Felix Klein (1849–1925), professor of mathematics at Göttingen in the generation after Gauss, gave an excellent appreciation of his predecessor:
In him [Gauss] the historical epochs separate; he is the highest manifestation of the past, which he closes, at the same time the foundation of the new, which he penetrates deeply with his last rays more thoroughly and more actively than is perhaps vivid in the consciousness of the time. If I may be permitted to use a figure of speech: Gauss appears to me like the Zugspitze in the over-all picture of our Bavarian mountains, as it appears to the observer from the North. The peaks rising gradually from the east culminate in a gigantic Colossus which steeply descends into the depths of a new formation, into which its spurs reach out for many miles and in which the waters gushing from it generate new life.139
Theodor Mommsen once expressed great admiration for the part played by aged men in furthering science, and added these words:
Our own experience tells us scientists above all, that great scientific accomplishment can be successful only in many years of restlessly continued work. It is perhaps correct that in the case of men like Gauss the great aperçus by which they advanced the knowledge of the world, all appeared in their youthful years; but the seed is only half of scientific activity, and the harvest time is no less indispensable if an important scientist is to fulfill his destiny.
Felix Klein called the years 1798–1807 Gauss’ Heldenzeit (heroic period), that is, the period of crowning productivity. His precision and clearness in thinking as well as the simplicity of presentation remained with him in old age. He devoted his later years more to optics, electricity, magnetism, and geodesy, although he never completely stopped work in astronomy and pure mathematics.
In 1870 during the Franco-Prussian War the Royal Irish Academy at Dublin protested against the siege of Paris on account of the danger to treasures of art and science there and also called on the German universities to participate in this manifesto.
Richard Wilhelm Dove (1833–1907), professor of ecclesiastical law and prorector of the University of Göttingen, rejected this proposal very decidedly. Since Dove had said in his letter that the German people in their intellectual struggle were still trying to make true the proud word of Paracelsus: “Englishmen, Frenchmen, Italians, ihr mir nach, nicht ich euch.” Karl Hillebrand, the well-known historian and cosmopolitan publicist, accused him of “German arrogance.” In 1887 at the sesquicentennial jubilee of the University of Göttingen when Dove printed the above-mentioned letter along with other documents of the university’s history, he attempted to justify himself by means of the following statement:
It is sufficient to call the one name Gauss in order to demonstrate that the victor’s prize by the unanimous decision of educated nations has really been ungrudgingly given to great German scholars.
Frobenius, in his eulogy of Kronecker before the Berlin Academy of Sciences on June 29, 1893, expressed himself thus on the work of Gauss:
The theory of numbers, which in Diophantus and Fermat bore the character of an entertaining exercise in thinking, an intellectual game, after the preliminary work of Euler, Lagrange, and Legendre had been elevated by Gauss to the rank of a science. The prince of mathematicians called it the queen of mathematics, and it deserved this title not only by its high rank, but also by the proud abstractness in which it sat on the throne, far from all other fields of knowledge, far from the other mathematical disciplines. In his theory of circle division the genius of Gauss made algebra tributary to it.140
In writing of the relationship between music and mathematics, J. J. Sylvester, the great British mathematician, predicted the day “. . . when the human intelligence, elevated to its perfect type, shall shine forth glorified in some future Mozart-Dirichlet or Beethoven-Gauss—a union already not indistinctly foreshadowed in the genius and labours of a Helmholtz!”141
Moritz A. Stern, pupil of Gauss and later professor of mathematics at Göttingen, had this to say in an address delivered there on the occasion of his master’s centenary: “As in the case of only few known to history, in Gauss mathematical depth of thought was united with the talent of the observer, with the genius’ practical insight into the invention of new means of observation, and with the most complete skill and endurance in calculation. Like the lion in the fable, Germany at that time could say, I have borne only one, but this one is a lion.”142
When Alexander von Humboldt returned from his American tour in 1804, he wrote the following year to Emperor Friedrich Wilhelm III: “The only man who can give new splendor to the Berlin Academy is named Carl Friedrich Gauss.”
