卡尔·西格尔1896—1981

生平

生于普鲁士王国柏林，1915年进入柏林洪堡大学，修读数学、天文和物理。1917年中止学业，加入德国军队。第一次世界大战后，加入哥廷根大学，其导师是爱德蒙·兰道。毕业后当了一段时间助教，1922年成为法兰克福大学教授。1938年回到哥廷根，1940年经挪威到美国，加入普林斯顿高等研究院。1951年再回哥廷根当教授，直到1959年退休。

他的研究范畴是数论、不定方程和天体力学。1978年，获沃尔夫数学奖。

Carl Ludwig Siegel (31 December 1896 – 4 April 1981) was a German mathematician specialising in analytic number theory. He is known for, amongst other things, his contributions to the Thue–Siegel–Roth theorem in Diophantine approximation, Siegel's method, Siegel's lemma and the Siegel mass formula for quadratic forms. He has been named one of the most important mathematicians of the 20th century.

André Weil, without hesitation, named Siegel as the greatest mathematician of the first half of the 20th century. Atle Selberg said of Siegel and his work:

He was in some ways, perhaps, the most impressive mathematician I have met. I would say, in a way, devastatingly so. The things that Siegel tended to do were usually things that seemed impossible. Also after they were done, they still seemed almost impossible.

Biography

Siegel was born in Berlin, where he enrolled at the Humboldt University in Berlin in 1915 as a student in mathematics, astronomy, and physics. Amongst his teachers were Max Planck and Ferdinand Georg Frobenius, whose influence made the young Siegel abandon astronomy and turn towards number theory instead. His best-known student was Jürgen Moser, one of the founders of KAM theory (Kolmogorov–Arnold–Moser), which lies at the foundations of chaos theory. Other notable students were Kurt Mahler, the number theorist, and Hel Braun who became one of the few female full professors in mathematics in Germany.

Siegel was an antimilitarist, and in 1917, during World War I he was committed to a psychiatric institute as a conscientious objector. According to his own words, he withstood the experience only because of his support from Edmund Landau, whose father had a clinic in the neighborhood. After the end of World War I, he enrolled at the University of Göttingen, studying under Landau, who was his doctoral thesis supervisor (PhD in 1920). He stayed in Göttingen as a teaching and research assistant; many of his groundbreaking results were published during this period. In 1922, he was appointed professor at the Goethe University Frankfurt as the successor of Arthur Moritz Schönflies. Siegel, who was deeply opposed to Nazism, was a close friend of the docents Ernst Hellinger and Max Dehn and used his influence to help them. This attitude prevented Siegel's appointment as a successor to the chair of Constantin Carathéodory in Munich. In Frankfurt he took part with Dehn, Hellinger, Paul Epstein, and others in a seminar on the history of mathematics, which was conducted at the highest level. In the seminar they read only original sources.

Career

Siegel's work on number theory, diophantine equations, and celestial mechanics in particular won him numerous honours. In 1978, he was awarded the first Wolf Prize in Mathematics, one of the most prestigious in the field. When the prize committee decided to select the greatest living mathematician, the discussion centered around Siegel and Israel Gelfand as the leading candidates. The prize was ultimately split between them.

Siegel's work spans analytic number theory; and his theorem on the finiteness of the integer points of curves, for genus > 0, with the case of genus 1 an earlier paper in his collected works, is historically important as a major general result on diophantine equations, when the field was essentially undeveloped. The methods included those Weil used in his thesis on finite generation of rational points on abelian varieties (a thesis much guided by Siegel) and versions of the famous Thue-Siegel-Roth Theorem on diophantine approximation. has a detailed discussion of the history. He worked on L-functions, discovering the (presumed illusory) Siegel zero phenomenon. His work, derived from the Hardy–Littlewood circle method on quadratic forms, appeared in the later, adele group theories encompassing the use of theta-functions. The Siegel modular varieties, which describe Siegel modular forms, are recognised as part of the moduli theory of abelian varieties. In all this work the structural implications of analytic methods show through.