One of the happy events of Gauss’ old age was the visit paid him on July 26, 1849, by Bernhard August von Lindenau, astronomer and minister of state of the Kingdom of Saxony. He was the last of the old friends from the beginning of the century whom Gauss saw.
After Lindenau’s visit Gauss seemed to rest more on his laurels. He explained to intimate friends that he did not like to be driven in his scientific work and that his working time was noticeably shorter in comparison with earlier years. At other times he complained of the burden of teaching his courses, which prevented him from carrying out some major research. His work dealt with the theory of the convergence of series, actuarial studies, and mechanical problems connected with the rotation of the earth, resulting from Foucault’s experiment and the theoretical studies of Lagrange, Plana, Hansen, and Clausen. He had the Reichenbach meridian circle equipped with new microscopes, ordered optical instruments from Oertling, a well-known mechanic in Berlin, and also had a large Foucault pendulum set up, in order to show the rotation of the earth.
Although at times he grew weary of long arithmetical calculations, Gauss derived a certain pleasure from them as a rule. He used many different artifices and used to tell his students that there was a certain poetry in the calculation of logarithmic tables. It was difficult for him to forget that he was a man of science, even during his recreations. For years he played whist regularly with the same friends. It was his custom to write up how many aces each one had had in his hand in every game, in order to get an empirical corroboration of certain laws of the calculus of probabilities. He made very few errors in calculating and used many means of checking results. In extended numerical calculating he observed perfect order; every number was written in the neatest manner possible. Each number was in exactly the right place. Row after row manifested the same accuracy.
He always strove to carry out the work as accurately as the auxiliary means allowed. The last decimal in seven- or ten-place logarithms had to be verified as much as possible, and he carried out full-scale research to determine to what extent the last decimal m various tables was accurate. He got special pleasure from calculating with incorrect tables, because he then had the attractive job of correcting misprints or errors in calculating. His greatest joy was in simplifying long calculations of analytical or numerical nature and in compressing the result of a week’s work on one octavo page, thus making it intuitively evident to the connoisseur. Even where he had to make extracts from the works of others, the content of a volume or the excerpt of an entire official document was brought together in a very small space in an unusually clear manner.
Gauss was always attempting to find some new application for mathematics. He kept numerous little notebooks with punctual and neat entries. There was an index of the length of life of many famous men and of his deceased friends, calculated in days. At nine o’clock the third evening before his death he calculated the number of days that he had lived and made this entry in an actuarial book he had possessed for many years. Another covered the monthly income of the Hanoverian railroads. He kept another on the walking distance (number of paces) from the observatory to the various places he often visited. There was one with the day and number of electrical storms in various years. One of the most interesting such registers gave the dates of birth of his children, date of vaccination, dates of cutting the first eight teeth, and date of beginning to walk. Each date was accompanied by the number of days old the child was at the time. He kept a chart of all the keys to the observatory and his home and entered an exact sketch of each key.
In his family and his home nothing was unimportant. Although he lived modestly, he enjoyed social intercourse. This enjoyment was somewhat limited in his last years for reasons of health. He did not like to travel, and never went farther than Austria.
Gauss was a great friend of music, especially of singing. When he heard a beautiful song, or, for that matter, any song that appealed to him, he wrote it down. His notes are as small and neat as though printed. One of his favorite songs was the well-known “Als ich ein Junggeselle war”; another was the English song that begins, “Tell me the tales that to me were so dear, long long ago.” He wrote down Mignon’s “Kennst Du das Land” and copied the following, which he designated as Jean Paul’s favorite song:
Namen nennen Dich nicht
Dich bilden GrifFel und Pinsel,
sterbliche Kunstler nicht nach
Lieder singen Dich nicht
Sie alle reden wie Nachhall
Ferneste Zeiten von Dir.
Wie Du lebest und bist
So trag ich einzig im Herzen
Holde Gehebte Dein Bild.
In 1850 Gauss copied down the revolutionary weavers’ song as published in the Volksblatt of Nathusius, a song of which he definitely did not approve. Two additional songs that made a strong appeal to him were the patriotic “Schleswig-Holstein Meer umschlungen,” by Chemnitz and Bellmann, and “Unser Leben gleicht der Reise eines Wanderers in der Nacht.” As a university student Gauss read Lohlein’s Klavierschule, Euler’s Nova theoria musicae, Bach’s Ueber die beste Art, Klavier zu spielen, and Margary’s (?) Anleitung zum Klavierspielen, although this biographer knows of no evidence that he ever played a musical instrument. He enjoyed the following concerts in Göttingen: Carl Maria von Weber (August, 1820), Paganini (May 28, 1830), Liszt (November 24, 1841), and Jenny Lind (February 2 and 4, 1850). It is doubtful whether he knew Johannes Brahms and Joseph Joachim during their student period in Göttingen.