In his vivid manner of expressing himself the Duke of Cambridge once said: “One often criticizes Göttingen, but as long as we have the library and Gauss, we can let them scold.”
Alexander von Humboldt, to whom he made this remark, replied thus: “I agree, but it is my duty to request your royal highness to change the order of rank of the treasures and to name first the foremost mathematician of our age, the great astronomer, the brilliant physicist,”
In 1808 Schumacher wrote Gauss that if he could have the title “pupil of Gauss” he would never demand another title. In 1810 he wrote his master: “I sign myself like Dissen143 always called me: Λίει ò περι τον Γαυσσιον.”
Schumacher’s letters are unusually filled with the most inordinate flattery and admiration of Gauss, much of which was justified and all of which was sincere. Young Eisenstein and Encke adopted a similar attitude.
Kummer, one of the leading mathematicians of the late nineteenth century, has given a clear and exact estimate of Gauss’ achievements:
Among all the major and minor works of Gauss there is none which through new methods and new results did not start essential progress in the field concerned; they are masterpieces which bear in themselves that character of classicity which guarantee that they will be used and studied with diligence, for all times, preserved not merely as monuments of the historical development of science, but also by future generations of mathematicians of all nations, as the basis of every more penetrating study and as a rich source of fertile ideas. With these extraordinary advantages of the Gaussian writings, indeed partly even on account of them, their effect on mathematical studies, namely in Germany, was for a long time extremely slight. In presentation all Gaussian writings have that perfect clearness and precision which in an absolutely penetrating study excludes even the possibility of misunderstandings, but this presentation, just as the methods themselves, is not calculated to facilitate the study of Gaussian writings. This character of his writings was also in full harmony with Gauss’ own character. At his sublime position in science, on which he stood isolated for a rather long time, he possessed so great an autarchy that he scarcely perceived the need of attracting others to him and educating them.144
Thirty years later G. Hauck paid tribute to some of Gauss’ practical work: “Gauss did not disdain to work practically with the theodolite and then on the basis of this work created practical methods of precision which have become the common property of all the civilized world and with which he has presented to humanity one of its most valuable gifts. Thus geodesy has become a model for the rational, applied activity of a theoretical science. Every surveyor is anointed with a drop of Gaussian oil.”145
In his article on Gauss in the Allgemeine Deutsche Biographic, Moritz Cantor stated that the Disquisitiones arithmeticae should be called the Magna Charta of the theory of numbers.
Highest praise of Gauss came from a French source: ‘For loftiness of character, as for the power of genius, he was the greatest of all.”146
In closing this chapter it is pertinent to quote a remark made in 1950 by Albert Einstein, than whom no one is better qualified to evaluate the work of Gauss:
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 t
he system of absolute measurement in the field of electromagnetism. In my opinion it is impossible to achieve a coherent objective picture of the world on the basis of concepts which are taken more or less from inner psychological experience.147
On another occasion Einstein had this to say of Gauss:
The best that Gauss has given us was likewise an exclusive production. If he had not created his geometry of surfaces, which served Riemann as a basis, it is scarcely conceivable that anyone else would have discovered it. I do not hesitate to confess that to a certain extent a similar pleasure may be found by absorbing ourselves in questions of pure geometry.
Appendix B — Honors, Diplomas, and Appointments of Gauss
1. Matriculation papers. University of Göttingen, October 15, 1795.
2. Doctor’s diploma. University of Helmstedt, July 16, 1799.
3. Full member, club in the Hotel d’Angleterre, Brunswick, August 5, 1802.
4. Corresponding member. Imperial Academy of Sciences in St. Petersburg, January 31, 1802.
5. Royal Society of Sciences in Göttingen, “amicus et familiaris litterarum commerciis conjunctus,” November 13, 1802.
6. Institut National, class of mathematical and physical sciences, corresponding member of the section for geometry, Paris, January 24–30, 1804. Signed by Carnot, President, and Delambre, Secretary.
7. Fellow, Royal Society of London, April 12, 1804.
8. Call to University of Göttingen, July 25, 1807. Signed at Hanover by Brandes.
9. Corresponding member. Royal Academy of Sciences in Munich, April 6, 1808.
10. The mathematical class of the Royal Academy of Sciences in Berlin unanimously named Gauss a full member and called him there; the entire academy approved this election on April 18, 1810, and the King of Prussia added his approval.
