Karl Sigmund
Encyclopedia
Karl Sigmund is a Professor of Mathematics at the University of Vienna
and one of the pioneers of evolutionary game theory
.
, 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 Etudes 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 Josef Hofbauer on mathematical ecology
, chemical kinetics
and population genetics
, but especially on the new field of evolutionary game dynamics and replicator equation
s. 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
.
, 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.
In 2010 he received an honorary doctorate (Doctor Philosophiae Honoris Causa) from the University of Helsinki
.
. 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. Karl Menger
was a member of the Vienna Circle.
; 11 edited volumes; 25 essays; and 5 co-authored books. He has written and published a book called Games of Life, printed in 1994 by Oxford University Press, which has been translated into several languages.
University of Vienna
The University of Vienna is a public university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world...
and one of the pioneers of evolutionary game theory
Evolutionary game theory
Evolutionary game theory is the application of Game Theory to evolving populations of lifeforms in biology. EGT is useful in this context by defining a framework of contests, strategies and analytics into which Darwinian competition can be modelled. It originated in 1973 with John Maynard Smith...
.
Career
Sigmund was schooled in the Lycée Francais de Vienne. From 1963 to 1968 he studied at the Institute of Mathematics at the University of ViennaUniversity of Vienna
The University of Vienna is a public university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world...
, 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 Etudes in Bures sur Yvette near Paris ('69-'70), the Hebrew University in Jerusalem (1970-'71), the University of Vienna
University of Vienna
The University of Vienna is a public university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world...
(1971-'72) and the Austrian Academy of Sciences
Austrian Academy of Sciences
The Austrian Academy of Sciences is a legal entity under the special protection of the Federal Republic of Austria. According to the statutes of the Academy its mission is to promote the sciences and humanities in every respect and in every field, particularly in fundamental research...
(1972-'73). In 1972 he received habilitation
Habilitation
Habilitation is the highest academic qualification a scholar can achieve by his or her own pursuit in several European and Asian countries. Earned after obtaining a research doctorate, such as a PhD, habilitation requires the candidate to write a professorial thesis based on independent...
.
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
Ergodic theory
Ergodic theory is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics....
and dynamical systems. From 1977 on, Sigmund became increasingly interested in different fields of biomathematics, and collaborated with Peter Schuster
Peter Schuster
Peter K. Schuster is a renowned theoretical chemist, known for his work with the German Nobel Laureate Manfred Eigen in developing the quasispecies model...
and Josef Hofbauer on mathematical ecology
Theoretical ecology
Theoretical ecology is the scientific discipline devoted to the study of ecological systems using theoretical methods such as simple conceptual models, mathematical models, computational simulations, and advanced data analysis...
, chemical kinetics
Chemical kinetics
Chemical kinetics, also known as reaction kinetics, is the study of rates of chemical processes. Chemical kinetics includes investigations of how different experimental conditions can influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition...
and population genetics
Population genetics
Population genetics is the study of allele frequency distribution and change under the influence of the four main evolutionary processes: natural selection, genetic drift, mutation and gene flow. It also takes into account the factors of recombination, population subdivision and population...
, but especially on the new field of evolutionary game dynamics and replicator equation
Replicator equation
In mathematics, the replicator equation is a deterministic monotone non-linear and non-innovative game dynamic used in evolutionary game theory. The replicator equation differs from other equations used to model replication, such as the quasispecies equation, in that it allows the fitness landscape...
s. Together with Martin Nowak
Martin Nowak
Martin A. Nowak is Professor of Biology and Mathematics and Director of the Program for Evolutionary Dynamics at Harvard University.-Career:Martin Nowak studied biochemistry and mathematics at the University of Vienna, and earned his Ph. D. in 1989, working with Peter Schuster on quasi-species...
, 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
Laxenburg
Laxenburg is a town in the district of Mödling in the Austrian state of Lower Austria, near Vienna.- History :The place is well-known for its castle, Schloss Laxenburg, which, beside Schönbrunn, was the most important summer seat of the Habsburg dynasty....
, Lower Austria
Lower Austria
Lower Austria is the northeasternmost state of the nine states in Austria. The capital of Lower Austria since 1986 is Sankt Pölten, the most recently designated capital town in Austria. The capital of Lower Austria had formerly been Vienna, even though Vienna is not officially part of Lower Austria...
.
Honours and recognition
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 SocietyAustrian Mathematical Society
The Austrian Mathematical Society is the national mathematical society of Austria and a member society of the European Mathematical Society.-History:...
, 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
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
in 1998.
In 2010 he received an honorary doctorate (Doctor Philosophiae Honoris Causa) from the University of Helsinki
University of Helsinki
The University of Helsinki is a university located in Helsinki, Finland since 1829, but was founded in the city of Turku in 1640 as The Royal Academy of Turku, at that time part of the Swedish Empire. It is the oldest and largest university in Finland with the widest range of disciplines available...
.
Other details
During the last decade, Sigmund became increasingly interested in the history of mathematics and in particular, the Vienna CircleVienna Circle
The Vienna Circle was an association of philosophers gathered around the University of Vienna in 1922, chaired by Moritz Schlick, also known as the Ernst Mach Society in honour of Ernst Mach...
. He co-edited the mathematical works of Hans Hahn
Hans Hahn
Hans Hahn was an Austrian mathematician who made contributions to functional analysis, topology, set theory, the calculus of variations, real analysis, and order theory.-Biography:...
and Karl Menger
Karl Menger
Karl Menger was a mathematician. He was the son of the famous economist Carl Menger. He is credited with Menger's theorem. He worked on mathematics of algebras, algebra of geometries, curve and dimension theory, etc...
and organised in 2001 an exhibition on the exodus of Austrian mathematicians fleeing the Nazis
Nazism
Nazism, the common short form name of National Socialism was the ideology and practice of the Nazi Party and of Nazi Germany...
and in 2006 an exhibition on Kurt Gödel
Kurt Gödel
Kurt Friedrich Gödel was an Austrian logician, mathematician and philosopher. Later in his life he emigrated to the United States to escape the effects of World War II. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the...
. From 2003 to 2005 he was vice-president of the Austrian Science Fund
Austrian Science Fund
The Fonds zur Förderung der wissenschaftlichen Forschung is the most important Austrian funding organization for basic research. The FWF supports research in science, engineering, and the humanities through a large variety of grant programmes, prizes and by funding infrastructure...
(FWF).
Because of his intimate knowledge of the Vienna Circle, Sigmund was invited to the Illinois Institute of Technology
Illinois Institute of Technology
Illinois Institute of Technology, commonly called Illinois Tech or IIT, is a private Ph.D.-granting university located in Chicago, Illinois, with programs in engineering, science, psychology, architecture, business, communications, industrial technology, information technology, design, and law...
to speak at the inaugural Remembering Menger event on April 9, 2007. Karl Menger
Karl Menger
Karl Menger was a mathematician. He was the son of the famous economist Carl Menger. He is credited with Menger's theorem. He worked on mathematics of algebras, algebra of geometries, curve and dimension theory, etc...
was a member of the Vienna Circle.
Publications
Sigmund's publications include 133 scientific papers, including 18 in NatureNature (journal)
Nature, first published on 4 November 1869, is ranked the world's most cited interdisciplinary scientific journal by the Science Edition of the 2010 Journal Citation Reports...
; 11 edited volumes; 25 essays; and 5 co-authored books. He has written and published a book called Games of Life, printed in 1994 by Oxford University Press, which has been translated into several languages.