This is an old revision of this page, as edited by Meznaric (talk | contribs) at 08:04, 2 March 2007. The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.
Revision as of 08:04, 2 March 2007 by Meznaric (talk | contribs)(diff) ← Previous revision | Latest revision (diff) | Newer revision → (diff)Maurice Fréchet (September 2, 1878 – June 4, 1973) was a French mathematician. His major contribution is the introduction of abstract spaces, where he applied the intuitive Euclidean geometry to form abstract relationships between the elements of the space. Particularly important are his generalisations of the concept of limit, continuity, convergent sequence and Cauchy sequence to the abstract setting. This led him to coin the term compact space. These new concepts were incredibly successful and are today considered to be the iron repertoire of any good analysis course. The entire field of functional analysis has emerged from Fréchet's ideas. He was a student of Jacques Hadamard at École Normale Supérieure.
Biography
Early life
He was born to a Protestant family in Maligny to Jacques and Zoé Fréchet. At the time of his birth, his father was a director of a Protestant orphanage in Maligny and was later in his youth appointed a head of a Protestant school. However, the newly established Third Republic was not sympathetic to the religious education and so the laws were enacted requiring all education to be secular. As a result, his father lost his job. To generate some income his mother set up a boarding house for foreigners in Paris. His father was able later to obtain another teaching position within the secular system - it was not a job of a headship, however, and the family could not expect as high standards as they might have otherwise.
Maurice attended the secondary school Lycée Buffon in Paris where he was taught mathematics by Jacques Hadamard. Hadamard recongised the potential of young Maurice and decided to tutor him on an individual basis. After Hadamard moved to the University of Bordeaux in 1894, Hadamard continuously wrote to Fréchet, setting him mathematical problems and harshly critisicing his errors. Much later Fréchet admitted that the problems caused him to live in a continual fear of not being able to solve some of them, even though he was very grateful for the special relationship with Hadamard he was priviliged to enjoy.
After completing high-school Fréchet was required to enroll in the military service. This is the time when he was deciding whether to study mathematics or physics - he chose mathematics out of dislike of chemistry classes he would have had to take otherwise. Thus in 1900 he enrolled to École Normale Supérieure to study mathematics.
He started publishing quite early, having published four papers in 1903. He also published some of his early papers in the American Mathematical Society due to his contact with American mathematicians in Paris - particularly Edwin Wilson.
Middle life
Fréchet served at many different institutions during his academic career. From 1907-1908 he served as a professor of mathematics at the the Lycée in Besançon, then moved in 1908 to the the Lycée in Nantes to stay there for a year. After that he served at the University of Poitiers between 1910-1919.
He married in 1908 to Suzanne Carive and had four children: Hélène, Henri, Denise and Alain.
First World War
His major works are, in chronological order:
- Les Espaces abstraits, 1928 (Abstract spaces)
- Récherches théoriques modernes sur la théorie des probabilités, 1937-1938 (Modern theoretical research in the theory of probability)
- Les Probabilités associées à un système d'évenements compatibles et dependants, 1939-1943 (The Probabilities Associated with a System of Compatible and Dependent Events)
- Pages choisies d'analyse générale 1953 (Selected Pages of General Analysis)
- Les Mathématiques et le concret 1955 (Mathematics and the concrete)
The Fréchet metric is a metric function upon an infinite cartesian product of metric spaces <X1,d1>,<X2,d2>..., defined by:
See also
References
- O'Connor, John J.; Robertson, Edmund F., "René Maurice Fréchet", MacTutor History of Mathematics Archive, University of St Andrews
- René Maurice Fréchet at the Mathematics Genealogy Project
 | This article about a French mathematician is a stub. You can help Misplaced Pages by expanding it. |