Rudolf Lipschitz

Rudolf Otto Sigismund Lipschitz (14 May 1832 – 7 October 1903) was a German mathematician who made contributions to mathematical analysis (where he gave his name to the Lipschitz continuity condition) and differential geometry, as well as number theory, algebras with involution and classical mechanics.

Biography

Rudolf Lipschitz was born on 14 May 1832 in Königsberg. He was the son of a landowner and was raised at his father's estate at Bönkein which was near Königsberg. He entered the University of Königsberg when he was 15, but later moved to the University of Berlin where he studied with Gustav Dirichlet. Despite having his studies delayed by illness, in 1853 Lipschitz graduated with a PhD in Berlin.

After receiving his PhD, Lipschitz started teaching at local Gymnasiums. In 1857 he married Ida Pascha, the daughter of one of the landowners with an estate near to his father's. In 1857 he earned his habilitation at the University of Bonn and remained there as a privatdozent. In 1862 Lipschitz became an extraordinary professor at the University of Breslau where he spent the following two years. In 1864 Lipschitz moved back to Bonn as a full professor. He was the first Jewish full professor at Bonn University. He was appointed Bonn's first chair of Mathematics in 1869. He remained there for the rest of his career. Here he examined the dissertation of Felix Klein. Lipschitz died on 7 October 1903 in Bonn.

Rediscovery of Clifford algebra

Lipschitz discovered Clifford algebras in 1880, two years after William K. Clifford (1845–1879) and independently of him, and he was the first to use them in the study of orthogonal transformations. Up to 1950 people mentioned "Clifford–Lipschitz numbers" when they referred to this discovery of Lipschitz. Yet Lipschitz's name suddenly disappeared from the publications involving Clifford algebras; for instance Claude Chevalley (1909–1984) gave the name " Clifford group" to an object that is never mentioned in Clifford's works, but stems from Lipschitz's. Pertti Lounesto (1945–2002) contributed greatly to recalling the importance of Lipschitz's role.Jacques Helmstetter, Artibano Micali: ''Quadratic Mappings and Clifford Algebras'', Birkhäuser, 2008,
Introduction, p. ix ''ff.''
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Selected publications

''Lehrbuch der Analysis'' (two volumes, Bonn 1877, 1880);
''Wissenschaft und Staat'' (Bonn, 1874);
''Untersuchungen über die Summen von Quadraten'' (Bonn, 1886);
''Bedeutung der theoretischen Mechanik'' (Berlin, 1876).

See also

* Cauchy–Lipschitz theorem
* Lipschitz domain
* Lipschitz quaternion
* Lipschitz continuity
** Uniform, Hölder and Lipschitz continuity
* Lipschitz distance
* Lipschitz-continuous maps and contractions
* Concave moduli and Lipschitz approximation
* Dini–Lipschitz criterion
* Dini–Lipschitz test

References

External links

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* (digitalized document, provided without fee by Göttingen Digitalization Project, in German)

{{DEFAULTSORT:Lipschitz, Rudolf
19th-century German mathematicians
1832 births
1903 deaths
University of Bonn faculty
Scientists from Königsberg
People from the Province of Prussia
Mathematical analysts