Rudolf Lipschitz
Encyclopedia
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 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).
s 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.
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and professor at the University of Bonn
University of Bonn
The University of Bonn is a public research university located in Bonn, Germany. Founded in its present form in 1818, as the linear successor of earlier academic institutions, the University of Bonn is today one of the leading universities in Germany. The University of Bonn offers a large number...
from 1864. Peter Gustav Dirichlet was his teacher. He supervised the early work of Felix Klein
Felix Klein
Christian Felix Klein was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory...
.
While Lipschitz gave his name to the Lipschitz continuity condition
Lipschitz continuity
In mathematical analysis, Lipschitz continuity, named after Rudolf Lipschitz, is a strong form of uniform continuity for functions. Intuitively, a Lipschitz continuous function is limited in how fast it can change: for every pair of points on the graph of this function, the absolute value of the...
, he worked in a broad range of areas. These included number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, algebras
Algebra over a field
In mathematics, an algebra over a field is a vector space equipped with a bilinear vector product. That is to say, it isan algebraic structure consisting of a vector space together with an operation, usually called multiplication, that combines any two vectors to form a third vector; to qualify as...
with involution, mathematical analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
, differential geometry and classical mechanics
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...
.
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, a forgotten pioneer
Lipschitz discovered Clifford algebraClifford algebra
In mathematics, Clifford algebras are a type of associative algebra. As K-algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems. The theory of Clifford algebras is intimately connected with the theory of quadratic forms and orthogonal...
s 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
Claude Chevalley
Claude Chevalley 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...
(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.