11. Foreign member, Italian Society of Sciences, Verona, May 4, 1810. Signed by Octavius Cagnoli, Secretary.
12. Knight of the Order of the Westphalian Crown (Jérôme Napoléon), Göttingen, August 19, 1810. Signed by Minister of State Count von Fürstenstein.
13. Lalande Prize; French Academy, 1810.
14. Knight Commander’s Cross, first class, of the Guelph Order. Notification signed by Count Münster at Hanover, December 28, 1815.
15. Letters patent conferring the title of Royal Hofrath, signed by King George III at Carlton House, November 29, 1816.
16. Full member. Society for the Advancement of All Natural Sciences in Marburg, March 26, 1817.
17. Knight’s Cross, Dannebrog Order, April, 1817; Commander’s Cross, June 28, 1840.
18. Foreign Member, Royal Bourbon Society, Academy of Sciences, Naples, September 4, 1818. Notification signed by Teodoro Monticelli. (Note by Gauss: Monticelli died at Naples, October 7, 1845.)
19. Honorary member. Society for the Propagation of Mathematical Sciences, Hamburg, October 17, 1818.
20. Honorary Member, Courland Society for Literature and Art, Mitan, June 1, 1819.
21. Foreign Member, Royal Society of Edinburgh, June 5, 1820.
22. Full foreign member. Royal Bavarian Academy of Sciences, October 23, 1820.
23. Foreign Associate, Institut de France, Royal Academy of Sciences, Paris, September 4, 1820.
24. Director of Geodetic Survey, Kingdom of Hanover, 1821.
25. Member, Royal Danish Society of Sciences, May 1, 1821. Notification signed at Copenhagen by Oersted, Secretary.
26. Foreign Member, Royal Swedish Academy of Sciences at Stockholm, June 5, 1821.Notification signed by Berzelius. Secretary. Diploma dated June 26, 1821.
27. Fellow of the American Academy of Arts and Sciences, Boston, Massachusetts, January 30, 1822. Notification signed by John Quincy Adams, President; John Thornton Kirkland, Vice-President; John Farrar and Josiah Quincy, Secretaries.
28. Prize, Copenhagen Society of Sciences, for memoir on conformal projection, 1822.
29. Raise in salary to 2,500 thalers. Board of Curators, University of Göttingen. Signed by Curator, Baron Karl Friedrich Alexander von Arnswaldt, December 29, 1824.
30. Appointed full professor, 1828.
31. Member, Royal Academy of Palermo, 1828.
32. Associate, Royal Astronomical Society of London, April 13, 1832. Notification signed by Francis Baily, President, and Augustus DeMorgan, Secretary.
33. Corresponding member. Academy of Sciences at Bologna, January 3, 1833.
34. Foreign member. Royal Academy of Sciences of Turin, January 20, 1833. Notification signed by Count Prosper Balbo, Minister of State and President.
35. Foreign Member, Royal Bohemian Society of Sciences, Prague, December 1, 1833.
36. Director of Hanoverian Board of Weights and Measures, 1836.
37. Honorary Member, Physical Union, Frankfort, August 17, 1836.
38. Chevalier of the Royal Order of the Legion of Honor, August 26, 1837.
39. Copley Medal, Royal Society of London, 1838.
40. Foreign correspondent. Royal Academy of Sciences and Belles-Lettres of Brussels, December 14, 1841. Signed by Quetelet.
41. Knight of the Peace Class of the order pour le mérite for sciences and arts, Berlin, May 31, 1842.148
42. Member, Royal Society of Sciences at Uppsala, June 3, 1843,
43. Honorary member. Royal Irish Academy, March 16, 1843. Diploma dated at Dublin, October 5, 1851.
44. Knight of the Swedish Order of the North Star, Stockholm, October 14, 1844,
45. Member, first class. Royal Institute of Sciences, Belles-Lettres and Beaux Arts in Holland, Amsterdam, April 19, 1845. Signed by W. H. de Vriese, Secretary ad interim.