Gauss’ physical appearance was impressive, according to his students. He was of medium height, perhaps slightly below average. His hair was blond and in later years a beautiful silvery white. His penetrating, clear blue eyes constituted a striking feature. His hands and feet were well formed and of normal size. He walked gracefully and with a measured gait. His black satin cap was a favorite article of clothing. Gauss was a typical Nordic and Nether-Saxon. He enjoyed conversation but never Used more words than were necessary. He was heavy set, but not Corpulent, and gave the appearance of being sturdy. His countenance conveyed an impression of affability and mildness. His eyebrows were rather heavy and, characteristic for an astronomer, the right one was noticeably higher than the left one. A high forehead symbolized great intelligence. His voice was pleasing. He had a rather prominent Roman nose. Gauss was nearsighted and had to use spectacles part of the time, yet his eyes and ears were keen, accurate, and well trained both in observation and experiment. He practiced moderation in all habits, enjoyed his glass of wine,67 and smoked a pipe as well as an occasional cigar.
Personal or domestic distraction could and did occasionally exert a paralyzing effect on his scientific work, in spite of his great power of concentration. He has never been pictured as the absent-minded-professor type. The writer knows of only one such anecdote, but regards it as purely apocryphal. It is found in Carpenter’s Mental Physiology, where the author gives it as an example of the remarkable power of concentration and attention. The story is that Gauss, while engaged in one of his most profound investigations, was interrupted by a servant who told him that his wife (to whom he was known to be deeply attached, and who was suffering from a severe illness) was worse. He seemed to hear what was said, but either did not comprehend it or immediately forgot it, and went on with his work. After some little time, the servant came again to say that his mistress was much worse, and to beg that he would come to her at once; to which he replied: “I will come presently.” Again he lapsed into his previous train of thought, entirely forgetting the intention he had expressed, most probably without having distinctly realized to himself the import either of the communication or of his answer to it. Not long afterward when the servant came again and assured him that his mistress was dying and that if he did not come immediately he would probably not find her alive, he lifted up his head and calmly replied, “Tell her to wait until I come,” a message he had doubtless often sent when pressed by his wife’s request for his presence while he was
similarly engaged.
As the son of poor parents Gauss was not accustomed to the luxury and refinements of more modern times. The limited means of his early years were sufficient for his simple needs. He practiced economy and laid aside a “nest egg” for a rainy day. Gauss was slow to accept financial aid from others. Throughout his life he remained true to his feelings of honor and intellectual independence. In the Napoleonic period he refused offers of financial aid from his friend Olbers and Laplace to pay the French war contribution. On the other hand he did not hesitate to accept support from his protector, the Duke of Brunswick. Although conditions of poverty in his youth were severe, they did not leave any scar on his later life. At the same time it must be admitted that Gauss was not the serene Olympian as he has occasionally been pictured. His wants were simple, and material possessions were sometimes regarded by him as exerting a disturbing influence on scientific work.
Gauss used to say that he was entirely a mathematician, and he rejected the desire to be anything different at the cost of mathematics. It is true that the research in physical science offered him a type of recreation. He called mathematics the queen of the sciences, and the theory of numbers the queen of mathematics, saying that she often condescended to serve astronomy and other sciences, but that under all circumstances top rank belonged to her. Gauss regarded mathematics as the principal means of educating the human mind. He recognized the value of studying classical literature, and said that although he chose mathematics as a career he had not neglected the latter. Gauss recommended to his students the study of the ancient mathematicians, in particular Euclid and Archimedes.
It was his custom to tell his friends that if others would meditate as long and as deeply as he did on mathematical truths, they would be able to make his discoveries. He said that often he meditated for days on a piece of research without finding a solution, which finally became clear to him after a sleepless night. His conversation with friends sometimes was interrupted for meditation; sometimes the conversation would be continued after a gap of several days.
Newton was probably the mathematician to whom Gauss was most closely related by discovery and temperament. To Newton alone he applied the adjective summus. He occasionally compared Newton and Leibniz, and, although recognizing the great talent of Leibniz and his merit in discovering the calculus. Gauss regretted that Leibniz had dissipated his energy by being too much the jack of all trades. Gauss was indignant about the legend of the apple in connection with the discovery of the law of gravitation. He thought it too simple an explanation. Gauss’ version ran thus: “Some dumb upstart came to Newton and asked him how he had arrived at his great discoveries. Since Newton realized what kind of a creature confronted him and wanted to get rid of him, he answered that an apple fell on his nose, whereupon the fellow went away, completely satisfied.”
In the manifold conditions of human life Gauss saw an extended field for the application of mathematical theories. The answering of economic, financial, and statistical questions furnished him rich material for such research. He placed special value on tables of mortality and the investigation of laws governing the length of human life, partly for further application in calculating life insurance, annuities, and widow’s funds. Gauss took special interest in mortality rates of infancy and old age. He felt that there were too many extraneous influences to derive laws between those two periods of life. He used to tell his friends that he had carried on research on the mean life expectancy of children up to age one and a half years which exhibited such admirable regularity that it was almost like astronomical observations. Likewise it was his view that at an advanced age the mean length of human life follows a definite law, although we do not possess sufficient data for a satisfactory answer to this question. He said that we would be able to perfect these data by rewarding with premiums people who could prove that they were ninety or a hundred years old, adding that if he were a rich man he would offer large capital for this purpose.
