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Person: Choquet, Gustave Alfred Arthur
Gustave Choquet was a French mathematician who worked in functional analysis, potential theory, topology and measure theory.
Mathematical Profile (Excerpt):
- This was a peaceful place, well away from the fighting, and Gustave's earliest memories were of happy times in a tiny village in this region.
- There he was taught by an exceptional teacher, M Flamant and Choquet wrote that he learnt more from M Flamant than he did at the lycée or at university.
- This made a tremendous impression on the young Choquet and M Flamant's approach to learning and teaching would influence his whole life.
- There were no secondary schools in the village of Saultain, so Choquet had to attend the lycée at Valenciennes.
- Choquet derived particular satisfaction at school from solving difficult problems in geometry.
- While still studying in Valenciennes, Choquet sat the 'concours général', the nation-wide mathematics competition, in 1933 and was ranked in first place beating Roger Apéry who was ranked second.
- At the École Normale Supérieure, Choquet took Georges Valiron's course on analytic functions, and courses by Georges Darmois which he found inspirational.
- Certainly Choquet and Denjoy discussed their research but Choquet wanted to follow his own ideas and never asked Denjoy to suggest a research topic.
- Choquet's research went well and in 1938 he published his first three papers: Étude des homéomorphies planes Ⓣ(Study of plane homeomorphisms); Étude de certains réseaux de routes Ⓣ(Study of some road networks); and Prolongement d'homéomorphies Ⓣ(Extension of homeomorphisms).
- Choquet obtained a Jane Eliza Proctor fellowship to finance a year at Princeton.
- Although Choquet had published 28 papers by 1946, he had never submitted a thesis for a doctorate.
- A second great theme is his theory of integral representations in compact convex sets and weakly complete cones, now usually known as 'Choquet theory', which launched a huge development.
- In 1988, Choquet was elected to Honorary Membership of the London Mathematical Society.
- His work on integral representations over convex sets was so seminal that this area is now known as 'Choquet theory'.
- Choquet's work on capacities is also particularly striking.
- The importance of Choquet's work on capacities can be seen from the fact that in 2008 the International Journal of Approximate Reasoning produced a 'Special Issue on Choquet integration in honour of Gustave Choquet'.
- One of the earliest and also deepest and most comprehensive of these approaches had been worked out by Gustave Choquet in his 1953/54 paper 'Theory of capacities'.
- He died November 14 last year in Lyon at the age of 91, so this is a good time and place to appreciate those parts of his scientific work related to this issue and to see why, nowadays and with full justification, the integral w.r.t. a monotone non-additive measure is called Choquet integral.
- Choquet's famous paper 'Theory of capacities', comprising 165 pages, is a monograph rather than an ordinary article.
- In La naissance de la théorie des capacités: réflexion sur une expérience personnelle Ⓣ(Beginnings of capacity theory: reflection on personal experience) (1986), Choquet gives an interesting historical account of the development of the theory of capacities.
- Choquet produced a number of important books.
- Another three-volume work Lectures on analysis (1969) was based on Choquet's course in analysis given at Princeton during the autumn term in 1967.
- Another book, again based on a course given by Choquet, was also published in 1969, namely Outils topologiques et métriques de l'analyse mathématique.
- She took the name Yvonne Choquet-Bruhat and has a biography in this archive.
- We have already mentioned the fact that Choquet was made an honorary member of the London Mathematical Society.
Born 1 March 1915, Solesmes, near Valenciennes, Nord, France. Died 14 November 2006, Lyon, France.
View full biography at MacTutor
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Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive