Humboldt, in writing to Schumacher about Jacobi on July 3, 1844, made the following statement: “He is serene and miles gloriosus, recognizing in the triumvirate only two besides himself, Gauss and Cauchy—tout le reste lui parait de la vermine. I don’t like these exclusions.”
When Hansteen sent Abel’s memoir on elliptic transcendentals to Schumacher with a request that he print them in his journal as soon as possible, he told Schumacher that when he handed Abel the last number of the Astronomische Nachrichten, the latter became pale and had to run to a bar and take some strong liquor to overcome his excitment. Abel felt that his method, which he had discovered several years previously, was general and more comprehensive than Jacobi’s theorems. Abel feared that Jacobi would publish before he did. In recounting this incident by letter to Gauss on June 6, 1828, Schumacher added: “When you publish your researches it will probably cost him even more liquor.”
One of the most peculiar attacks ever made on Gauss, indeed the most bitter among the few attacks, was made by Eugen Dühring (1833–1921). It is an interesting curiosum showing how far a brilliant, but pathologically deranged, mind can go, and should be preserved in the archives of science. Dühring had written a splendid essay on the principles of mechanics96 and won a coveted prize. He worshiped Robert Mayer and bitterly attacked anyone who he thought had in any way wronged Mayer. His principal target was Helmholtz, whom he used to call “Helmklotz.” Dühring made a study of personalities ranging from Archimedes to Lagrange. He was strongly anti-Semitic. The offenses against Mayer of most of those he attacked are obscure. In later years he published a magazine which he called the Personalist and Emancipator, a semi-monthly against “corrupt” science. In his eyes Abel was a plagiarizer. When Justus von Liebig and Clausius defended Gauss and Riemann, he launched out at them too. Dühring used sharp words against Cauchy.
Dühring wrote that university advertising had lifted Gauss up to heaven and stamped him a god. He accused Gauss of being religiously narrow, of having accomplished nothing worth while in mathematics, and of being too proud of his title Hofrat. Dühring scoffed at the peasant origin of Gauss, as well as his support by the Duke of Brunswick. He wrote that Gauss represented no type in the sense of the eighteenth century. Dühring liked to think of himself as an iconoclast in the temple of science; in reality, he was an arsonist, for he went beyond the mere besmirching of many great names. In the field of non-Euclidean geometry he really let himself go, for we read in the chapter on Gauss and “Gauss worship”:
His megalomania rendered it impossible for him to take exception to any tricks that the deficient parts of his own brain played on him, particularly in the realm of geometry. Thus he arrived at a pretentiously mystical denial of Euclid’s axioms and theorems, and proceeded to set up the foundations of an apocalyptic geometry not only of nonsense but of absolute stupidity. . . . They are abortive products of the deranged mind of a mathematical professor, whose mania for greatness proclaims them as new and superhuman truths! The mathematical delusions and deranged ideas in question are the fruits of a veritable paranoia geometrica.
It is astounding how history has turned the tables on Dühring and now applies the term “paranoia” to his distorted aberrations.
In June, 1844, Gauss received a letter from Humboldt recommending highly a most brilliant young mathematician, Ferdinand Gotthold Maximilian Eisenstein (1823–1852), the last survivor of six children of a Jewish mercantile family in Berlin. During the vacation in 1844 he visited Gauss, who was literally carried away by the genius of young Eisenstein. Humboldt had given him a hundred thalers for the trip. Eisenstein’s papers began to appear in 1843 and came out rapidly; in a short lifetime he published fifty papers, principally in the theory of numbers and elliptic functions. He worshiped Gauss and Gauss looked on him almost as a son; he was his favorite mathematician. Eisenstein was never very healthy and was hypochondriac. He longed for companionship and did not get along too well with his family, Dirichlet, Jacobi, Stern, Gauss, Encke, and others tried to cheer him up. The University of Breslau conferred the doctorate on him in 1845. Gauss wrote the foreword to his Mathematische Abhandlungen (1847). In rapid succession he became a member of the Académies of Sciences in Breslau and Berlin, and of the Royal Society in Göttingen. His advancement was due largely to Humboldt and Gauss. Eisenstein was also talented in music. It is tempting to speculate what he would have accomplished had he attained an advanced age. Gauss deeply mourned his early death. Moritz Cantor quotes Gauss as having said there had been only three epoch-making mathematicians in all history: Archimedes, Newton, and Eisenstein. History has reversed the decision and given Gauss himself the place he gave Eisenstein.
