International Society for

Group Theory in Cognitive Science



Society President:
Michael Leyton (USA)

Eloise Carlton (USA),
Vladimir Dorodnitsyn (Russia),
Roy Eagleson (Canada),
Athanassios Economou (USA),
Mario Ferraro (Italy),
Victor Finn (Russia),
Nathaniel Friedman (USA),
Ted Goranson (USA),
Bill Hammel (USA),
Slavik Jablan (Jugoslavia),
Vladimir Koptsik (Russia),
Joan Lasenby (UK),
Yanxi Liu (USA),
Guerino Mazzola (Switzerland),
Denes Nagy (Japan),
Thomas Noll (Germany),
Frank Park (Korea),
Jean Petitot (France),
Vladimir Petrov (Russia),
Robin Popplestone (USA),
Robert Rosen (Canada),
Charles Schmidt (USA),
Barry Smith (USA),
George Stiny (USA),
Alexander Voloshinov (Russia),
Dorothy Washburn (USA),
Robert Wechsler (Germany).


Group theory in:

Robotics, Problem-Solving, Planning, Learning, Language, Perception, Art, Design, Engineering, Manufacturing, Epistemology, Measurement, Computation, Neuroscience, Anthropology, Semiotics.

Group Theory has emerged as a powerful tool for analyzing cognitive structure. The number of cognitive disciplines using group theory is now enormous. The power of group theory lies in its ability to identify organization, and to express organization in terms of generative actions that structure a space. The International Society for Group Theory in Cognitive Science is an academic organization devoted to the dissemination of significant group-theoretic research in all the areas of Cognitive Science.

The society has a number of divisions, covering different research areas. These include:
Division of Mathematical Robotics
Division of Perception and Computer Vision
Division of Neuroscience
Division of Mathematical and Computational Aesthetics
Division of Engineering and Manufacturing


The Division of Mathematical and Computational Aesthetics is simultaneously an independent society called the International Society for Mathematical and Computational Aesthetics. Although its board is drawn from members of the above board who are working on mathematical and computational aesthetics, it also has additional members who use other branches of mathematics besides group theory on the analysis of aesthetics. You can obtain information on this by clicking:


The society maintains a large archive of papers and books on the use of group theory in cognitive science.   It is our goal to make this archive as complete as possible.  If you are working in the area of group-theoretic cognitive science, or know of papers in this area, please inform us. These will be entered into the society archive.  Furthermore, since most future papers will be written in formats accessible by the web, we can advertise your papers through the society web-pages and make them accessible through our site.  We are currently engaged in putting together an extensive handbook of group theory in cognitive science, as well as a book series and journal.


We are currently mounting descriptions of the major books on group-theoretic cognitive science. Please check back here for this.


The society is putting together a number of web tutorials and links on various branches of mathematics relevant to group-theoretic cognitive science. 


The following site is an entire book on the web, on finite state machines, regular expressions, etc., which gives extensive mathematical discussion together with many animations.   It was created by board-member Chuck Schmidt:


The following is a lengthy physics-based book on Lie groups that can be downloaded from the internet. It is written by board-member Bill Hammel:

Please check back here for additional tutorials as they appear.

If you wish to find out more about this society, please contact: Professor Michael Leyton, Center for Discrete Mathematics & Theoretical Computer Science (DIMACS), Rutgers University: