14 May 1832|
|Died||7 October 1903
|Institutions||University of Bonn|
|Doctoral advisor||Peter Gustav Lejeune Dirichlet
|Doctoral students||Felix Klein|
|Known for||Lipschitz continuity
Lipschitz integral condition
Rudolf Otto Sigismund Lipschitz (14 May 1832 – 7 October 1903) was a German mathematician and professor at the University of Bonn from 1864. Peter Gustav Lejeune Dirichlet was his teacher. He supervised the early work of Felix Klein. While Lipschitz gave his name to the Lipschitz continuity condition, he worked in a broad range of areas. These included number theory, algebras with involution, mathematical analysis, differential geometry and classical mechanics.
He wrote: 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).
Lipschitz was born the son of a landowner and was raised at his father's estate at Bönkein which was near Königsberg. He grew up a sickly child but nonetheless entered the University of Königsberg at a young age, graduating with a PhD in 1853. In 1857 he married Ida Pascha, the daughter of one of the landowners with an estate near to his father's. Then in 1862 he became an extraordinary professor at Breslau.
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.
- Lipschitz domain
- Lipschitz continuity
- Continuous function#Uniform.2C H.C3.B6lder and Lipschitz continuity
- Metric space#Lipschitz-continuous maps and contractions
- Modulus of continuity#Concave moduli.2C and Lipschitz approximation
- Dini–Lipschitz criterion
- Dini-Lipschitz test
- R. Lipschitz (1880). "Principes d'un calcul algébrique qui contient comme espèces particulières le calcul des quantités imaginaires et des quaternions". C. R. Acad. Sci. Paris 91: 619–621, 660–664.
- R. Lipschitz (signed) (1959). "Correspondence". Ann. Of Math. 69 (1): 247–251. doi:10.2307/1970102.
- Chevalley, Claude (1997). The Algebraic Theory of Spinors and Clifford Algebras (Collected Works Vol. 2 ed.). Springer-Verlag. pp. 48, 113. ISBN 978-3-540-57063-9.
- Lounesto, Pertti (1997). Clifford Algebras and Spinors. Cambridge University Press. p. 220. ISBN 978-0-521-59916-0.
- Jacques Helmstetter, Artibano Micali: Quadratic Mappings and Clifford Algebras, Birkhäuser, 2008, ISBN 978-3-7643-8605-4 Introduction, p. ix ff.
- O'Connor, John J.; Robertson, Edmund F., "Rudolf Lipschitz", MacTutor History of Mathematics archive, University of St Andrews.
- Rudolf Lipschitz at the Mathematics Genealogy Project
- H. Kortum. "1903 Obituary". In Jahresbericht DMV 16. pp. 56–59. Retrieved 16 July 2006. (digitalized document, provided without fee by Göttingen Digitalization Project, in German)