**Wilhelm Wirtinger** was an Austrian mathematician who worked in complex analysis, geometry, algebra, number theory, Lie groups and knot theory.

- Johannes Wirtinger was an outstanding scientist and medical researcher who made significant discoveries concerning typhus.
- Wirtinger studied mathematics at the University of Vienna, beginning his course in 1884.
- Gustav von Escherich had studied at the University of Vienna and worked at Graz before taking up a position in Vienna in 1884, the year Wirtinger began his course.
- He taught Wirtinger about the new approach to analysis which Weierstrass had developed.
- However, it was Emil Weyr who inspired Wirtinger with his courses on synthetic geometry and this led to Wirtinger's first two publications and his doctoral thesis.
- Along with William Osgood he attended Klein's seminar and Wirtinger and Klein became life-long friends.
- Wirtinger habilitated at the University of Vienna in 1890 and, in addition to teaching there, he was appointed as an assistant to Emanuel Czuber at the Technical University in Vienna.
- His most important work during these years, however, was the book Untersuchungen über Thetafunktionen Ⓣ(Studies of theta functions) (1895) which led to Wirtinger receiving the Beneke Prize from the Faculty of Philosophy of Göttingen.
- In it Wirtinger combined ideas from Riemann's function theory with ideas from Klein to prove results of great significance.
- It was this book, which he had developed from work begun at Göttingen, that brought Wirtinger's name to the fore as a leading mathematician.
- Wirtinger's range of mathematics was quite exceptional.
- This list would certainly make one believe that Wirtinger's range within pure mathematics was very wide but his interests went well beyond pure mathematics.
- As a consequence of the outstanding work he had published, in 1895 Wirtinger was promoted Extraordinary Professor at Vienna where he lectured on a wide variety of topics and continued to produce outstanding research.
- He also worked on a paper with Adolf Krazer (1858-1926) but Wirtinger became occupied with other work and the paper appeared with Krazer as the only author.
- Many mathematicians at this stage in their careers wrote textbooks based on lecture courses they were giving but Wirtinger was so full of new ideas and solving problems that he was totally engrossed in research.
- Wirtinger returned to a chair at the University of Vienna in 1903.
- Wirtinger held this chair for 32 years.
- Another of Wirtinger's colleagues was Hans Hahn who was a privatdozent in Vienna from 1905 and, after several years away, returned to a chair in Vienna in 1921.
- Wirtinger also took on administrative duties in the University, in particular he was Dean of the Faculty of Arts in the academic year 1915-16.
- Let us say a little about Wirtinger's teaching at the University of Vienna.
- In the other two years Wirtinger gave advanced lectures on function theory and on algebraic or elliptic functions.
- In addition to these courses, Wirtinger ran a two-hour seminar but he here found it somewhat harder to interact with students due to his deafness and, as a consequence, usually lectured rather than encouraging student contributions.
- We should also mention, when describing his teaching, that Wirtinger was interested in the history of mathematics and also in philosophy.
- In 1906 Wirtinger published Über die Entwicklung einiger mathematischer Begriffe in neuerer Ⓣ(On the development of some recent mathematical concepts).
- Not so Wirtinger, who sat and watched the waves on the lake and thought about the mathematical theory which lay behind them.
- When Kurt Reidemeister was appointed as associate professor of geometry at the University of Vienna in 1923 he became a colleague of Wirtinger.
- At that time Wirtinger was interested in knot theory and he showed Reidemeister how to compute the fundamental group of a knot from its projection.
- Wirtinger's method was first published in work of Emil Artin in 1925.
- Wirtinger certainly did not lessen his mathematical activity as he grew older.
- Among the mathematicians who Wirtinger taught while he held the chair at Vienna are Otto Schreier, Kurt Gödel, Johann Radon and Olga Taussky-Todd.
- It was not only with his research and teaching that Wirtinger contributed to the mathematical sciences but also through his interest in mathematical education.
- In 1936, after the reestablishment of IMUK, Wirtinger was elected an honorary member of the committee.
- Wirtinger received many honours for his achievements.
- In 1907 the Royal Society of London awarded him their Sylvester Medal and Wirtinger travelled to England to receive the honour.
- The title was conferred on Wirtinger (and others including Castelnuovo, Dickstein, Enriques and Loria) at the International Congress of Mathematicians held in Oslo.

Born 15 July 1865, Ybbs an der Donau, Melk, Niederösterreich, Austria. Died 15 January 1945, Ybbs an der Donau, Melk, Niederösterreich, Austria.

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Origin Austria

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive