 Maurice René Fréchet

Maurice René Fréchet
Maurice René FréchetBorn September 2, 1878
Maligny, FranceDied June 4, 1973 (aged 94)
Paris, FranceNationality French Fields Mathematics Institutions University of Bordeaux
University of Strasbourg
École des HautesÉtudes
École Normale SupérieureAlma mater École Normale Supérieure Doctoral advisor Jacques Hadamard Doctoral students Nachman Aronszajn
Robert Fortet
Đuro Kurepa
Ky Fan
Jean VilleKnown for metric spaces
Functional analysisMaurice Fréchet (French pronunciation: [moʁis ʁəne fʁeʃɛ]) (September 2, 1878 – June 4, 1973) was a French mathematician. He made major contributions to the topology of point sets and introduced the entire concept of metric spaces. He also made several important contributions to the field of statistics and probability, as well as calculus. His dissertation opened the entire field of functionals on metric spaces and introduced the notion of compactness. Independently of Riesz, he discovered the representation theorem in the space of Lebesgue square integrable functions.
Contents
Biography
Early life
He was born to a Protestant family in Maligny, Yonne 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 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 recognised 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 criticising 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 privileged to enjoy.
After completing highschool 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 19071908 he served as a professor of mathematics at the Lycée in Besançon, then moved in 1908 to the Lycée in Nantes to stay there for a year. After that he served at the University of Poitiers between 19101919.
He married in 1908 to Suzanne Carive and had four children: Hélène, Henri, Denise and Alain.
First World War
Fréchet was planning to spend a year in the United States at the University of Illinois but his plan was disrupted when the First World War broke out in 1914. He was mobilised on 4 August the same year. Because of his diverse language skills, gained when his mother ran the establishment for foreigners, he served as an interpreter for the British Army. However, this was not a safe job and he spent two and a half years very near or at the front. The French egalitarian ideas meant that very many academics were mobilised to serve in the trenches and many of them were lost during the war. It is remarkable that during his service in the war he still managed to produce frequent cutting edge mathematical papers, even with very little time available to devote to mathematics.
After the war
After the end of the war, Fréchet was chosen to go to Strasbourg to help with the reestablishment of the university. He served as a professor of higher analysis and Director of the Mathematics Institute. Despite being burdened with administrative work, he was again able to produce a large amount of high quality research.
In 1928 Fréchet decided, with encouragement from Borel, to move back to Paris. He held various positions in Paris until his retirement in 1948. Despite his major achievements, he was not overly appreciated in France. As an illustration, while being nominated numerous times, he was not elected a member of the Academy of Sciences until the age of 78.
Fréchet was an Esperantist, publishing some papers and articles in the international language.^{[1]} He also served as president of the Internacia Scienca Asocio Esperantista ("International Scientific Esperantist Association") from 195053.^{[2]}
Main works
His first major work was his outstanding PhD thesis that he submitted in 1906. The thesis was titled Sur quelques points du calcul fonctionnel and was concerned with the calculus of functionals. Here Fréchet introduced the concept of a metric space, although the name is due to Hausdorff. The level of abstraction used by Fréchet is similar to that in group theory, allowing one to develop an axiomatic system to study a large array of mathematical objects. The system can then be applied in very many particular cases. Fréchet^{[3]} developed here ideas from the article Deux types fondamentaux de distribution statistique^{[4]} (1938; an English translation Two Basic Types of Statistical Distribution) of Czech geographer, demographer and statistician Jaromír Korčák.
Here is a list of his most important works, in chronological order:
 Sur les opérations linéaires IIII, 19041907 (On linear operators)
 Les Espaces abstraits, 1928 (Abstract spaces)
 Recherches théoriques modernes sur la théorie des probabilités, 19371938 (Modern theoretical research in the theory of probability)
 Les Probabilités associées à un système d'événements compatibles et dépendants, 19391943 (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)
See also
 Fréchet space
 Fréchet–Urysohn space
 Fréchet derivative
 Differentiation in Fréchet spaces
 Topological space
 Functional analysis
 Fréchet distribution
 Fréchet mean
 Fréchet distance
 Fréchet filter
Notes
 ^ [http://archive.numdam.org/ARCHIVE/CM/CM_19541956__12_/CM_19541956__12__81_0/CM_19541956__12__81_0.pdf La kanonaj formoj de la 2, 3, 4dimensiaj paraanalitikaj funkcioj (Esperanto) ]
 ^ from the Esperanto Wikipedia
 ^ Fréchet, Maurice R. (1941). "Sur la loi de répartition de certaines grandeurs géographiques". Journal de la Société de Statistiques de Paris 82: 114–122.
