Leopold Kronecker

Leopold Kronecker
Leopold Kronecker in 1865
Born	(1823-12-07)7 December 1823 Liegnitz, Province of Silesia, Prussia
Died	29 December 1891(1891-12-29) (aged 68) Berlin, German Empire
Residence	Prussia
Nationality	Prussian
Fields	Mathematics Logic
Institutions	Berlin Academy University of Berlin
Alma mater	University of Berlin
Doctoral advisor	Johann Encke Peter Gustav Lejeune Dirichlet
Doctoral students	Kurt Hensel Adolf Kneser Mathias Lerch Franz Mertens Paul Stäckel Ernst Kötter
Known for	Kronecker delta Kronecker symbol Kronecker product Kronecker–Weber theorem Kronecker's theorem Kronecker's lemma

Leopold Kronecker (7 December 1823 – 29 December 1891) was a German mathematician who worked on number theory, algebra and logic. He criticized Cantor's work on set theory, and was quoted by Weber (1893) as having said, "Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk" ("God made the integers, all else is the work of man."). Kronecker was a student and lifelong friend of Ernst Kummer.

Leopold Kronecker was born on 7 December 1823 in Liegnitz, Prussia (now Legnica, Poland) in a wealthy Jewish family. His parents, Isidor and Johanna (née Prausnitzep), took care of their children's education and provided them with private tutoring at home – Leopold's younger brother Hugo Kronecker would also follow a scientific path, later becoming a notable physiologist. Kronecker then went to the Liegnitz Gymnasium where he was interested in a wide range of topics including science, history and philosophy, while also practicing gymnastics and swimming. At the gymnasium he was taught by Ernst Kummer, who noticed and encouraged the boy's interest in mathematics.

In 1841 Kronecker became a student at the University of Berlin where his interest did not immediately focus on mathematics, but rather spread over several subjects including astronomy and philosophy. He spent the summer of 1843 at the University of Bonn studying astronomy and 1843–44 at the University of Breslau following his former teacher Kummer. Back in Berlin, Kronecker studied mathematics with Peter Gustav Lejeune Dirichlet and in 1845 defended his dissertation in algebraic number theory written under Dirichlet's supervision.