Eisenstein, according to his own account, merely visited the so-called “democratic clubs” several times, but did not join them during the Revolution of 1848. He was only mildly involved, but the conservative Gauss was greatly concerned when he heard about Eisenstein’s activity, and wrote thus to Encke on August 11, 1849:
From Mr. Dirichlet I believe I must conclude that our young friend, to whom I ask you kindly to give the enclosure, was exposed to the crudest insults on the unhappy night of March 18–19 (1848). I almost suppose that this is a misunderstanding (namely a misunderstanding of Dirichlet’s story on my part). For that Eisenstein would have stood on the barricades is quite impossible, and if by an unhappy accident he had landed among the rioters, been captured, beaten with a club, and led off to Spandau, then certainly the democratic newspaper reporters would have made the most of something which fitted into their trash (even if it was the consequence of an unhappy error). In my enclosure I didn’t want to mention the matter to Eisenstein himself.
On July 16, 1849, occurred the greatest outward triumph97 of Gauss’ life—the celebration of his golden jubilee. It was exactly fifty years since he had attained his doctorate at the University of Helmstedt and offered in his dissertation the first rigorous proof of the fundamental theorem of algebra. Gauss was deeply moved on his day of reminiscence, honor, and retrospection. A large circle of friends, admirers, and grateful pupils had gathered around him to do him honor. Among those present were Jacobi, Dirichlet, Gerling, the astronomer Hansen, and Professor W. H. Miller, the mineralogist and crystallographer from Cambridge University. He received renewal of diplomas, medals, orders, congratulatory documents, and—what he prized most highly— honorary citizenship from the cities of Brunswick and Göttingen.
The Aula was decorated with flowers for a session of the Royal Society of Sciences. Gauss delivered a lecture on “Contributions to the Theory of Algebraic Equations,” returning to a subject he had embraced in his dissertation and treating it from a more general viewpoint.
At a banquet in his honor he spoke of the ever active, serious scientific effort which had always blessed the university, and stressed the thought: “Trivial words have never rated in Göttingen.” Then he gratefully emphasized the benevolence of the university’s Board of Curators, under whose discerning direction the representatives of science, protected against the adversities of life, had been almost undisturbed in their research and therefore in the enjoyment of such peace frequently attained a noteworthy old age.
An interesting sidelight on the jubilee occurred when Gauss was about to light his pipe with a piece of the manuscript of his Disquisitiones arithmeticae. Dirichlet was horrified at what seemed to him sacrilege, rescued the paper from Gauss’ hands, and treasured it for the rest of his life. The editors of Dirichlet’s works found the manuscript among his papers.
Jacobi wrote a letter to his brother on September 21, 1849, in which he gave a glimpse of the banquet at the jubilee:
You probably know that I was with Dirichlet at Gauss’ jubilee. I had the seat of honor there beside him and delivered a great speech. You know in 20 years he has quoted neither me nor Dirichlet; this time however after several glasses of sweet wine he was so carried away that be said to Dirichlet, who boasted to him of having studied his writings more than any
one else, that he had not merely studied, he had gone far beyond them. It is no longer easy to enter a scientific conversation with Gauss; he seeks to avoid it, while he discusses the most uninteresting things in a continuous stream. Except for Hansen and Gerling of Marburg nobody was there; our journey was therefore important in order to support to some extent a manifestation in honor of mathematics.