 ^ Jaromír Korčák (1938): Deux types fondamentaux de distribution statistique. Prague, Comité d’organisation, Bull. de l'Institut International de Statistique, vol. 3, pp. 295–299.
External links
 O'Connor, John J.; Robertson, Edmund F., "Maurice René Fréchet", MacTutor History of Mathematics archive, University of St Andrews, http://wwwhistory.mcs.standrews.ac.uk/Biographies/Frechet.html.
 Maurice René Fréchet at the Mathematics Genealogy Project.
Categories: Functional analysts
 Probability theorists
 French statisticians
 1878 births
 1973 deaths
 People from Yonne
 20thcentury mathematicians
 French mathematicians
 Mathematical analysts
 Alumni of the École Normale Supérieure
 Lycée Buffon alumni
 University of Strasbourg faculty
 French Esperantists
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Maurice René Fréchet — Maurice René Fréchet, né à Maligny le 2 septembre 1878 et mort à Paris le 4 juin 1973, est un mathématicien français. Mathématicien prolifique, il travailla entre autres en topologie, en … Wikipédia en Français
Maurice Rene Frechet — Maurice René Fréchet Maurice René Fréchet Maurice René Fréchet, né à Maligny le 2 septembre 1878 et mort à Paris le 4 juin 1973, est un mathématicien français. Mathématicien prolifique, il travailla e … Wikipédia en Français
Maurice René Fréchet — (* 2. September 1878 in Maligny, Département Yonne; † 4. Juni 1973 in Paris) war ein französischer Mathematiker. Inhaltsverzeichnis … Deutsch Wikipedia
Maurice Fréchet — Maurice René Fréchet Maurice René Fréchet Maurice René Fréchet, né à Maligny le 2 septembre 1878 et mort à Paris le 4 juin 1973, est un mathématicien français. Mathématicien prolifique, il travailla e … Wikipédia en Français
Maurice Frechet — Maurice René Fréchet Maurice René Fréchet (* 2. September 1878 in Maligny; † 4. Juni 1973 in Paris) war ein französischer Mathematiker. Fréchet ging am Lycée Buffon in Paris zur Schule, wo Hadamard sein Lehrer war und seine mathematische Begabung … Deutsch Wikipedia
Maurice Fréchet — Maurice René Fréchet Maurice René Fréchet (* 2. September 1878 in Maligny; † 4. Juni 1973 in Paris) war ein französischer Mathematiker. Fréchet ging am Lycée Buffon in Paris zur Schule, wo Hadamard sein Lehrer war und seine mathematische Begabung … Deutsch Wikipedia
Maurice Fréchet — Maurice René Fréchet Maurice René Fréchet, (Maligny, 2 de septiembre de 1878 París, 4 de junio de 1973), fue un matemático francés. Trabajó en topología, teoría de la probabilidad y la estadística … Wikipedia Español
FrechetMetrik — Fréchet Metrik (nach Maurice René Fréchet) ist ein Begriff aus der Funktionalanalysis. Sie stellt eine Verbindung zwischen Metrik und Norm her. Inhaltsverzeichnis 1 Definition 2 Anwendungen 3 Literatur 4 Siehe auch … Deutsch Wikipedia
Frechet — Fréchet ist der Name von Maurice René Fréchet (1878 1973), französischer Mathematiker Nach diesem benannt sind: Fréchet Filter, Mengenfilter Fréchet Ableitung, verallgemeinert den Begriff der Ableitung aus der Differentialrechnung auf normierte… … Deutsch Wikipedia
FréchetMetrik — (nach Maurice René Fréchet) ist ein Begriff aus der Funktionalanalysis. Sie stellt eine Verbindung zwischen Metrik und Norm her. Inhaltsverzeichnis 1 Definition 2 Anwendungen 3 Literatur 4 … Deutsch Wikipedia