Not long ago academic engineer Allan McRobie visited a museum in Figueres, Spain, dedicated to Salvador Dalí, and entered a private library, untouched since the famous surrealist’s death in 1989. On a table sat a book, called Paraboles et Catastrophes, by French mathematician René Thom.

It contained a handwritten dedication from Thom to Dalí, addressed as “The Master”, dated 1983. Opening it, McRobie found drawings on several pages; mostly line sketches of nudes. One depicted a naked person, arms aloft, leaping for joy.

It was, McRobie speculates, perhaps the last drawing Dalí ever did. If so, it was particularly appropriate for both the artist and the mathematician.

Dalí was born in 1904, a member of the Spanish aristocracy. Thom was born in 1923 in the French town of Montbéliard, the son of shopkeepers. The mathematician would heavily influence Dalí’s final decade – the artist co-opted equations and symbols from Thom’s books, used his terminology and even named a painting “Topological detachment of Europe: Homage to Rene Thom”. The pair worked in very different spheres but both were mavericks, beloved by many, scorned by others, recognised as polymaths who refused to be constrained by the boundaries of their disciplines.

The word ‘spheres’ is rather apt. Thom’s best known achievements start with the geometry of curved surfaces, a deceptively simple-sounding topic that brief investigation quickly reveals to be eye-wateringly complicated.

Fame came early for Thom. He went to school and university in Paris. At the latter, he completed his PhD thesis, called Fibre Spaces in Spheres and Steenrod Squares. The ideas explored within it led, seven years later, to him being awarded the Fields Medal, the premier prize for mathematics.

In 1968 he completed his second major work, Structural Stability and Morphogenesis. In it he established what he called ‘catastrophe theory’, which describes how dynamical systems undergo sudden, large-scale changes because of tiny shifts in initial conditions. The text, pretty much impossible for anyone except mathematical theorists to comprehend, went far beyond geometry. Thom used his theory to explain not just curves but also language, embryo growth and even the shapes of genitals. He continued to explore ever stranger applications – military organisation, for instance. He also invented ‘semiophysics’, which combined mathematics and the sign-based analysis of language known as semiotics.

Meanwhile, catastrophe theory developed a life of its own. American mathematician Stephen Smale recast it as the basis of his own work, known as chaos theory.

It also became the stuff of pop science. It was incorporated into books about prison riots and dog fights. It became popular with psychoanalysts and was lauded by French philosopher Jean-François Lyotard, who dubbed it “postmodern science”.

French auteur Jean-Luc Godard made a film about Thom, which contributed to making him a controversial character in the conservative world of mathematics. It was a role he rather liked. His output remained prodigious. McRobie notes “there is a Thom space, a Thom isomorphism, a Thom class, the Thom Transversality Theorem, the Dold-Thom Theorem, the Thom-Porteous Formula, and the Thom Conjecture”.

It is perhaps not surprising that Dalí – who often used science and mathematics in his work – asked to meet Thom. The artist’s later works are full of catastrophe theory. The word ‘topology’ – the broader maths field in which the theory resides – crops up in many Dalí artwork titles. Geometric shapes based on curves intersecting with sharp angles and swallowtails overlay many paintings.

Dalí’s last acknowledged public painting, “Swallow’s Tail and Cello (Catastrophe Series)”, is pure Thom. The drawings in Dalí’s copy of Paraboles et Catastrophes were likely done even later, in his final months. McRobie remarks that they are “remarkable because Thom makes no mention … of the connection between catastrophe theory and life drawing”.

Indeed, it fell to McRobie himself to do that. His book relating Thom’s mathematics to the shapes of nude bodies in art, The Seduction of Curves, was published by Princeton University Press in 2017.

René Thom died in 2002. His influence, however, seems set to continue, like Dalí’s, for quite a while yet.

Originally published by Cosmos as René Thom: Dalí’s favourite mathematician

### Andrew Masterson

Andrew Masterson is a former editor of Cosmos.

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