1.10. Some historical notes 35 remember the pride he felt in that first discovery. (Gauss requested that a regular 17-gon be carved on his tombstone. The request was carried out.) Such an incident involved the Hungarian mathematician, J´ anos Bolyai, whose father was one of Gauss’s closest friends. J´ anos Bolyai (1802–1860) is a discoverer of non-Euclidean geometry. When he told Gauss of his work, Gauss was full of private praise but refused to review Bolyai’s work publicly — even though Bolyai was being publicly criticized by others. Also Gauss claimed (in private) to have already done the same work. Fortunately, the mathematical world today credits Bolyai and the Russian mathematician N. I. Lobachevsky (1793–1856) with the discovery of non-Euclidean geome- try. The other case of Gauss’s indifference involves the Norwegian mathe- matician Niels Henrik Abel (1802–1829). At the time Norway was a mathe- matical backwater, and Abel was a genius living in poverty. At 21 he proved that the fifth-degree equation, unlike the quadratic equation, has no “nice” solution expressible as a formula with roots. Printed at his own expense, the work was ignored. A manuscript sent to the French mathematician Cauchy was lost. (Cauchy had a bad habit of doing such things.) Then, when Abel published work in an area called “elliptic functions”, Gauss complimented Abel, but in a letter to a fellow mathematician said he had already done this work — and much more. He also made a sinister comment that Abel’s symbols were just like his own — hinting at the possibility of dishonesty – then saying, “I will also point out that I cannot recall ever having talked with anyone about these matters.” Abel set out on a tour of the continent, hoping to see Gauss. But Gauss was inaccessible. Time went by. Abel visited several universities, but he never went to G¨ ottingen and never met Gauss. Abel returned to Oslo even poorer. At the age of 26 he died of consumption. Abel is ranked as one of the greatest mathematicians of the nineteenth century. Gauss would certainly have profited from a meeting with Abel, and Abel, as well as mathematics, would have profited too. In 1807 the German government, upset by the prospect of Gauss’s ac- cepting a position in St. Petersburg, offered Gauss a position as professor of astronomy and director of the observatory in G¨ ottingen he accepted. At the time people made little distinction between mathematics, physics, and astronomy researchers regularly did work in all three areas. Gauss continued his work in mathematics, studying and making signifi- cant contributions to the theory of surfaces and curvature, number theory, geometry, probability, statistics, and the theory of errors. He also made con- tributions to astronomy, and various parts of physics, including the theory of electromagnetism. (A television manufacturer once promoted its product by emphasizing the built-in “degausser”.)

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