# Leopold Kronecker

Leopold Kronecker ( born December 7, 1823 in Legnica, † December 29, 1891 in Berlin) was a German mathematician. The physiologist Hugo Kronecker (1839-1914) was his brother.

## Life

Leopold Kronecker comes from an educated and wealthy Jewish merchant family. He enjoyed an excellent school education, first by private tutors, then at Liegnitz high school, among other things by his mathematics teacher, who later became a university professor Ernst Eduard Kummer.

In 1841 he began the study of philosophy at the University of Berlin and visited during lectures in mathematics, science, philosophy and classical philology. After brief forays to the universities of Bonn and Breslau, he returned in 1844 to Berlin, where he received his doctorate in 1845 with his work " De Unitatibus Complexis " ( "On complex units") to Doctor of Philosophy. He became in 1843 a member of the fraternity Fridericia Bonn.

After he left the University and operated for several years as a successful businessman. In 1855, he was financially independent and returned as a private scholar returned to the University of Berlin. Among his pupils was, among others, Georg Cantor. 1861 Kronecker became a full member of the Berlin Academy of Sciences. An offer of a professorship in Göttingen, he refused 1868. He remained in Berlin and followed there in 1883 his former teacher sorrow on his chair after. With the participation of Weierstrass, Helmholtz, Schroeter and fox he edited the journal founded by Crelle of Mathematics.

Leopold Kronecker died on December 29, 1891 from the effects of bronchitis. His grave is located in the Protestant Old St. Matthew's Cemetery in Tempelhof- Schöneberg.

## Work

His research provided fundamental contributions to algebra and number theory, but also for analysis and function theory. Over time, he became a follower of finitism, was valid only mathematical objects whose existence could be secured by explicit constructions, and tried the math relying solely on the natural numbers defined. Thus he came into conflict with many important mathematicians of his time; in particular he attacked Georg Cantor and set theory to the public and sharp, where he studied these very unconstructive in long distances. Kronecker was convinced that with the set theory for the concrete analysis there was nothing to win. Also his statement became known: " The integers has made the good God, all else is the work of man. " Kronecker finitism made him a precursor of mathematical constructivism.

After David Hilbert Kronecker compared the number theorist with the Lotus-eaters, " which, once they have taken to from this diet something that can never be more of it ."

Named after him are:

- The set of Kronecker -Weber,
- Is the Kronecker delta,
- The Kronecker lemma,
- Is the Kronecker symbol,
- The Kronecker product and
- The Kronecker structure.