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René Thom, the French mathematician who died on October 25 aged 79, was best known as the inventor of catastrophe theory, which seeks to describe, in a way that is impossible using differential calculus, those situations in which gradually changing forces lead to so-called catastrophes, or abrupt changes.
Catastrophe theory has been applied with mixed results to a number of different phenomena in the real world, such as the stability of ships at sea and their capsizing, earthquakes, cliff falls, the development of clouds and bridge collapse.
It has been applied even less successfully to "social" phenomena such as the "fight-or-flight" behaviour of animals, prison riots, the outbreak of war and stock market crashes.
More fruitfully, perhaps, the theory inspired the later works of Salvador Dalí, whose Topological Abduction of Europe: Homage to René Thom (1983), showed an aerial view of a fractured landscape juxtaposed with Thom's equation that attempts to explain it.
Thom's expertise was in a mathematical field known as topology, which studies the shapes and symmetries of abstract multi-dimensional geometric objects; catastrophe theory developed as a by-product of this discipline.
Thom argued that there is only a limited number of ways in which sudden and catastrophic events take place, and suggested a methodology by which these processes could be described with their own abstract mathematical forms.
Thom's work involved the visualisation or computer simulation of some very complex higher-dimensional shapes, including such things as "periodic folds", "pinching bifurcations", and "saddle connection catastrophes" - or, more poetically, the "cusp", the "swallowtail" and the "butterfly".
He believed that this methodology could be developed in order to predict sudden shifts in behaviour which might arise from relatively small changes in circumstances.
Thom's theory, set out in a paper published in 1968, then elaborated in Structural Stability and Morphogenesis (1972), caused a sensation in the mathematical world and analysts were soon trying to apply it in fields such as biology, sociology and finance, but with no consistent results.
Catastrophe theory became an established area of mathematical research and had a notable impact on the development of new ideas, in particular chaos theory. However, its wider relevance remains dubious and many scientists and mathematicians are unconvinced of its value.
When Thom won the Fields Medal (which is the mathematical equivalent of the Nobel Prize) in 1958, it was not for his work on catastrophe theory, but for his work on "cobordism" theory, an even more obscure branch of pure mathematics which has been defined as "a way of organising and classifying manifolds whose stable tangent bundles admit additional structure".
René Frédéric Thom was born at Montbéliard, near the border with Switzerland, on September 2 1923. His parents were shopkeepers.
A gifted child, by the age of 10 he was said to have been able to visualise shapes in four dimensions. He won a scholarship to Collége Cuvier at Montbéliard and received his baccalaureat in elementary mathematics from Besançon in 1940.
After the German invasion, Thom's parents sent him and his brother south to avoid unpleasantness, although they themselves remained in Montbéliard.
Thom and his brother eventually reached Switzerland but soon afterwards returned to France. Thom then moved to Lyon to continue his education, receiving a baccalauréat in philosophy in 1941.
The same year he entered the Lycée Saint-Louis in Paris and applied to enter the Ecole Normale Superiéure, getting in at the second attempt in 1943.
He became strongly influenced by the pure mathematician Henri Cartan and the so-called "Bourbaki" school of mathematics and, in 1946, moved to Strasbourg to study under Cartan. In 1951 he earned a doctorate in mathematics for a thesis supervised by Cartan, entitled Fibre Spaces in Spheres and Steenrod Squares.
The same year Thom was awarded a travel scholarship to visit America, where he met Einstein and the mathematicians Hermann Weyl and Norman Steenrod, and attended seminars given by Kunihiko Kodaira.
After returning to France in 1953, Thom taught at Grenoble University for a year before moving to Strasbourg University, where he was appointed professor in 1957.
In 1964 he moved to the Institut des Hautes Etudes Scientifique at Bures-sur-Yvette, near Paris. The mathematics faculty at that time was dominated by Thom's colleague Alexander Grothendieck, whose seminars attracted the best students.
Rather put out by his colleague's technical superiority, Thom left the strictly mathematical world to tackle more general and philosophical notions such as the theory of catastrophe.
He also wrote papers on linguistics, philosophy and theoretical biology. He retired in 1988.
Thom regarded his mathematics as more closely related to poetry and philosophy than empirical, experiment-based science, on which he tended to look down: "Proving," he once argued, "is not a natural activity for mathematicians.
" On another occasion he declared that: "If one must choose between rigour and meaning, I shall unhesitatingly choose the latter."
In his memoirs, What Mad Pursuit, the British scientist Francis Crick recalled meeting Thom in the early 1960s at a scientific meeting held in Italy to discuss progress on cracking the chemical code of DNA.
Almost immediately, Crick recalled, Thom informed him that some of his [Crick's] recent research was wrong because, though it had been verified experimentally, it did not conform with mathematical theory.
Thom, Crick observed with wry amusement, referred disparagingly to laboratory-based science as "Anglo-Saxon".