Therese Gauss wrote to her brother Eugene in St. Charles, Missouri, on December 5, 1850, and gave in her letter some interesting details of the jubilee:
A year and half ago in July ’49, he [Gauss] celebrated his fiftieth anniversary jubilee of the doctorate—or rather the university and the city celebrated it for him with general love and sympathy. He himself was very much opposed to having this day noticed, but, without his knowledge, everything had been prepared for it. From near and far the university had invited strangers; father’s friends and eminent scholars came, many delegations from other cities, who brought him congratulations, honorary doctor’s diplomas, and three new orders. From Brunswick and Göttingen he received honorary citizenship; from the King, congratulations in his own handwriting and a higher order. There was no end of letters and communications. In the morning festive processions began to congratulate him, all the authorities of the city, of the university, of the public school, strangers, acquaintances—probably about fifty persons. Then father himself delivered a lecture in the Aula of the university, which was overcrowded with spectators and listeners and had been decorated with garlands and flowers like a fairy hall. Even the houses in the streets were decorated with flowers; in the city there were waves of people in festive attire, as on a holiday. When, at last, in the evening at seven, father came home from the great banquet, he was indeed quite exhausted, and it was well that the torchlight procession that the students had intended for him was abandoned upon his wish, but the love and sympathy which had been shown him from all sides had, in spite of all fatigue, pleased him indescribably. How sad it was though, that where so many strangers had congregated on his day of honor, not one of his beloved sons could be with him!! Even Joseph had been compelled to decline, as his position as railway director did not then make his absence from Hanover possible.
Since the University of Helmstedt, which had conferred the doctorate on Gauss, no longer existed in 1849, it was the University of Göttingen which renewed the diploma for the jubilee. On March 23, 1849, the University of Kasan had conferred an honorary doctorate on him, probably at the instigation of Lobachevsky, who felt grateful that Gauss had gotten him into the Royal Society of Göttingen. Of all the honors received, Gauss appreciated most the honorary citizenship conferred by Brunswick and Göttingen. The latter document is dated July 14, 1849. The city council of Brunswick had been reminded of the approaching jubilee by Friedrich Wilhelm Schneidewin (1810–1856), who was professor of classical philology in Göttingen from 1836 to 1856. He was a native of Helmstedt and had served as a high school teacher in Brunswick from 1833 to 1836. The text of the letter of honorary citizenship of Brunswick, dated July 8, 1849, is preserved, although the document itself is apparently lost. At the ceremony it was Schneidewin who handed Gauss the document. His letter of thanks to the city council and officials of Brunswick was dated August 5, 1849. It required several weeks for Gauss to thank in writing all those who had honored him at the jubilee. Duke Wilhelm of Brunswick had conferred on him the Commander’s Cross of the Order of Henry the Lion. His letter of thanks to the Duke, dated August 2, was full of deep emotion and special gratitude, for in it he reviewed his early life and referred to the aid he had received from the Duke’s ancestor.
Another honor which pleased Gauss immensely at the time of the jubilee was the congratulatory letter from his Alma Mater, the Collegium Carolinum, forerunner of today’s Institute of Technology. Humboldt had written him a hearty letter of congratulation on July 12, regretting his inability to be present. Schumacher was also unable to attend.
On August 20, 1849, Gauss wrote to his old friend Wilhelm Arnold Eschenburg (1778–1861), a government official in Detmold, a touching letter of thanks for his congratulations, in which the following passages occur:
Through your letter of greeting at my doctoral jubilee, dear Eschenburg, you have caused me a very great joy. While most of the other letters received on this occasion had their last roots more or less in some scientific relationship or other, your letter is intended not for the astronomer or geometer, but for the unforgettable boyhood friend. Reminiscences of boyhood and youth vividly came before me. From the first time when I became acquainted with you as a fellow pupil (October, 1789), I felt attracted to you. There are renewed in me the images of our boyhood games, when we, the worthy Drude98 in our midst, shouting with joy went to the Wends’ tower99 or the grunen Jäger.100 There is renewed in me the image of your deceased father101 in later years, who always appeared to me as a model of the καλòς κἀγαθóς, and his family like a temple of purest earthly happiness under special protection of a kind guardian angel.
I always imagine your own home, too, in similar glory, according to all that I have found out about your wife and children from your letters and otherwise. There has lingered with me a very pleasant impression of your son,102 who once visited me here several years ago, and who supposedly is the same one whom you mention as an officer of justice attached to a regiment of Lippe troops. I heartily wish you happiness on your retirement [1848]. Public conditions are so unpleasant everywhere in Germany that nobody who is involved in them is to be envied. Even in Lippe Detmold—which 1 had always thought of as a patriarchal little land, in which genuine purity of morals sits on the throne, so that I had once even thought of moving there for my last days—a part of the Pandora’s box seems to have been shaken out of the so-called March achievements. May the storms in Germany soon wear themselves out and may you enjoy a peaceful happiness to an advanced age.
