Leopold Kronecker
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Leopold Kronecker (German: [ˈkʁoːnɛkɐ]; 7 December 1823 – 29 December 1891) was a German mathematician who worked on number theory, algebra and logic. He criticized Georg 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").[1] Kronecker was a student and life-long friend of Ernst Kummer.
Biography
Leopold Kronecker was born on 7 December 1823 in
In 1841 Kronecker became a student at the
After obtaining his degree, Kronecker did not follow his interest in research on an academic career path. He went back to his hometown to manage a large farming estate built up by his mother's uncle, a former banker. In 1848 he married his cousin Fanny Prausnitzer, and the couple had six children. For several years Kronecker focused on business, and although he continued to study mathematics as a hobby and corresponded with Kummer, he published no mathematical results.[4] In 1853 he wrote a memoir on the algebraic solvability of equations extending the work of Évariste Galois on the theory of equations.
![](http://upload.wikimedia.org/wikipedia/commons/thumb/1/1c/KroneckerGrab.jpg/220px-KroneckerGrab.jpg)
Due to his business activity, Kronecker was financially comfortable, and thus he could return to Berlin in 1855 to pursue mathematics as a private scholar. Dirichlet, whose wife
Although he held no official university position, Kronecker had the right as a member of the Academy to hold classes at the University of Berlin and he decided to do so, starting in 1862. In 1866, when Riemann died, Kronecker was offered the mathematics chair at the University of Göttingen (previously held by Carl Friedrich Gauss and Dirichlet), but he refused, preferring to keep his position at the Academy. Only in 1883, when Kummer retired from the university, was Kronecker invited to succeed him and became an ordinary professor.[5] Kronecker was the supervisor of Kurt Hensel, Adolf Kneser, Mathias Lerch, and Franz Mertens, amongst others.
His philosophical view of mathematics put him in conflict with several mathematicians over the years, notably straining his relationship with Weierstrass, who almost decided to leave the university in 1888.[3] Kronecker died on 29 December 1891 in Berlin, several months after the death of his wife. In the last year of his life, he converted to Christianity.[2] He is buried in the Alter St Matthäus Kirchhof cemetery in Berlin-Schöneberg, close to Gustav Kirchhoff.
Scientific activity
Mathematics research
An important part of Kronecker's research focused on
In algebraic number theory Kronecker introduced the theory of divisors as an alternative to Dedekind's theory of ideals, which he did not find acceptable for philosophical reasons. Although the general adoption of Dedekind's approach led Kronecker's theory to be ignored for a long time, his divisors were found useful and were revived by several mathematicians in the 20th century.[7]
Kronecker also contributed to the concept of
Also named for Kronecker are the
Philosophy of mathematics
Kronecker's finitism made him a forerunner of intuitionism in foundations of mathematics.
Honours
Kronecker was elected as a member of several academies:[2]
- Prussian Academy of Sciences (1861)
- French Academy of Sciences (1868)
- Royal Society (1884).
The
Publications
- Kronecker, Leopold (1978) [1901], Vorlesungen über Zahlentheorie, Berlin, New York: MR 0529431
- Kronecker, Leopold (1968) [1895], MR 0237286
References
- ISBN 978-1400829040
Weber, Heinrich L. 1891–1892. Kronecker. Jahresbericht der Deutschen Mathematiker-Vereinigung 2:5-23. (The quote is on p. 19.) - ^ ISBN 978-1-906165-22-2.
- ^ ISBN 978-1-85233-425-3.
- ISBN 978-981-4282-29-1.
- ISBN 978-0-8160-5338-4.
- ISBN 978-0-691-11880-2.
- ISBN 978-3-7643-7002-2.
Further reading
- ISBN 978-0-671-62818-5
- ISBN 978-0-393-32229-3
- S2CID 120885744
- Edwards, Harold (1989), "Kronecker's Views on the Foundations of Mathematics", in Rowe, D. E.; McCleary, J. (eds.), The History of Modern Mathematics, vol. 1, Academic Press, pp. 67–78, ISBN 978-0-12-599661-7
- Kronecker, Leopold (1996) [1887], "On the concept of number", in Ewald, William B. (ed.), From Kant to Hilbert: A Source Book in the Foundations of Mathematics, vol. 2, Oxford University Press, pp. 947–955, ISBN 978-0-19-850536-5
- ISBN 978-0-674-32449-7
- S2CID 177800385
External links
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