Wilhelm Wirtinger (19 July 1865 – 16 January 1945) was an

Austria Austria, , bar, Östareich officially the Republic of Austria, is a country in the southern part of Central Europe, lying in the Eastern Alps. It is a federation of nine states, one of which is the capital, Vienna, the most populous ...

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, structure, space, models, and change. History On ...

, working in

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathemati ...

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...

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 arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

Lie group In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additio ...

s and

knot theory In the mathematical field of topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are ...

Biography

He was born at Ybbs on the Danube and studied at the

University of Vienna The University of Vienna (german: Universität Wien) is a public research university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world. With its long and rich histor ...

, where he received his doctorate in 1887, and 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 a ...

in 1890. Wirtinger was greatly influenced by

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 group ...

with whom he studied at the

University of Berlin Humboldt-Universität zu Berlin (german: Humboldt-Universität zu Berlin, abbreviated HU Berlin) is a German public research university in the central borough of Mitte in Berlin. It was established by Frederick William III on the initiative o ...

and the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded ...

Honours

In 1907 the

Royal Society of London The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

awarded him the

Sylvester Medal The Sylvester Medal is a bronze medal awarded by the Royal Society (London) for the encouragement of mathematical research, and accompanied by a £1,000 prize. It was named in honour of James Joseph Sylvester, the Savilian Professor of Geometry a ...

, for his contributions to the general theory of functions.

Work

Research activity

He worked in many areas of mathematics, publishing 71 works. His first significant work, published in 1896, was on

theta function In mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. As Grassmann algebras, they appear in quantum field theo ...

s. He proposed as a generalization of

eigenvalues In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted b ...

, the concept of the

spectrum of an operator In mathematics, particularly in functional analysis, the spectrum of a bounded linear operator (or, more generally, an unbounded linear operator) is a generalisation of the set of eigenvalues of a matrix. Specifically, a complex number \lambda is ...

, in an 1897 paper; the concept was further extended by

David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many a ...

and now it forms the main object of investigation in the field of

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 o ...

. Wirtinger also contributed papers on

, and

s. He collaborated with

Kurt Reidemeister Kurt Werner Friedrich Reidemeister (13 October 1893 – 8 July 1971) was a mathematician born in Braunschweig (Brunswick), Germany. Life He was a brother of Marie Neurath. Beginning in 1912, he studied in Freiburg, Munich, Marburg, and Göttinge ...

, showing in 1905 how to compute the

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(\mathbb^3 \setminus K). Other conventions co ...

. Also, he was one of the editors of the ''Analysis'' section of

Klein's encyclopedia Felix Klein's ''Encyclopedia of Mathematical Sciences'' is a German mathematical Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, an ...

. During a conversation, Wirtinger attracted the attention of Stanisław Zaremba to a particular

boundary value problem In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to t ...

, which later became known as the mixed boundary value problem.According to Zaremba himself: see the "

mixed boundary condition In mathematics, a mixed boundary condition for a partial differential equation defines a boundary value problem in which the solution of the given equation is required to satisfy different boundary conditions on disjoint parts of the boundary of ...

" entry for details and references.

Teaching activity

A partial list of his students includes the following scientists: * *

Wilhelm Blaschke Wilhelm Johann Eugen Blaschke (13 September 1885 – 17 March 1962) was an Austrian mathematician working in the fields of differential and integral geometry. Education and career Blaschke was the son of mathematician Josef Blaschke, who taught ...

Hilda Geiringer Hilda Geiringer (28 September 1893 – 22 March 1973), also known as Hilda von Mises and Hilda Pollaczek-Geiringer, was an Austrian mathematician. Life Geiringer was born in 1893 in Vienna, Austria into a Jewish family. Her father, Ludwig Geiri ...

Kurt Gödel Kurt Friedrich Gödel ( , ; April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel had an imme ...

* Wilhelm Gross *

Eduard Helly Eduard Helly (June 1, 1884 in Vienna – 28 November 1943 in Chicago) was a mathematician after whom Helly's theorem, Helly families, Helly's selection theorem, Helly metric, and the Helly–Bray theorem were named. Life Helly earned his doct ...

* *

Erwin Schrödinger Erwin Rudolf Josef Alexander Schrödinger (, ; ; 12 August 1887 – 4 January 1961), sometimes written as or , was a Nobel Prize-winning Austrian physicist with Irish citizenship who developed a number of fundamental results in quantum theory ...

* *

Olga Taussky-Todd Olga Taussky-Todd (August 30, 1906, Olomouc, Austria-Hungary (present-day Olomouc, Czech Republic) – October 7, 1995, Pasadena, California) was an Austrian and later Czech-American mathematician. She published more than 300 research papers on a ...

Leopold Vietoris Leopold Vietoris (; ; 4 June 1891 – 9 April 2002) was an Austrian mathematician, World War I veteran and supercentenarian. He was born in Radkersburg and died in Innsbruck. He was known for his contributions to topology—notably the Mayer–V ...

Roland Weitzenböck Roland Weitzenböck (26 May 1885 – 24 July 1955) was an Austrian mathematician working on differential geometry who introduced the Weitzenböck connection. He was appointed professor of mathematics at the University of Amsterdam in 1923 at the ...

Selected publications

*, available a
DigiZeitschirften
In this important paper, Wirtinger introduces several important concepts in the theory of functions of several complex variables, namely

Wirtinger derivatives In complex analysis of one and several complex variables, Wirtinger derivatives (sometimes also called Wirtinger operators), named after Wilhelm Wirtinger who introduced them in 1927 in the course of his studies on the theory of functions of sev ...

and the tangential Cauchy–Riemann condition. The paper is deliberately written from a formal point of view, i.e. without giving a rigorous derivation of the properties deduced. *. *.

Notes

Biographical references

*, available a
DigiZeitschirften
An ample commemorative paper containing a list of Wirtinger's publications.

External links

* * * from the ICMI
History of ICMI
'

Web site A website (also written as a web site) is a collection of web pages and related content that is identified by a common domain name and published on at least one web server. Examples of notable websites are Google, Facebook, Amazon, and Wikipe ...

. {{DEFAULTSORT:Wirtinger, Wilhelm 19th-century Austrian mathematicians Austro-Hungarian mathematicians 1865 births 1945 deaths Royal Medal winners University of Vienna alumni 20th-century Austrian mathematicians People from Melk District Academic staff of the University of Innsbruck Academic staff of the University of Vienna