# René Thom

### Guardian obituary

Wide-ranging French mathematician whose creation of catastrophe theory paved the way for the more influential chaos theory

The relatively new science of chaos theory has had a huge impact on research in fields as diverse as meteorology, ecology, economics, physiology, genetics, astronomy and the stock market. It is used to model highly complex systems, from population growth and epidemics to erratic heart palpitations.

Some scientists believe that chaos theory will join relativity and quantum mechanics as the third great theory of the 20th century. But it has a close cousin in the form of catastrophe theory, which was sired by René Thom, the French mathematician, who has died aged 79. He believed his theory held out hope of predicting disastrous phenomena such as earthquakes, prison riots and the outbreak of war.

Before turning to catastrophe theory, Thom had already earned international distinction for his work on topology, the branch of mathematics which involves studies of the shapes and symmetries of abstract geometric objects, and whose influence now extends to many other areas. In 1958 his work won him the Fields Medal, the equivalent in mathematics of a Nobel prize. This was awarded for an influential theory called cobordism, described as lying on the margins between algebra and geometry.

Thom was born in Montbéliard, near the Swiss border. His parents were shopkeepers. He went to the local primary school, where he was reputed to have learned by the age of 10 to visualise in four dimensions, and first showed his academic potential in his scholarship examinations.

He got his baccalaureate in mathematics from Besançon just before Hitler's invasion of France in 1940. Thom's parents sent him and his brother south to avoid the conflict. After a few months he returned to France to continue his education in Lyons, where he completed a baccalaureate in philosophy in June 1941. He was thwarted at his first attempt to get a place at the Ecole Normale Supérieure in Paris in 1942, but in 1943 applied successfully.

Although life was hard under German occupation, it was an exciting time at the Ecole Normale Supérieure for a young mathematician like Thom. It was here that he met the distinguished academic Henri Cartan, who introduced him to the Bourbaki approach to mathematics.

Bourbaki is the collective pseudonym for the authorship of 36 volumes of comprehensive texts, started in 1939 by an elite group of French mathematicians, designed to present mathematics in a contemporary and original way, and to illustrate its axiomatic structure. In 1946, Thom moved to Strasbourg to continue working under Cartan, and with other leading mathematicians of the Bourbaki school. He got his doctorate in 1951 under Cartan's supervision, for a thesis entitled Fibre Spaces In Spheres And Steenrod Squares, in which the foundations of the theory of cobordism appeared.

He won a fellowship to the United States and later recalled his awe at meeting some of the giants of mathematics at Princeton, including Albert Einstein and Hermann Weyl. After returning to France, he taught at Grenoble in 1953-54, and then at Strasbourg, where he was appointed a professor in 1957. In 1964 he moved to the Institut des Hautes Etudes Scientifiques at Bures-sur-Yvette. A change in direction appeared in his work as, in addition to papers on topology, he began to study and write on linguistics, philosophy and theoretical biology.

Thom was a shy, somewhat reserved man, who liked to gently prod his colleagues into questioning their assumptions. He admitted that, in part, his switch of topics was provoked when he found himself in the shadow of another intellectual giant, Alexandre Grothendieck, the mathematician whose work was to lead to a unification of geometry, number theory, topology and complex analysis.

Thom described how he felt he had nothing new to offer in the wake of Grothendieck's crushing superiority. So he decided to leave what he called the strictly mathematical world to explore more general notions, like the theory of morphogenesis, which led him towards a very general form of "philosophical" biology.

His studies culminated in his book Structural Stability And Morphogenesis, published in 1972, outlining a theory to describe those situations in which gradually changing forces lead to so-called catastrophes, or to abrupt changes that could have widespread application in the physical and biological sciences and in the social sciences.

Many mathematicians developed the catastrophe theory, but it never had the success achieved later by chaos theory because it failed to live up to its promise of useful predictions. Nevertheless, catastrophe theory was inspired by Thom's passion to understand the world geometrically. Late in his career, Salvador Dali painted Topological Abduction Of Europe: Homage To René Thom (1983), an aerial view of a seismically fractured landscape juxtaposed with the equation that strives to explain it.

Thom's contributions to other fields did not always sit comfortably with colleagues. In his book What Mad Pursuit, Francis Crick, the Nobel prizewinner who was a co-discoverer of the structure of DNA, recounted a meeting with him where scientists were discussing progress in cracking the genetic code. Thom suggested that some of Crick's recent research might be wrong because, though supported experimentally, it did not comport with mathematical theory. Crick opined that Thom did not understand how science worked: "what he did understand he didn't like, and referred to it disparagingly as 'Anglo-Saxon'."

Thom was awarded the Grand Prix Scientifique de la Ville de Paris in 1974 and made an honorary member of the London Mathematical Society in 1990. His wife, Suzanne, and three children, Françoise, Elizabeth and Christian, survive him.

