**Karl Sigmund** is an Austrian mathematician who is one of the pioneers of evolutionary game theory. He is also interested in the history of science.

- Although it had a number of French pupils, at the time when Karl attended the vast majority of the pupils were Austrian.
- Sigmund undertook research advised by Leopold Schmetterer and was awarded his doctorate in 1968 for his thesis Über Verteilungsmaße von Maßfolgen auf lokalkompakten Gruppen Ⓣ(On distribution measures on locally compact groups).
- After completing his doctorate, Sigmund went first as a postdoctoral worker for a year to the University of Manchester in England where he spent the academic year 1968-69.
- Sigmund then spent a second postdoctoral year, 1969-70, at the Institut des Hautes Études, Bures sur Yvette, France.
- Sigmund's second paper, published in 1970, was Generic Properties of Invariant Measures for Axiom A-Diffeomorphisms.
- When Sigmund published this 1970 paper he gave his address as Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel.
- Sigmund spent two further years undertaking postdoctoral studies both back in Austria, the academic year 1971-72 being spent at the University of Vienna and 1972-73 also spent in Vienna at the Austrian Academy of Sciences.
- Throughout the various years leading to his appointment as a full professor in Vienna, Sigmund had continued to work on ergodic theory, measure theory, topological dynamics and dynamical systems.
- A major change in the direction of Sigmund's research occurred around 1977 after discussions with the theoretical biochemist Peter Schuster and the mathematical biologist Josef Hofbauer.
- Sigmund and Hofbauer began collaborating in 1978 and the result of this collaboration was the book The Theory of Evolution and Dynamical Systems (1988).
- The mathematician Karl Sigmund was there and gave a talk on what was a new topic for him: the prisoner's dilemma.
- Or we walked in the Vienna forest, visiting a meadow called 'Himmel' (Heaven), where a sign noted that here Sigmund Freud first understood the nature of dreams.
- Sigmund discussed the prisoner's dilemma and similar topics in his books Evolutionary Games and Population Dynamics (1998), The Calculus of Selfishness (2010), and Games of Life: Explorations in Ecology, Evolution, and Behaviour (2017).
- Let us return to giving some details of Sigmund's career.
- Sigmund was head of the Institute of Mathematics at The University of Vienna in 1983-85.
- With such a range of interests, it is perhaps not entirely surprising that Sigmund should become interested in the history of science.
- They were right in the middle of an amazing philosophical firework, one that sent Ernst Mach, Ludwig Boltzmann, Karl Popper, and Wittgenstein soaring into the sky.
- Let us now look at some of the honours given to Sigmund.
- Also in 2012, Sigmund received the Isaacs' Award of the International Society on Dynamic Games.
- On Tuesday, 4 June 2013, the University of Vienna presented the "UNIVIE Teaching Award 2013" for outstanding teaching achievements to Karl Sigmund.
- A Symposium in honour of Sigmund was held at the University of Vienna in October 2015.

Born 26 July 1945, Gars am Kamp, Lower Austria, Austria.

View full biography at MacTutor

Origin Austria

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