Beginning in 1845 the academic senate at Göttingen entrusted Gauss with a gigantic task, a study and reorganization of the fund for professors’ widows. He devoted himself to it with his usual vigor; here his mathematical ability and knowledge of financial operations linked up with his practical talent in organizing. This job took much of his time as late as 1851, and his work saved the fund from ruin. His long memoir discussed the principles which govern the administration of such a fund; it is printed in Volume IV of the Collected Works. Gauss received recognition for this achievement, and widows as well as orphans were grateful to him. In a letter to Gerling on July 26, 1845, he explained what the situation was:
Now several words about the work mentioned at the beginning of this letter. It concerns the local fund for professors’ widows, where a year ago the number of widows had increased so much (to 22), that the income was no longer sufficient to pay the pensions, although other adversities were connected with it—long-drawn-out law suits, in which all interest is absent and on the other hand considerable court costs are to be borne in cash—and that worries were therefore stirred up. I did not share these worries to the extent that I would have attached a preponderant importance to the present large number of widows (which since then has decreased by 3), but rather I see a much greater danger in the present inordinately large number of participants (50 or 51, while several decades ago there were only 30 or a few more). The fund subsists almost entirely on its property, while the contributions are quite insignificant (10 thalers annual contribution, 250 thalers annual pension, both gold). In addition there is an obscure version of a highly important part of the statutes, to which, in my judgment, a highly unintelligible interpretation has been given in practice. Several months ago I was commissioned to investigate the situation basically, which I am convinced can occur only by selling for cash and balancing with the property the three types of obligations of the fund, namely: (1) to the present 19 widows, (2) to the possible survivors of the present 51 members, (3) to the survivors of all future members. Especially difficult (that is, protracted) is the calculation of (2), and it cannot be completed except by means of an auxiliary table for an obligatory income, in which annual differences and years are the basis. I have now begun and almost finished the construction of such an auxiliary table, difference of age, −1 . . . +20 and age from the maximum up to twenty years back, all by individual years and according to two rates of interest, 4 per cent and 3,5 per cent, and according to Brune’s mortality table, after I used almost all my time for a month on It. In itself such a work is demanding, over 100,000 figures (according to my method of writing, where half or more is calculated in the head), a work very protracted for the mind, but I submitted in view of the usefulness of that work, for which it is a preparation, for the university to which I owe my position in life, although I have to count not on thanks for it, but only on vexation.
In Quetelet’s Annuaire Gauss found the ratio of widows to existing marriages as one to four. He felt that this was inaccurate and that many widows’ funds were ruined by the use of such figures. In his opinion, the ratio which is valid for a whole land is not valid for individual provinces, and even less for individual classes of society. He thought for professors’ widows the ratio 1:2 would yield too few. In the case of the Göttingen widows’ fund, even if the ratio were known to be 7:12, no use could have been made of it. Gauss found that, owing to laxity of administration, the Göttingen fund had accurate information on existing marriages for only two years, 1794 and 1845, even though the fund had existed for over one hundred years when he attacked the problem.
On January 31, 1846, Gauss gave Gerling some further details on his work for the fund:
Our widows’ fund affair has cost me an enormous amount of time. Studying, with the help of more than 100 years of accounts, for the construction of detailed auxiliary tables (using Brune’s mortality tables, certainly the only ones which are based on correct principles), and the actual application of them to 42 married couples and 20 widows, according
to two different rates of interest, have demanded a work of about 5 months, later the working out of a memoir on the condition as well as a critical revision of earlier negotiations, on which the existing regulation is based—again more than 6 weeks. Now I have finally worked out a new memoir with proposals for remedy of the threatening evils, which is accepted by the whole commission under me, but which, as I have great cause to fear, will be received by a large number of the academic senate in an extremely Abderian manner. In order to be able to bear this as calmly as possible, I (foreseeing such success) withdrew six months ago.
Gauss’ special hobbies included public finance, its sources and duties, the administration of banks and railroads, the relationship between paper money and value of the metal, amortizations, and the like. Daily he rapidly scanned the press for financial news, particularly market reports and the course of foreign bonds. He considered paper money very dangerous for the credit of nations, because governments in time of trouble could too easily be led to overestimate their financial strength. Gauss was glad that the Kingdom of Hanover had not introduced paper money in his day. He was a definite enemy of all petty finance operations, if they only burden the public, without leading to any important result, and he used to call them “penny-pinching” (Pfennig-fuchsereien), ascribing to their authors little intelligence and feeling of fairness. Gauss was known to his friends as a wise investor, although actually none of them knew how wealthy he really was. Perhaps it is well that his talents in this field were not more widely known, for he would surely have been continually annoyed by inquiries and thus hindered in his scientific work. The opinion has been expressed that he would have made an excellent minister of finance. On one occasion he expressed himself about the matter; it occurs in a letter to Schumacher, June 27, 1846, just after the death of Bessel:
Carl Friedrich Gauss, Titan of Science_A Study of His Life and Work Page 27