Thom, René Frédéric (1923– )

French mathematician who developed catastrophe theory in 1966. He is a specialist in the fields of differentiable manifolds and topology.

Thom was born in Montbéliard in the Vosges and studied in Paris at the Ecole Normale Supérieure. He was professor at Strasbourg 1954–63 and then at the Institute of Advanced Scientific Studies at Bures-sur-Yvette.

Thom formulated a precise series associated with ‘space spherical bundles’ and demonstrated that the fundamental class of open spherical bundles showed topological invariance and formed a differential geometry. In his work on the theory of forms Thom showed that there are complete homological classes that cannot be the representation of any differential form, and formulated auxiliary spaces, now known as Thom spaces.

In 1956, Thom developed the theory of transversality, and contributed to the examination of singularities of smooth maps. This work laid the ground for his statement of the catastrophe theory, which is, in fact, a model, not yet an explanation. He proposed seven ‘elementary catastrophes’, which he hoped would be sufficient to describe processes within human experience of space-time dimensions. The seven elementary catastrophes are the fold, cusp, swallow-tail, butterfly, hyperbolic, elliptic, and parabolic. Of these, the cusp is both the simplest and the most useful.

In his book Stabilité structurelle et morphogenèse/Structural Stability and Morphogenesis (1972), Thom discusses how the concept of structural stability may be applied to the life sciences. He also introduces the notion of the ‘universal unfolding’ of a singularity.