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Wilhelm Wirtinger (15 July 1865 – 15 January 1945) was an Austrian mathematician, working in complex analysis, geometry, algebra, number theory, Lie groups and knot theory.

Wilhelm Wirtinger
Wilhelm Wirtinger.jpg
Wilhelm Wirtinger
Born(1865-07-15)15 July 1865
Died15 January 1945(1945-01-15) (aged 79)
Ybbs an der Donau, Greater German Reich
Alma materUniversity of Vienna
Known forComplex analysis of one and several variables
AwardsSylvester Medal (1907)
Scientific career
InstitutionsUniversity of Innsbruck
University of Vienna
Doctoral advisorEmil Weyr
Gustav Ritter von Escherich
Doctoral studentssee the "Teaching activity" section


He was born at Ybbs 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.


In 1907 the Royal Society of London awarded him the Sylvester Medal, for his contributions to the general theory of functions.


Research activityEdit

He worked in many areas of mathematics, publishing 71 works.[1] His first significant work, published in 1896, was on theta functions. He proposed as a generalization of eigenvalues, the concept of the spectrum of an operator, in an 1897 paper; the concept was further extended by David Hilbert and now it forms the main object of investigation in the field of spectral theory. Wirtinger also contributed papers on complex analysis, geometry, algebra, number theory, and Lie groups. He collaborated with Kurt Reidemeister on knot theory, showing in 1905 how to compute the knot group.[2] Also, he was one of the editors of the Analysis section of Klein's encyclopedia.

During a conversation, Wirtinger attracted the attention of Stanisław Zaremba to a particular boundary value problem, which later became known as the mixed boundary value problem.[3]

Teaching activityEdit

A partial list of his students includes the following scientists:

Selected publicationsEdit

See alsoEdit


  1. ^ According to Hornich (1948).
  2. ^ I.e. the fundamental group of a knot complement.
  3. ^ According to Zaremba himself: see the "mixed boundary condition" entry for details and references.

Biographical referencesEdit

External linksEdit