# Carl Ludwig Siegel

### Affiliation

From the University of St. Andrews:

[Carl] 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. These include his improvement of Thue's theorem, given in his 1920 dissertation, and its application to certain polynomial Diophantine equations in two unknowns, proving an affine curve of genus at least 1 over a number field has only a finite number of integral points in 1929. In his two-part 1929 paper, Siegel made a substantial contribution to transcendence theory, especially a new method for the algebraic independence of values of certain E-functions. He proved that if *J*^{0} is the Bessel function of index 0, then for any non-zero algebraic integer r he showed that *J*^{0}*(r)* is transcendental.