Carl Ludwig Siegel was bornon December 31, 1896 in Berlin, German Empire, German, is Mathematician. Carl Ludwig Siegel is considered to be one of the greatest mathematicians of the 20th century. Nothing is known about his life prior to his admission at the Humboldt University at the age of nineteen. Although he initially wanted to pursue astronomy, his interest was turned towards number theory under the guidance of his teachers at Humboldt. Later, he wrote his dissertation on Diophantine approximations, earning his doctoral degree from the University of Göttingen, beginning his career at Johann Wolfgang Goethe-Universität of Frankfurt am Main two years later. But even before that, he was able to establish himself as an eminent mathematician with his ‘Thue–Siegel–Roth theorem’. An anti-Nazi and an antimilitarist, he left his homeland at the onset of the Second World War, teaching in the USA from 1940 to 1951. Otherwise, he lived mostly in Germany devoting himself to teaching and mathematical research. Today, he is especially noted for his work on number theory and celestial mechanics. Apart from publishing number of groundbreaking papers on these subjects, he had also written several textbooks on them.

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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.

1915

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. Another notable student was Kurt Mahler, the number theorist.

1917

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 Georg-August University of Göttingen, studying under 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. 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. Siegel's reminiscences about the time before World War II are in an essay in his collected works.

1936

In 1936 he was a Plenary Speaker at the ICM in Oslo. 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. In 1968 he was elected a foreign associate of the U.S. National Academy of Sciences.

1970

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.

1978

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.

2013

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, appeared in 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.

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