The plan of moving to Lippe-Detmold was evidently conceived by Gauss in 1837 or 1838, at the time of disturbance over the Göttingen Seven.
XXI
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Gathering Up the Threads: A Broad Horizon
Among his friends in Great Britain Gauss counted the astronomer Airy, Sir David Brewster, Humphrey Lloyd, General Edward Sabine, and the family so well known in the annals of astronomy—William Herschel, his sister Caroline, and his son Sir John Herschel.103 With all these people Gauss corresponded regularly; in 1825 he visited Caroline Herschel at Hanover. Occasionally Sir John Herschel sent him some young Englishman with a letter of introduction. The friendship with Lloyd and Sabine came about through common interest in terrestrial magnetism. Another Englishman who was on intimate terms with Gauss was Thomas Archer Hirst (1830–1892). He took his doctorate at Marburg in 1852 and visited Gauss the same year, presenting to him a copy of his dissertation, Ueber conjugirte Diameter im dreiaxigen Ellipsoid. Gerling of Marburg arranged the visit. Hirst served for many years at the Royal Naval College in Greenwich.
One of the first Americans to visit Göttingen was Benjamin Franklin; at the time he was making plans for the University of Pennsylvania, but this occurred some years before the time of Gauss. Aaron Burr visited Germany in 1809–1810, and spent Christmas Day, 1809, in Göttingen. Through letters of introduction he met Gauss and Arnold Heeren, taking tea with the latter. He was greatly impressed by Gauss, who showed him about the observatory and conversed at length with him. His letter of introduction to Gauss was from E. A. W. Zimmermann, the early patron of the scientist.104
During the second half of his life Gauss had a lively interest in America, for a group of Harvard students began to enroll in Göttingen: J. G. Cogswell, Edward Everett, Ticknor, Bancroft, Longfellow, Motley, and William Emerson, the brother of Ralph Waldo. Of these Harvard men Gauss was on especially intimate terms with Cogswell and Everett. Everett studied in Göttingen from 1815 to 1817; on January 30, 1822, he caused Gauss and Olbers to be elected Fellows of the American Academy of Arts and Sciences in Boston. His letter to Gauss, accompa
nying the diploma, was written in excellent German and dated March 31, 1822. In it he referred to Gauss’ kindness during his student days in Göttingen and reminded him that his scientific work was properly esteemed in America. Everett made mention of Bowditch’s review (1820) of the Theoria motus in a journal he edited. The diploma was signed by John Quincy Adams, John Thornton Kirkland, John Farrar, and Josiah Quincy. On his American tour in 1836 Joseph Gauss visited Edward Everett during his term as governor of Massachusetts.
Joseph Green Cogswell (1786–1871), the well-known librarian and bibliographer, was one of the early American students in Göttingen. He served as librarian of Harvard College, 1820–1823. In 1840 he was highly recommended to Gauss by Humboldt and visited him in Göttingen, seeking advice in spending several hundred thousand dollars for the Astor Library in New York, which he served as bibliographer and superintendent from 1848 to 1861. He acquired from Gauss a copy of the Theoria motus and his manuscript of 321 pages in folio of explanations and commentary upon it. Cogswell also got for the Astor Library a copy of Gauss’ Determinatio attractionis (1818) with a twenty-eight-page autographed quarto manuscript by Gauss of this memoir and a fifty-eight-page quarto manuscript of illustrations and remarks on the memoir. Other items acquired for the library included the 1817 memoir on quadratic residues and a twenty-nine-page quarto autographed manuscript by Gauss, as well as a manuscript of three hundred pages in folio of astronomical calculations illustrating the orbits of Juno, Pallas, Ceres, and Vesta, and one of thirteen pages of formulas.
Rear Admiral Charles Henry Davis, U.S.N, later renowned for his victories in the Civil War, was one of Gauss’ frequent correspondents; he translated and published in 1857 the English edition of his Theoria motus.
Carl Friedrich Gauss, Titan of Science_A Study of His Life and Work Page 32