Carl Ludwig Siegel (December 31, 1896 - April 4, 1981) was a German mathematician specialising in number theory.

He 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 astonomy and turn towards number theory instead.

In 1917 he was drafted into the German Army and had to interrupt his studies. After the end of World War I, he enrolled at the 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 University of Frankfurt.

In 1938, he returned to Göttingen before emigrating in 1940 via Norway to the U.S., where he joined the Institute for Advanced Study at Princeton University, 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 and 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 prizes in the field of mathematics.

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. See also Siegel lemma , Thue-Siegel-Roth theorem, Brauer-Siegel theorem .