Karl Sigmund (born July 26, 1945) is a Professor of Mathematics at the University of Vienna and one of the pioneers of evolutionary game theory.
Sigmund was schooled in the Lycée Francais de Vienne. From 1963 to 1968 he studied at the Institute of Mathematics at the University of Vienna, and obtained his Ph.D. under the supervision of Leopold Schmetterer. He spent his postdoctorate years (1968 to 1973) at Manchester ('68-'69), the Institut des hautes études scientifiques in Bures-sur-Yvette near Paris ('69-'70), the Hebrew University in Jerusalem (1970-'71), the University of Vienna (1971-'72) and the Austrian Academy of Sciences (1972-'73). In 1972 he received habilitation.
In 1973, Sigmund was appointed C3-professor at the University of Göttingen, and in 1974 became a full professor at the Institute of Mathematics in Vienna. His main scientific interest during these years was in ergodic theory and dynamical systems. From 1977 on, Sigmund became increasingly interested in different fields of biomathematics, and collaborated with Peter Schuster and on mathematical ecology, chemical kinetics and population genetics, but especially on the new field of evolutionary game dynamics and replicator equations. Together with Martin Nowak, Christoph Hauert and Hannelore Brandt, he worked on game dynamical approaches to questions related with the evolution of cooperation in biological and human populations.
Since 1984, Sigmund has also worked as a part-time scientist at the International Institute for Applied Systems Analysis (IIASA) in Laxenburg, Lower Austria.
Sigmund was head of the Institute of Mathematics at the University of Vienna from 1983 to 1985, managing editor of the scientific journal Monatshefte für Mathematik from 1991 to 2001, vice-president (1995 to 1997) and president (1997 to 2001) of the Austrian Mathematical Society, corresponding member (1996) and full member (1999) of the Austrian Academy of Sciences, and member of the Leopoldina (2003). He has also given many plenary lectures, for instance at the International Congress of Mathematicians in 1998. He was awarded the Gauss Lectureship in 2003.
In 2010 he received an honorary doctorate (Doctor Philosophiae Honoris Causa) from the University of Helsinki. In 2012 he received the Isaacs Award.
During the last decade, Sigmund became increasingly interested in the history of mathematics and in particular, the Vienna Circle. He co-edited the mathematical works of Hans Hahn and Karl Menger and organised in 2001 an exhibition on the exodus of Austrian mathematicians fleeing the Nazis and in 2006 an exhibition on Kurt Gödel. From 2003 to 2005 he was vice-president of the Austrian Science Fund (FWF).
Because of his intimate knowledge of the Vienna Circle, Sigmund was invited to the Illinois Institute of Technology to speak at the inaugural Remembering Menger event on April 9, 2007.
The publication of thousands of documents by the United States Department of Justice related to Jeffrey Epstein on January 30, 2026 has revealed that Karl Sigmund had at least two private meetings with Epstein, one on September 15, 2018 in Epstein's private New York City residence (see the document with label EFTA00481644), the other on March 22, 2019 at Café Landtmann in Vienna (see the document with label EFTA01034682), four months before Epstein's final arrest. These meetings had been arranged by Sigmund's former doctoral student Martin Nowak. In his exchange with Epstein on the second meeting, Sigmund also tried to establish contact with the Rothschild family to promote the work of his wife . Asked by Epstein if his wife wasn't worried about his "bad press", Sigmund responds, "your suspicion 're bad press' is totally unfounded! Completely off the mark! The best way to dispel any lingering doubts would be if I brought Anna along for our next treff in Café Landmann."
Sigmund's publications include 133 scientific papers, including 18 in Nature; 11 edited volumes; 25 essays; and 5 co-authored books.