Wilhelm Wirtinger
Encyclopedia
Wilhelm Wirtinger was an Austria
n mathematician
, working in complex analysis
, geometry
, algebra
, number theory
, Lie group
s and knot theory
.
on the Danube
and studied at the University of Vienna
, where he received his doctorate in 1887, and his habilitation
in 1890. Wirtinger was greatly influenced by Felix Klein
with whom he studied at the University of Berlin and the University of Göttingen.
, for his contributions to the general theory of functions.
into spectral theory
. Wirtinger also contributed papers on complex analysis
, geometry
, algebra
, number theory
, and Lie group
s. He collaborated with Kurt Reidemeister
on knot theory
, showing in 1905 how to compute the knot group
(fundamental group
of a knot complement
). Also, he was one of the editors of the Analysis section of Klein's encyclopedia
.
, Leopold Vietoris
, Erwin Schrödinger
, Olga Taussky-Todd, and Kurt Gödel
.
History of ICMI Web site.
Austria
Austria , officially the Republic of Austria , is a landlocked country of roughly 8.4 million people in Central Europe. It is bordered by the Czech Republic and Germany to the north, Slovakia and Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the...
n 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....
, working in complex analysis
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
, geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
, 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...
, Lie group
Lie group
In mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure...
s and knot theory
Knot theory
In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical language, a knot is an embedding of a...
.
Biography
He was born at YbbsYbbs
Ybbs is a river in Lower Austria, and in Austria also the common short form to designate the little town Ybbs an der Donau.Its source is located on the Zellerrain Pass near Mariazell...
on the Danube
Danube
The Danube is a river in the Central Europe and the Europe's second longest river after the Volga. It is classified as an international waterway....
and studied at the University of Vienna
University of Vienna
The University of Vienna is a public university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world...
, where he received his doctorate in 1887, and his habilitation
Habilitation
Habilitation is the highest academic qualification a scholar can achieve by his or her own pursuit in several European and Asian countries. Earned after obtaining a research doctorate, such as a PhD, habilitation requires the candidate to write a professorial thesis based on independent...
in 1890. Wirtinger was greatly influenced by 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...
with whom he studied at the University of Berlin and the University of Göttingen.
Honours
In 1907 the Royal Society of London awarded him the Sylvester MedalSylvester Medal
The Sylvester Medal is a bronze medal awarded by the Royal Society for the encouragement of mathematical research, and accompanied by a £1,000 prize...
, for his contributions to the general theory of functions.
Research activity
He worked in many areas of mathematics: according to he authored 71 works. His first significant work, published in 1896, was on theta functions. He proposed a generalization of eigenvalues, the spectrum of an operator, in an 1897 paper; the concept was extended by David HilbertDavid Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
into spectral theory
Spectral theory
In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces. It is a result of studies of linear algebra and the solutions of...
. Wirtinger also contributed papers on complex analysis
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
, geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
, 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...
, and Lie group
Lie group
In mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure...
s. He collaborated with Kurt Reidemeister
Kurt Reidemeister
Kurt Werner Friedrich Reidemeister was a mathematician born in Braunschweig , Germany.He received his doctorate in 1921 with a thesis in algebraic number theory at the University of Hamburg under the supervision of Erich Hecke. In 1923 he was appointed assistant professor at the University of Vienna...
on knot theory
Knot theory
In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical language, a knot is an embedding of a...
, showing in 1905 how to compute the knot group
Knot group
In mathematics, a knot is an embedding of a circle into 3-dimensional Euclidean space. The knot group of a knot K is defined as the fundamental group of the knot complement of K in R3,\pi_1....
(fundamental group
Fundamental group
In mathematics, more specifically algebraic topology, the fundamental group is a group associated to any given pointed topological space that provides a way of determining when two paths, starting and ending at a fixed base point, can be continuously deformed into each other...
of a knot complement
Knot complement
In mathematics, the knot complement of a tame knot K is the complement of the interior of the embedding of a solid torus into the 3-sphere. To make this precise, suppose that K is a knot in a three-manifold M. Let N be a thickened neighborhood of K; so N is a solid torus...
). Also, he was one of the editors of the Analysis section of Klein's encyclopedia
Klein's encyclopedia
In mathematics, Klein’s encyclopedia refers to a German mathematical encyclopedia published in six volumes from 1898 to 1933. Felix Klein and Wilhelm Meyer were organizers of the encyclopedia. Its title in English is "Encyclopedia of mathematical sciences including their applications", which is...
.
Teaching activity
Among his students were Wilhelm BlaschkeWilhelm Blaschke
Wilhelm Johann Eugen Blaschke was an Austro-Hungarian differential and integral geometer.His students included Shiing-Shen Chern, Luis Santaló, and Emanuel Sperner....
, Leopold Vietoris
Leopold Vietoris
Leopold Vietoris was an Austrian mathematician and a World War I veteran who gained additional fame by becoming a supercentenarian...
, Erwin Schrödinger
Erwin Schrödinger
Erwin Rudolf Josef Alexander Schrödinger was an Austrian physicist and theoretical biologist who was one of the fathers of quantum mechanics, and is famed for a number of important contributions to physics, especially the Schrödinger equation, for which he received the Nobel Prize in Physics in 1933...
, Olga Taussky-Todd, and Kurt Gödel
Kurt Gödel
Kurt Friedrich Gödel was an Austrian logician, mathematician and philosopher. Later in his life he emigrated to the United States to escape the effects of World War II. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the...
.
See also
- Wirtinger derivativesWirtinger derivativesIn complex analysis of one and several complex variables, Wirtinger derivatives , named after Wilhelm Wirtinger who introduced them in 1927 in the course of his studies on the theory of functions of several complex variables, are partial differential operators of the first order which behave in a...
- Wirtinger inequality (2-forms)Wirtinger inequality (2-forms)In mathematics, the Wirtinger inequality for 2-forms, named after Wilhelm Wirtinger, states that the exterior \scriptstyle\nuth power of the standard symplectic form ω, when evaluated on a simple -vector ζ of unit volume, is bounded above by \scriptstyle\nu!...
- Wirtinger's inequality for functions
- Wirtinger presentation
- Wirtinger's representation and projection theoremWirtinger's representation and projection theoremIn mathematics, Wirtinger's representation and projection theorem is a theorem proved by Wilhelm Wirtinger in 1932 in connection with some problems of approximation theory. This theorem gives the representation formula for the holomorphic subspace \left.\right. H_2 of the simple, unweighted...
External links
from the ICMIICMI
The International Commission on Mathematical Instruction is an international organisation with a focus on mathematics education, founded in 1908 at the International Congress of Mathematicians in Rome. It aims to improve teaching standards around the world, through programmes, workshops and...
History of ICMI Web site.