| Carl Ludwig Siegel | |
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Carl Ludwig Siegel in 1975
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| Born | December 31, 1896 Berlin, Imperial Germany |
| Died | April 4, 1981 (aged 84) Göttingen, West Germany |
| Fields | Mathematics |
| Institutions | Johann Wolfgang Goethe-Universität Institute for Advanced Study |
| Alma mater | University of Göttingen |
| Doctoral advisor | Edmund Landau |
| Known for | Number theory |
| Notable awards | Wolf Prize in Mathematics |
Carl Ludwig Siegel (December 31, 1896 – April 4, 1981) was a mathematician specialising in number theory and celestial mechanics. He was one of the most important mathematicians of the 20th century.[1]
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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 student was Jürgen Moser, one of the founders of KAM theory (Kolmogorov-Arnold-Moser), which lies at the foundations of chaos theory.
In 1917 Siegel was drafted into the German Army. Since he refused military service, he was committed to a psychiatric institute. 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 Georg-August University of Göttingen, studying under Edmund Landau, who was his doctoral thesis supervisor (Ph.D. 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 Johann Wolfgang Goethe-Universität of Frankfurt am Main 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.[2] In Frankfurt he took part in a seminar 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. Siegel's reminiscences about the time before WWII are in an essay in his collected works.
In 1938, he returned to Göttingen before emigrating in 1940 via Norway to the United States, where he joined the Institute for Advanced Study in Princeton, where he had already spent a sabbatical in 1935. He returned to Göttingen only after World War II, when he accepted a post as professor in 1951, which he kept until his retirement in 1959.
Siegel's work on number theory, diophantine equations, and celestial mechanics in particular won him numerous honours. In 1978, he was awarded the Wolf Prize in Mathematics, one of the most prestigious in the field.
Siegel's work spans analytic number theory; and his theorem on the finiteness of the integer points of curves, for genus > 1, is historically important as a major general result on diophantine equations, when the field was essentially undeveloped. He worked on L-functions, discovering the (presumed illusory) Siegel zero phenomenon. His work derived from the Hardy-Littlewood circle method on quadratic forms proved very influential on the later, adele group theories encompassing the use of theta-functions. The 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.
André Weil, without hesitation, named[3] Siegel as the greatest mathematician of the first half of the 20th century. In the early 1970s Weil gave a series of seminars on the history of number theory prior to the 20th century and he remarked that Siegel once told him that when the first person discovered the simplest case of Faulhaber's formula then, in Siegel's words, "Es gefiel dem lieben Gott." (It pleased the dear Lord.) Siegel was a profound student of the history of mathematics and put his studies to good use in such works as the Riemann-Siegel formula.
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