proof = 0, and it is demanded for proof that every doubt becomes impossible'. Carl Friedrich Gauss
Some mathematicians consider the German mathematician Gauss to be the greatest of all time, and almost all consider him to be one of the three greatest, along with Archimedes and Newton; in contrast, he is hardly known to the general public. He was extremely precocious as a child, but did not decide to become a mathematician until the age of seventeen, when he solved the problem of constructing the regular 17-gon, a problem that had been unsolved for almost 2000 years. Characteristically, he did not just solve the geometry problem, but rather provided deep mathematical insights and initiated a new area of study that combined geometry, analysis and number theory; in the same manner, when he was asked to supervise the geodetic survey of Hanover, he solved the computational problems that arose by founding the study of the intrinsic differential geometry of curved surfaces, which was to be fundamental to Riemannian geometry and Einstein's theory of relativity. Ultimately, he was to make major contributions to almost every area of mathematics.
Within mathematics, number theory was Gauss' first and greatest love; he called it the `Queen of Mathematics' (he has been called the `Prince of Mathematicians'). His first published work was the book Disquisitiones Arithmeticae published in 1801; it consisted almost wholly of original work and marked the beginning of modern number theory. In addition to introducing new ideas and concepts to number theory, the Disquisitiones helped create the modern rigorous approach to mathematics; he wanted the proofs in his writing to be above reproach. He wrote to a friend, `I mean the word proof not in the sense of lawyers, who set two half proofs equal to a whole one, but in the sense of mathematicians, where proof = 0, and it is demanded for proof that every doubt becomes impossible'.
Gauss was the first mathematician to be comfortable with the use of complex numbers and the geometry of the complex plane; he used them both in pure (e.g. number theory) and applied (e.g. electromagnetism) mathematics. He was the first to give a proof of the fundamental theorem of algebra that every polynomial with real or complex coefficients has at least one root; he gave four different proofs during his life. Stamp No. 1246 pictures the complex plane in honor of the bicentennial of his birth. Germany has also honored Gauss with a coin, and his portrait is on the German 10 Mark note.
In publishing his work, Gauss followed the motto Pauca sed matura (Few, but ripe) which appeared on his seal. Gauss would not publish a result until it was complete and he was entirely satisfied with its presentation; consequently, much of his work was unpublished with a considerable amount discovered only after his death. Gauss' writing style was terse, polished, and devoid of motivation. Abel said, `He is like the fox, who effaces his tracks in the sand with his tail'. Gauss, in defense of his style, said, `no self-respecting architect leaves the scaffolding in place after completing the building'. The quantity and depth of Gauss' unpublished work sometimes led to unpleasant consequences. When Gauss' lifelong friend Farkas Bolyai wrote to Gauss for an opinion on his son Janos's work on non-Euclidean geometry, Gauss wrote that it was fine work, but he could not praise it, for this would be self-praise since he had developed a similar theory years before; Janos was crestfallen and gave up mathematics as a career. Today Gauss, Bolyai, and Lobachevsky are considered co-discoverers of non-Euclidean geometry. A similar incident occurred with Jacobi over the theory of elliptic functions; Gauss also had prediscovered work of Abel and Cauchy, including Cauchy's integral theorem.
Gauss could be a stern, demanding individual, and it is reported that this resulted in friction with two of his sons that caused them to leave Germany and come to the United States; they settled in the midwest and have descendants throughout the plains states. I was living in Greeley, Colorado, when I read this in 1972; looking in the phone book, I found a listing for a Charlotte Gauss living two blocks from my apartment! After considerable internal debate, I called her and found that she was indeed related to Gauss. My wife, Paulette, and I visited several times with Charlotte and her sister Helen; they were bright, alert, and charming young women, ages 93 and 94, respectively. Their father, Gauss' grandson, had been a Methodist missionary to the region, and he had felt it unseemly to take pride in his famous ancestor (maybe there were some remnants of his father's feelings on leaving Germany); they were nevertheless happy to talk Gauss and their family. They showed us a baby spoon which their father had made out of a gold medal awarded to Gauss, some family papers, and a short biography of Gauss written by an aunt. I vividly remember Helen describing the reaction of one of her math teachers when he discovered he had a real, live, Gauss in his class.
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Carl Friedrich Gauss (1777-1855) |
Carl Friedrich Gauss (1777-1855) |
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German Federal Republic (1955), No. 725 |
German Federal Republic (1977), 1246 |
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Carl Friedrich Gauss (1777-1855) |
Carl Friedrich Gauss (1777-1855) |
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German Federal Republic (1977), No. 1811 |
French Antartica (1984), No. c84 |
In addition to being honored on stamps, Gauss is featured on the current 10 Deutsche Mark bill.
Gauss has also been honored on German coins. I have one, but was unable to produce a good scan.