[René Frédéric Thom, mathematician, born September 2 1923; died October 25 2002]

Pearce Wright, Thursday November 14, 2002 © Guardian Newspapers Limited

Some scientists believe that chaos theory will join relativity and quantum mechanics as the third great theory of the 20th century. But it has a close cousin in the form of catastrophe theory, which was sired by René Thom, the French mathematician, who has died aged 79. He believed his theory held out hope of predicting disastrous phenomena such as earthquakes, prison riots and the outbreak of war.

Before turning to catastrophe theory, Thom had already earned international distinction for his work on topology, the branch of mathematics which involves studies of the shapes and symmetries of abstract geometric objects, and whose influence now extends to many other areas. In 1958 his work won him the Fields Medal, the equivalent in mathematics of a Nobel prize. This was awarded for an influential theory called cobordism, described as lying on the margins between algebra and geometry.

Thom was born in Montbéliard, near the Swiss border. His parents were shopkeepers. He went to the local primary school, where he was reputed to have learned by the age of 10 to visualise in four dimensions, and first showed his academic potential in his scholarship examinations.

He got his baccalaureate in mathematics from Besançon just before Hitler's invasion of France in 1940. Thom's parents sent him and his brother south to avoid the conflict. After a few months he returned to France to continue his education in Lyons, where he completed a baccalaureate in philosophy in June 1941. He was thwarted at his first attempt to get a place at the Ecole Normale Supérieure in Paris in 1942, but in 1943 applied successfully.

Although life was hard under German occupation, it was an exciting time at the Ecole Normale Supérieure for a young mathematician like Thom. It was here that he met the distinguished academic Henri Cartan, who introduced him to the Bourbaki approach to mathematics.

Bourbaki is the collective pseudonym for the authorship of 36 volumes of comprehensive texts, started in 1939 by an elite group of French mathematicians, designed to present mathematics in a contemporary and original way, and to illustrate its axiomatic structure. In 1946, Thom moved to Strasbourg to continue working under Cartan, and with other leading mathematicians of the Bourbaki school. He got his doctorate in 1951 under Cartan's supervision, for a thesis entitled Fibre Spaces In Spheres And Steenrod Squares, in which the foundations of the theory of cobordism appeared.

He won a fellowship to the United States and later recalled his awe at meeting some of the giants of mathematics at Princeton, including Albert Einstein and Hermann Weyl. After returning to France, he taught at Grenoble in 1953-54, and then at Strasbourg, where he was appointed a professor in 1957. In 1964 he moved to the Institut des Hautes Etudes Scientifiques at Bures-sur-Yvette. A change in direction appeared in his work as, in addition to papers on topology, he began to study and write on linguistics, philosophy and theoretical biology.

Thom was a shy, somewhat reserved man, who liked to gently prod his colleagues into questioning their assumptions. He admitted that, in part, his switch of topics was provoked when he found himself in the shadow of another intellectual giant, Alexandre Grothendieck, the mathematician whose work was to lead to a unification of geometry, number theory, topology and complex analysis.

Thom described how he felt he had nothing new to offer in the wake of Grothendieck's crushing superiority. So he decided to leave what he called the strictly mathematical world to explore more general notions, like the theory of morphogenesis, which led him towards a very general form of "philosophical" biology.

His studies culminated in his book Structural Stability And Morphogenesis, published in 1972, outlining a theory to describe those situations in which gradually changing forces lead to so-called catastrophes, or to abrupt changes that could have widespread application in the physical and biological sciences and in the social sciences.

Many mathematicians developed the catastrophe theory, but it never had the success achieved later by chaos theory because it failed to live up to its promise of useful predictions. Nevertheless, catastrophe theory was inspired by Thom's passion to understand the world geometrically. Late in his career, Salvador Dali painted Topological Abduction Of Europe: Homage To René Thom (1983), an aerial view of a seismically fractured landscape juxtaposed with the equation that strives to explain it.

Thom's contributions to other fields did not always sit comfortably with colleagues. In his book What Mad Pursuit, Francis Crick, the Nobel prizewinner who was a co-discoverer of the structure of DNA, recounted a meeting with him where scientists were discussing progress in cracking the genetic code. Thom suggested that some of Crick's recent research might be wrong because, though supported experimentally, it did not comport with mathematical theory. Crick opined that Thom did not understand how science worked: "what he did understand he didn't like, and referred to it disparagingly as 'Anglo-Saxon'."

Thom was awarded the Grand Prix Scientifique de la Ville de Paris in 1974 and made an honorary member of the London Mathematical Society in 1990. His wife, Suzanne, and three children, Françoise, Elizabeth and Christian, survive him.

[René Frédéric Thom, mathematician, born September 2 1923; died October 25 2002]

Pearce Wright, Thursday November 14, 2002 © Guardian Newspapers Limited