Thom is survived by his wife, Suzanne, and by a son and two daughters.
(Filed: 13/11/2002) © Telegraph Group Limited
Catastrophe theory has been applied with mixed results to a number of different phenomena in the real world, such as the stability of ships at sea and their capsizing, earthquakes, cliff falls, the development of clouds and bridge collapse.
It has been applied even less successfully to "social" phenomena such as the "fight-or-flight" behaviour of animals, prison riots, the outbreak of war and stock market crashes.
More fruitfully, perhaps, the theory inspired the later works of Salvador Dalí, whose Topological Abduction of Europe: Homage to René Thom (1983), showed an aerial view of a fractured landscape juxtaposed with Thom's equation that attempts to explain it.
Thom's expertise was in a mathematical field known as topology, which studies the shapes and symmetries of abstract multi-dimensional geometric objects; catastrophe theory developed as a by-product of this discipline.
Thom argued that there is only a limited number of ways in which sudden and catastrophic events take place, and suggested a methodology by which these processes could be described with their own abstract mathematical forms.
Thom's work involved the visualisation or computer simulation of some very complex higher-dimensional shapes, including such things as "periodic folds", "pinching bifurcations", and "saddle connection catastrophes" - or, more poetically, the "cusp", the "swallowtail" and the "butterfly".
He believed that this methodology could be developed in order to predict sudden shifts in behaviour which might arise from relatively small changes in circumstances.
Thom's theory, set out in a paper published in 1968, then elaborated in Structural Stability and Morphogenesis (1972), caused a sensation in the mathematical world and analysts were soon trying to apply it in fields such as biology, sociology and finance, but with no consistent results.
Catastrophe theory became an established area of mathematical research and had a notable impact on the development of new ideas, in particular chaos theory. However, its wider relevance remains dubious and many scientists and mathematicians are unconvinced of its value.
When Thom won the Fields Medal (which is the mathematical equivalent of the Nobel Prize) in 1958, it was not for his work on catastrophe theory, but for his work on "cobordism" theory, an even more obscure branch of pure mathematics which has been defined as "a way of organising and classifying manifolds whose stable tangent bundles admit additional structure".
René Frédéric Thom was born at Montbéliard, near the border with Switzerland, on September 2 1923. His parents were shopkeepers.
A gifted child, by the age of 10 he was said to have been able to visualise shapes in four dimensions. He won a scholarship to Collége Cuvier at Montbéliard and received his baccalaureat in elementary mathematics from Besançon in 1940.
After the German invasion, Thom's parents sent him and his brother south to avoid unpleasantness, although they themselves remained in Montbéliard.
Thom and his brother eventually reached Switzerland but soon afterwards returned to France. Thom then moved to Lyon to continue his education, receiving a baccalauréat in philosophy in 1941.
The same year he entered the Lycée Saint-Louis in Paris and applied to enter the Ecole Normale Superiéure, getting in at the second attempt in 1943.
He became strongly influenced by the pure mathematician Henri Cartan and the so-called "Bourbaki" school of mathematics and, in 1946, moved to Strasbourg to study under Cartan. In 1951 he earned a doctorate in mathematics for a thesis supervised by Cartan, entitled Fibre Spaces in Spheres and Steenrod Squares.
The same year Thom was awarded a travel scholarship to visit America, where he met Einstein and the mathematicians Hermann Weyl and Norman Steenrod, and attended seminars given by Kunihiko Kodaira.
After returning to France in 1953, Thom taught at Grenoble University for a year before moving to Strasbourg University, where he was appointed professor in 1957.
In 1964 he moved to the Institut des Hautes Etudes Scientifique at Bures-sur-Yvette, near Paris. The mathematics faculty at that time was dominated by Thom's colleague Alexander Grothendieck, whose seminars attracted the best students.
Rather put out by his colleague's technical superiority, Thom left the strictly mathematical world to tackle more general and philosophical notions such as the theory of catastrophe.
He also wrote papers on linguistics, philosophy and theoretical biology. He retired in 1988.
Thom regarded his mathematics as more closely related to poetry and philosophy than empirical, experiment-based science, on which he tended to look down: "Proving," he once argued, "is not a natural activity for mathematicians.
" On another occasion he declared that: "If one must choose between rigour and meaning, I shall unhesitatingly choose the latter."
In his memoirs, What Mad Pursuit, the British scientist Francis Crick recalled meeting Thom in the early 1960s at a scientific meeting held in Italy to discuss progress on cracking the chemical code of DNA.
Almost immediately, Crick recalled, Thom informed him that some of his [Crick's] recent research was wrong because, though it had been verified experimentally, it did not conform with mathematical theory.
Thom, Crick observed with wry amusement, referred disparagingly to laboratory-based science as "Anglo-Saxon".
Thom is survived by his wife, Suzanne, and by a son and two daughters.
(Filed: 13/11/2002) © Telegraph Group Limited