**Carl Siegel** was a German mathematician who worked in algebraic number theory and also on celestial mechanics.

- Most certainly military life did not suit Siegel and he was eventually discharged from the army as one of their failures, for despite their best efforts they had failed to have him adapt to army life.
- One would have to believe that Siegel would have classed this as a success rather than a failure.
- After the war had ended, Siegel continued his studies at Göttingen, beginning in 1919.
- His doctoral dissertation at Göttingen was supervised by Edmund Landau and Siegel then continued to study for his habilitation.
- He was aged 61 when he was appointed and when he retired in 1922 Siegel was appointed as professor to succeed him at Frankfurt.
- Although Schönflies spent the six years of his retirement in Frankfurt, his days as an active mathematician were over by the time Siegel took up the professorship.
- There were, however, several young mathematicians on the staff at Frankfurt who would with Siegel create an excellent centre for mathematics.
- It was a strong and exciting department which Siegel joined in 1922.
- There were a number of activities on which the four mathematicians Siegel, Hellinger, Epstein, and Dehn collaborated.
- The history of mathematics seminar was not the only one which Siegel participated in at Frankfurt, for the professors organised also a proseminar and a seminar.
- Student numbers rapidly built up after Siegel was appointed.
- By 1928 Siegel was teaching 143 students in the differential and integral calculus course, and had to put in many hours work correcting students exercises.
- This did not affect Siegel who was an Aryan (to use the terminology of the time which Siegel hated) and, at this stage it did not affect Epstein, Hellinger or Dehn who, although Jewish, fell under a clause which exempted non-Aryans who had fought for Germany in World War I.
- Although Siegel was not affected by the Civil Service Law, he hated the Nazi regime and this was the beginning of a very unhappy time for him.
- In 1935 Siegel spent a year at the Institute for Advanced Study at Princeton in the United States.
- In late 1937 Siegel accepted a professorship at Göttingen and he moved there in early 1938.
- The Nazi regime had taken Germany to war in 1939 and Siegel felt that he could no longer remain in his native land.
- Dehn had fled from Germany in fear of his life and was teaching in Trondheim when Siegel visited him.
- Siegel saw German merchant ships in the harbour and only later, having left Norway for the United States, did he discover that the ships he had seen were the advanced party of the German invasion force.
- Siegel is especially famed for his work on the theory of numbers where he held an eminent role.
- Schneider, who was a student of Siegel's, gave three lectures on Siegel's contributions to number theory to the German Mathematical Union in 1982.
- In the 1929 paper Siegel made a substantial contribution to transcendence theory, especially a new method for the algebraic independence of values of certain EEE-functions.
- Siegel's research on the analytic theory of quadratic forms in 1935/37 was of fundamental importance and he broke new ground in considering quadratic forms in which the coefficients were from an algebraic number field.
- In particular he studied automorphic functions in several complex variables, Siegel's modular functions, which have led to a much deeper understanding.
- In this general area Siegel considered the theory of discontinuous groups and their fundamental domains, algebraic relations between modular functions and between modular forms, and Fourier series of modular forms.
- The paper lists eight major contributions which Siegel made to the subject.
- the restricted problem of three bodies and their integrals, which used the results Siegel had proved in (i).
- Siegel gave a much improved version of lunar theory as developed by Hill.
- Siegel developed general methods to determine periodic orbits near the equilibrium points.
- the problem of small divisors, where Siegel first obtained convergence results.
- Siegel gave examples of systems which did not possess convergent transformations into a normal form.
- An interesting episode, which tells us a lot about Siegel's approach to mathematics, occurred in the 1960s.
- Siegel enjoyed teaching, however, even elementary courses, and he published textbooks on the theory of numbers, celestial mechanics, and the theory of functions of several complex variables.

Born 31 December 1896, Berlin, Germany. Died 4 April 1981, Göttingen, Germany.

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Origin Germany, Prize Wolf

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive