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Rudolf Otto Sigismund Lipschitz (14 May 1832 – 7 October 1903) was a German
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
who made contributions to
mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...
(where he gave his name to the Lipschitz continuity condition) and differential geometry, as well as
number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Math ...
,
algebras In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure consisting of a set together with operations of multiplication and additio ...
with involution and
classical mechanics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical ...
.


Biography

Rudolf Lipschitz was born on 14 May 1832 in
Königsberg Königsberg (, ) was the historic Prussian city that is now Kaliningrad, Russia. Königsberg was founded in 1255 on the site of the ancient Old Prussian settlement ''Twangste'' by the Teutonic Knights during the Northern Crusades, and was na ...
. 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 The University of Königsberg (german: Albertus-Universität Königsberg) was the university of Königsberg in East Prussia. It was founded in 1544 as the world's second Protestant academy (after the University of Marburg) by Duke Albert of Pruss ...
when he was 15, but later moved to the
University of Berlin The Humboldt University of Berlin (german: link=no, Humboldt-Universität zu Berlin, abbreviated HU Berlin) is a public research university in the central borough of Mitte in Berlin, Germany. The university was established by Frederick Will ...
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 Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including ...
at the
University of Bonn The Rhenish Friedrich Wilhelm University of Bonn (german: Rheinische Friedrich-Wilhelms-Universität Bonn) is a public research university located in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the ( en, Rhine ...
and remained there as a
privatdozent ''Privatdozent'' (for men) or ''Privatdozentin'' (for women), abbreviated PD, P.D. or Priv.-Doz., is an academic title conferred at some European universities, especially in German-speaking countries, to someone who holds certain formal qualific ...
. In 1862 Lipschitz became an extraordinary professor at the
University of Breslau A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase ''universitas magistrorum et scholarium'', which ...
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 Christian Felix Klein (; 25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and grou ...
. Lipschitz died on 7 October 1903 in Bonn.


Rediscovery of Clifford algebra

Lipschitz discovered
Clifford algebra In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra. As -algebras, they generalize the real numbers, complex numbers, quaternions and several other hyperc ...
s in 1880, two years after
William K. Clifford William Kingdon Clifford (4 May 18453 March 1879) was an English mathematician and philosopher. Building on the work of Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of the Clifford algebra named in h ...
(1845–1879) and independently of him, and he was the first to use them in the study of
orthogonal transformation In linear algebra, an orthogonal transformation is a linear transformation ''T'' : ''V'' → ''V'' on a real inner product space ''V'', that preserves the inner product. That is, for each pair of elements of ''V'', we have ...
s. 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 Claude Chevalley (; 11 February 1909 – 28 June 1984) was a French mathematician who made important contributions to number theory, algebraic geometry, class field theory, finite group theory and the theory of algebraic groups. He was a foun ...
(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.''
/ref>


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 In mathematics, a Lipschitz domain (or domain with Lipschitz boundary) is a domain in Euclidean space whose boundary is "sufficiently regular" in the sense that it can be thought of as locally being the graph of a Lipschitz continuous function. Th ...
* Lipschitz quaternion *
Lipschitz continuity In mathematical analysis, Lipschitz continuity, named after German mathematician Rudolf Lipschitz, is a strong form of uniform continuity for functions. Intuitively, a Lipschitz continuous function is limited in how fast it can change: there ...
** 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

* * * (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