46. Letters patent conferring the honorary title of Geheimer Hofrath, dated at Göttingen, July 1, 1845. Signed by King Ernst August of Hanover.
47. Diploma of honorary member of the philosophical faculty. University of Prague, 1848.
48. Honorary doctorate and member of the Society of Sciences, University of Kasan, January 12, 1848.
49. Foreign honorary member. Imperial Academy of Sciences at Vienna, January 26, 1848.
50. Congratulatory diploma of the Royal Bavarian Academy of Sciences on the golden jubilee of his doctorate, Munich, July 10, 1849.
51. Commander’s Cross, second class, Guelph Order, July 11, 1849. Notification signed at Hanover by King Ernst August.
52. Congratulations of the Royal Hanoverian University Board of Curators on the golden jubilee of his doctorate, Hanover, July 14, 1849.
53. Congratulatory letter on the golden jubilee from C. W. Wippermann, electoral Hessian Minister of Finance, Kassel, July 15, 1849.
54. Jubilee congratulations of the Collegium Carolinum, Brunswick, July 15, 1849.
55. Commander’s Cross of the Order of Henry the Lion, conferred by Duke Wilhelm of Brunswick, July 16, 1849.
56. Jubilee congratulations of the University of Kasan, July, 1849 (on silk).
57. Renewal of doctor’s diploma by the University of Göttingen, July, 1849.149
58. Honorary citizenship of the city of Göttingen, July, 1849.
59. Jubilee congratulations of the Bavarian Academy of Sciences, July, 1849.
60. Honorary citizenship of the city of Brunswick, July, 1849.
61. Member, Spanish Academy of Sciences, Madrid, 1850.
62. Foreign honorary member. Imperial Russian Geographical Society, September 29, 1851.
63. Honorary member. Royal Church Deputation of the University, Göttingen, December 28, 1852 (in recognition of Gauss’ work on the insurance fund for widows of professors).
64. Honorary member. Imperial Academy of Sciences at Vienna, diploma dated December 31, 1852 (elected January 26, 1848).
65. Member, American Philosophical Society in Philadelphia. Diploma dated January 21, 1853 (received February 26, 1853).
66. Knight Commander’s Cross, first class, Guelph Order, Hanover, May 27, 1853. Diploma signed by King George.
No Date
68. Notification of the Hanoverian Cabinet Ministry concerning a special gift of 1,000 thalers in gold to Gauss.
69. Cambridge Philosophical Society.
70. Dutch Society of Sciences, Harlem.
71. Imperial Royal Lombard Institute at Milan.
72. Royal Saxon Society of Sciences, Leipzig.
Appendix C — The Will of Gauss
The following document is kept in the Gauss collection of the Municipal Archive and Library of the City of Brunswick, Germany (Inventory C, F. Gauss No, 151, MS No. 8), It is in Gauss’ handwriting, but without signature and date (believed to be about December, 1854):
In consideration of my advanced age and the continuing increase in strength and stubbornness of the complaints connected with it, it has seemed advisable to me to write down those explanations and terms which shall serve as a guide in settling my estate after my death.
§ 1.
Of my two marriages four children are still living, namely,
of the first marriage a son, Joseph, now government architect in Hanover,
of the second marriage two sons and a daughter, namely Eugene, merchant in St. Charles in North America in the state of Missouri; Wilhelm, farmer in the same state, his farm in Chariton County near New Brunswick.
Therese as my loyal nurse continually with me,
these my four children, eventually their legitimate descendants, I make my heirs, but under the following modifications:
§ 2.
My oldest son Joseph took possession of his maternal inheritance long ago. Likewise I paid out completely at the proper time to my sons of the second marriage their share in the estate of their mother according to the testamentary disposition, so that they have no further special claims —on the other hand the amount of the share of my daughter in her maternal estate has not yet been paid out to her and therefore before the division of my estate that amount (4,754 thalers gold plus interest) of course is to be deducted from it as an encumbering debt to my daughter.
Carl Friedrich Gauss, Titan of Science_A Study of His Life and Work Page 40