Leopold Kronecker

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Leopold Kronecker

Leopold Kronecker (born December 7, 1823 in Liegnitz , † December 29, 1891 in Berlin ) was a German mathematician .


Leopold Kronecker comes from an educated and wealthy Jewish merchant family. The physiologist Hugo Kronecker (1839–1914) was his brother. He enjoyed an excellent education, first from private teachers , then at the Liegnitzer Gymnasium, among other things, from his mathematics teacher, who later became a university professor, Ernst Eduard Kummer .

In 1841 he began to study philosophy at the University of Berlin and attended lectures in mathematics, natural sciences, philosophy and classical philology . After brief trips to the universities of Bonn and Breslau, he returned to Berlin in 1844, where he received his doctorate in philosophy in 1845 with his thesis “De Unitatibus Complexis” (“On Complex Units”) . In 1843 he became a member of the Fridericia Bonn fraternity .

After that he left the university and worked very successfully as a businessman for several years. In 1855 he was economically independent and returned to the University of Berlin as a private scholar . One of his students was Georg Cantor . In 1861 Kronecker became a corresponding member of the Göttingen Academy of Sciences and a full member of the Berlin Academy of Sciences . In 1868, he turned down an offer for a professorship in Göttingen . He stayed in Berlin and followed his former teacher Kummer to his chair in 1883. With the participation of Weierstrass , Helmholtz , Schroeter and Fuchs , he published the journal for mathematics founded by Crelle . In 1868 he became a corresponding member of the Académie des Sciences in Paris and in 1872 of the Russian Academy of Sciences in St. Petersburg . In 1884 he was elected a member of the Leopoldina and an external member of the Royal Society .

Leopold Kronecker died on December 29, 1891 of complications from bronchitis . His grave is in the Protestant Old St. Matthew Cemetery in Tempelhof-Schöneberg. It has been dedicated to the city of Berlin as an honorary grave since 1969 .


His research made fundamental contributions to algebra and number theory , but also to analysis and function theory . In the course of time he became a follower of finitism , accepted only mathematical objects whose existence could be secured by explicit constructions, and tried to define mathematics solely on the basis of natural numbers. As a result, he came into conflict with many important mathematicians of his time; in particular, he attacked Georg Cantor and his set theory publicly and sharply, examining them largely in a very unconstructive manner. Kronecker was convinced that nothing could be gained with set theory for concrete analysis. His saying also became known: “God made the whole numbers, everything else is human work.” Kronecker's finitism made him a forerunner of mathematical constructivism .

According to David Hilbert , Kronecker compared number theorists with the lotophages , "who, once they have eaten something from this diet, can never leave it".

The following are named after him:

Grave of Kronecker and his wife (St. Matthäus, Berlin)


Web links

Commons : Leopold Kronecker  - Collection of images, videos and audio files


  1. ^ Franz Richarz: List of members of the Fridericia fraternity in Bonn (February 18, 1843 to autumn 1847) as well as the Arminia fraternity in Bonn (1847 to 1849) and the fraternity association Germania in Bonn (1843 to 1849). Bonn 1894, p. 12.
  2. Holger Krahnke: The members of the Academy of Sciences in Göttingen 1751-2001 (= Treatises of the Academy of Sciences in Göttingen, Philological-Historical Class. Volume 3, Volume 246 = Treatises of the Academy of Sciences in Göttingen, Mathematical-Physical Class. Series 3, volume 50). Vandenhoeck & Ruprecht, Göttingen 2001, ISBN 3-525-82516-1 , p. 140.
  3. ^ Entry on Kronecker, Leopold (1823 - 1891) in the archive of the Royal Society , London
  4. ^ H. Weber: Leopold Kronecker . In: German Mathematicians Association (ed.): Annual report of the German Mathematicians Association . tape 2 . Reimer, 1893, ISSN  0012-0456 , p. 5–31 ( uni-goettingen.de - quote on p. 19).
  5. Hilbert said this in his speech Nature Recognition and Logic on the occasion of the congress of the Society of German Natural Scientists and Doctors in Königsberg on September 8, 1930. See quantumfuture.net
  6. ^ Limit formula at Mathworld
  7. Kurt Girstmair: Kronecker's solution of Pell's equation on the computer . In: Math. Semesterber. tape 53 , 2006, p. 45-64 .