https:\/\/www.lemonde.fr\/sciences\/article\/2023\/09\/27\/rene-thom-theoricien-des-catastrophes-a-l-honneur_6191211_1650684.html<\/p>\n\n\n\n
To mark the centenary of the birth of the mathematician and 1958 Fields Medal winner, the Acad\u00e9mie des Sciences and the Institut des Hautes \u00c9tudes Scientifiques paid tribute to him. Etienne Ghys, also a mathematician, looks back at the intellectual legacy of this extraordinary geometer, in his \u00ab\u00a0carte blanche\u00a0\u00bb with Le Monde.<\/p>\n\n\n\n
\u00ab\u00a0At a time when so many scientists are calculating all over the world, isn’t it desirable for those who can to dream? So concludes Ren\u00e9 Thom’s (1923-2002) book Stabilit\u00e9 structurelle et morphogen\u00e8se, written in 1972. The author is one of the most influential mathematicians of the 20th century. To mark the centenary of his birth, two symposia at the Acad\u00e9mie des Sciences and the Institut des Hautes \u00c9tudes Scientifiques have just reviewed the intellectual legacy of this outstanding geometer.<\/p>\n\n\n\n
A dreamer, no doubt. When he was preparing his thesis, his mentor, Henri Cartan, had a hard time channelling him. He wrote to him, for example: \u00ab\u00a0Refrain from stating theorems that are not only unproven, but whose statement does not even have a clearly defined meaning.\u00a0\u00bb A colleague of Henri Cartan’s explained that a dozen mathematicians could provide the missing demonstrations, but that only Ren\u00e9 Thom was capable of imagining such incredibly innovative statements. The thesis was defended in 1951, and Ren\u00e9 Thom was awarded the Fields Medal in 1958 for his discoveries in the field of differential topology, of which he was one of the pioneers. The medal was a great shock to him. He explained that he didn’t think he deserved it, which is not what medal winners usually think.<\/p>\n\n\n\n
He decided to go in a different direction, one that could be described as \u00ab\u00a0more applied\u00a0\u00bb. He postulated that, in general, a system (e.g. physical or biological) is in a stable state, and that at certain very particular moments it goes through what he called \u00ab\u00a0singular\u00a0\u00bb or \u00ab\u00a0catastrophic\u00a0\u00bb situations, jumping very rapidly from one domain of stability to another. It was therefore necessary to understand the nature of these singularities, and this was the birth of \u00ab\u00a0catastrophe theory\u00a0\u00bb, which enjoyed immense success in the 1970s.<\/p>\n\n\n\n
A question of boundary<\/strong><\/p>\n\n\n\n Thom lists seven elementary catastrophes with poetic names: \u00ab\u00a0fold\u00a0\u00bb, \u00ab\u00a0pucker\u00a0\u00bb, \u00ab\u00a0dovetail\u00a0\u00bb, \u00ab\u00a0butterfly\u00a0\u00bb, \u00ab\u00a0elliptical umbilicus\u00a0\u00bb, \u00ab\u00a0parabolic\u00a0\u00bb or \u00ab\u00a0hyperbolic\u00a0\u00bb. The English mathematician Erik Christopher Zeeman extended the field of application to increasingly varied situations: prison riots, dog aggression, stock market crashes and so on.<\/p>\n\n\n\n Many criticisms were levelled at this theory, and Thom analyzed them seriously, often acknowledging their validity. For example, he was criticized for failing to take into account the existence of chaotic dynamics (the theory of which was then being developed), or for having built a tool for understanding but not for predicting. He questioned the need for experimental validation in science, which led to violent, but often justified, reactions from biologists. His book Prediction is not an explanation (1991) examines all these issues with honesty and serenity.<\/p>\n\n\n\n Today, the concepts introduced by Thom, such as structural stability, genericity (the fact that a property applies to the general case) and transversality, are so important that they have entered the subconscious of all mathematicians.<\/p>\n\n\n\n Later, he turned to the philosophy of Aristotle. He recognized many aspects of this philosophy, such as defining an object or an idea through its edge. His thesis had already developed a theory of \u00ab\u00a0cobordism\u00a0\u00bb, and his catastrophes are nothing more than crossings of the edge of a domain of stability. In truth,\u00a0\u00bb he writes, \u00ab\u00a0there is a real unity in my thinking. I can only see it now, after much reflection, on a philosophical level. And I find this unity in the notion of the edge.<\/p>\n\n\n\n Salvador Dali’s last four paintings, in 1983, are Hommages \u00e0 Ren\u00e9 Thom.<\/p>\n","protected":false},"excerpt":{"rendered":" https:\/\/www.lemonde.fr\/sciences\/article\/2023\/09\/27\/rene-thom-theoricien-des-catastrophes-a-l-honneur_6191211_1650684.html To mark the centenary of the birth of the mathematician and 1958 Fields Medal winner, the Acad\u00e9mie des Sciences and the Institut des Hautes \u00c9tudes Scientifiques paid tribute to him. Etienne Ghys, also a mathematician, looks back at the intellectual legacy of this extraordinary geometer, in his \u00ab\u00a0carte blanche\u00a0\u00bb with Le Monde. \u00ab\u00a0At a … Continuer la lecture de Ren\u00e9 Thom, catastrophe theorist, in the spotlight<\/span>