Baily, my Lords are inclined to think that some of the persons in this list are perhaps not of that note which would justify their lordships in presenting this work.”
“To whom does your observation apply, Mr. Secretary?”
“Well, now let us examine the list; let me see; now—now—now—come! Here’s Gauss—who’s Gauss?”
“Gauss, Mr. Secretary, is the oldest mathematician now living, and is generally thought to be the greatest.”
Their lordships ultimately expressed themselves perfectly satisfied with the list.
When Alexander von Humboldt returned in 1804 from his American tour and remained in Paris for a time, he found the name of Gauss mentioned with the greatest respect. Before his tour he had never heard the name. In 1807 he wrote his first letter to Gauss and told him of Laplace’s high esteem for him. No other name in nineteenth-century mathematics has received recognition equal to that of Gauss. His standing in physics and astronomy was perhaps slightly less. Contemporary scholars recognized his unconditional intellectual superiority in his own field. Gauss enjoyed an almost superhuman respect and admiration at the hands of those competent to judge him. There were a half-dozen exceptions to this, persons motivated by purely personal feelings.77
As early as 1813, his friend Olbers while serving as a deputy of Bremen in Paris during the Napoleonic period tried to persuade Gauss to take a trip to Paris, assuring him he would find such a reception as no other scholar had ever received. Laplace is said to have urged Napoleon to spare Göttingen because “the foremost mathematician of his time lives there.” Even Legendre, who strongly disliked Gauss, in the foreword to the second edition of his Théorie des nombres (1808) spoke of Gauss’ Disquisitiones arithmeticae, praised its high value, rich content, and recognized its complete originality. Gauss’ career does not show a gradual rise, as in the case of most scientists; it begins at a high point and continues at that level.
In 1805, when the King of Prussia requested Humboldt to enter the Berlin Academy of Sciences in order to lend it the splendor of his name, acquired on the American tour, Humboldt informed the King that his appearance would not be of importance; the only man who could give the Berlin academy new splendor, he wrote the King, was Carl Friedrich Gauss.
Even Jacobi, who perhaps ranked second to Gauss in mathematical attainments among the contemporaries and who was inclined to be critical of Gauss’ character, admitted his intellectual supremacy. After spending a week with Gauss in 1840, Jacobi wrote his brother, the physicist: “Mathematics would be on an entirely different spot, if practical astronomy had not diverted this colossal genius from his glorious career.”
Was Gauss conscious of his high position in science? Yes, without question and at an early age. His demands of himself, however, were as great as those he made of others. Yet he was modest and never showed this consciousness of greatness unless there was some special stimulus. He never wore the various medals and orders which had been showered on him, except that when the King came to Göttingen he would wear the Guelph Order. As a youth. Gauss is said to have gloomily sensed the fact that he did not have a friend of equal genius with whom he could discuss his scientific problems.
In 1808 an excusable show of pride was manifested by Gauss. Breitkopf and Härtel were printing his Theoria motus corporum coelestium for the publisher Perthes. The printer proposed that the final reading of proof be dropped in order to save time and postage. Gauss boldly wrote to the publisher: “I place such a value on the correctness of this work, which has caused me much work for several years, and if I am not mistaken, will still be studied even after centuries, that I am satisfied if you charge to me the outlays made by Messrs. Breitkopf and Härtel in this respect, if I myself can first check all folios before and afterward.”
This assurance of superiority had the advantage of lifting him above petty polemics. When Schumacher called his attention to the fact that an Italian scientist in a periodical had made a “highly insolent” attack on Gauss’ theory of magnetism, and Schumacher wanted to know whether Gauss thought it desirable that someone else “straighten out the impudent fellow,” Gauss answered that he had already heard of the criticism from another source and added that the deductions of the critic were “dumb stuff,” a judgment which agreed with his own impression gained by reading another essay of the same author in the field of magnetism. Gauss added: “Supposedly that journal is in our library, but I do not consider it worth a library catalogue card, and since you report that it is rudely written, I shall in no case read it.”
Unfortunately the Italian critic did not live long enough to see the publication of this letter. Gauss not only ignored such criticism, but he prevented others from replying in his name, polemic natures were an abomination to him. Justus von Liebig, the great chemist, was once candidate for a professorship in Göttingen. He later told that Gauss and the geologist J. F. L. Hausmann (1782–1859) were against him because he was always involved in some polemic and they did not want to have a cantankerous colleague.
Modesty and self-criticism characterized Gauss’ behavior when he had to dissent from the views of those scientists he had learned to esteem highly. He stated that he distrusted his own views if they touched on a subject he had not studied thoroughly. On the other hand if some mathematical matter was involved for which he had rigorous proof he spoke out openly and freely. It must be added that non-Euclidean geometry was an exception to this behavior. He was timid if subjective opinions were concerned, or if the issue depended on individual estimate of probability.
In purely scientific matters Gauss could be very sharp in private, where he came upon stupidity, arrogance, or pretense. Of a friend he once wrote: “Mr. Benzenberg seems to wri
te his letters as well as his books in his sleep.” The astronomer Franz von Paula Gruithuisen (1774–1852), a professor in Munich,78 frequently aroused the ill will of Gauss, who accused him of “mad chatter” and said that whenever he picked up anything by Gruithuisen he expected to find nonsense. Gruithuisen claimed to have discovered a city and highways on the moon. Actually Gauss was greatly amused at the polemic between Gruithuisen and the philosopher Schelling. After Herbart had given him some of Schelling’s writings, he said: “The two opponents seem to me to be completely worthy of each other.”
On May 14, 1826, Gauss discussed in a letter to Olbers a cause célèbre in the history of astronomy. Encke had accused79 the Chevalier d’Angos (d. 1836), knight of the Maltese Cross, of deception in the matter of a comet he had allegedly discovered in 1784. The astronomical world regarded the case as proved after Encke’s publication. Gauss alone was more cautious and humane. He called d’Angos a “wind bag” and considered the deception very probable, but hesitated to pronounce him guilty until there was proof positive. He told Olbers in the letter: “I take the expression proof here not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of the geometer, where ½ proof = 0, and it is demanded for proof that every doubt becomes impossible.”
Carl Friedrich Gauss, Titan of Science_A Study of His Life and Work Page 29