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René Frédéric Thom

René Frédéric Thom

1923-

French Mathematician

Best known for his formulation of catastrophe theory, which has wide-ranging applications in both the natural sciences and the social sciences, René Thom is a topologist and mathematical philosopher of distinction. Not only was he the recipient of the Fields Medal in 1958, he has also been named a Knight of the Legion of Honor in France, and has received numerous other awards.

Born on September 2, 1923, in Montbéliard, France, Thom was the son of Gustav (a pharmacist) and Louise Ramel Thom. After earning an academic scholarship at the primary school in his hometown, Thom went on Collège Cuvier, also in Montbéliard, and earned his bachelor's degree in elementary mathematics from the University of Besançon in 1940. Soon afterward, however, the German army invaded France and Thom's parents encouraged him and his brother to flee. They made their way to the southern part of the country, and from there to Switzerland, where they were received with such a warm welcome that Thom fondly remembered it years later.

They helped with the harvest in the town of Romont, but soon Thom returned to France, where he earned another degree in philosophy. He migrated to Paris, where he attended the Lycée Saint-Louis before applying for admission to the highly prestigious Ecole Normale Supérieure in 1942. He failed to gain acceptance, however, but applied again the following year and was admitted.

Despite the fact that he was studying under conditions of wartime occupation, Thom's experience at the Ecole was a fruitful one. During this period, he was exposed to the approach of the Bourbaki group and to the work of Henri Cartan, which would have a great influence on Thom. His last year at the Ecole Normale Supérieure, after the liberation of Paris by Allied forces, was a particularly happy one in Thom's memory. In 1946 he moved to Strasbourg to work with Cartan, who served as advisor on his thesis, Fibre Spaces in Spheres and Steenrod Squares. Thom earned his doctorate in 1951, and taught at Grenoble from 1953 to 1954 before going to Strasbourg, where he remained until 1963.

Thom's thesis contained the basic ideas of cobordism, a classification scheme for manifolds—multidimensional topological surfaces—based on homotopy, a continuous deformation of one function into another. It was cobordism, presented by Thom in fully developed form in 1954, which earned him the Fields Medal in 1958. Many years later, Thom revealed that after receiving the coveted award, he had doubts about his own ability to continue generating meaningful results as a mathematician, and therefore turned his attention to singularities of differentiable maps, a topic he viewed as "more flexible and more concrete."

Appointed professor in 1957, Thom left Grenoble in 1963 and began teaching at the Institut des Hautes Etudes Scientifiques (IHES) in Bures-sur-Yvette. Without teaching responsibilities, he was free to concentrate on research, and prepared an article criticizing the movement to remove geometry from the general mathematics curriculum. In the years that followed, he moved increasingly into applied mathematics, turning his attention from optical problems in physics to the biological discipline of embryology.

The latter move was to prove pivotal, because from it arose Thom's famous catastrophe theory. Thom found that biological forms are subject to sudden changes, which he called catastrophes, findings he published in Structural Stability and Morphogenesis (1972). Catastrophe theory, grouped with geometry because its results are typically shown as curves and surfaces, attempts to explain predictable discontinuities in the output of systems subject to continuous inputs. Such predictions are beyond the reach of calculus, making Thom's theory invaluable to a wide array of disciplines outside of mathematics.

Catastrophe theory has been subject to criticism due to the fact that, as Thom himself has observed, "the theory did not permit quantitative prediction." It has nonetheless proven applicable in fields as diverse as hydrodynamics, linguistics, and industrial relations. Since the early 1970s, Thom has concerned himself primarily with matters of mathematical philosophy, a role that evolved in part from the need to defend and develop catastrophe theory.

JUDSON KNIGHT

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