René Frédéric Thom

René Frédéric Thom (born September 2, 1923, Montbéliard, France—died October 25, 2002, Bures-sur-Yvette) was a French mathematician who was awarded the Fields Medal in 1958 for his work in topology.

Thom graduated from the École Normale Supérieure (now part of the Universities of Paris) in 1946, spent four years at the nearby National Centre for Scientific Research, and in 1951 was awarded a doctorate by the University of Paris. He held appointments at the University of Grenoble (1953–54) and the University of Strasbourg (1954–63). In 1964 he became a professor at the Institute of Advanced Scientific Studies, Bures-sur-Yvette.

Thom was awarded the Fields Medal at the International Congress of Mathematicians in Edinburgh in 1958 for his numerous important contributions in topology, particularly his generalization of work by Russian mathematicians Vladimir Rokhlin and Lev Pontryagin on the concept of cobordism. Cobordism is a tool for classifying differentiable manifolds. Two manifolds of dimension n are cobordant if there exists a manifold-with-boundary of dimension n + 1, whose boundary is their disjoint union.

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Thom was best known, however, for catastrophe theory, an attempt to model abrupt behavioral changes—such as the transition from liquid to gas or, in human events, from peace to war—with functions on surfaces that have folds and cusps. The mathematical insight was valuable, but the subject became controversial when some of Thom’s friends and colleagues made rather extravagant claims on the applicability of catastrophe theory. In addition, it was realized that many of the associated ideas, under different terminology, had already been employed by applied mathematicians.

Thom’s publications include Stabilité structurelle et morphogénèse (1972; Structural Stability and Morphogenesis) and Théorie des catastrophes et biologie (1979; “Catastrophe Theory in Biology”).