**Maurice Fréchet** was a French mathematician who made major contributions to the topology of point sets and defined and founded the theory of abstract spaces.

- Before Maurice was born the constitution of the Third Republic had been drawn up.
- Jacques Fréchet lost his job as headmaster and was unemployed.
- This had the benefit that Maurice grew up surrounded by those speaking foreign languages and he developed an international outlook which was to remain with him throughout his life.
- After the French education system settled down from the impact of the legal restraints put upon it, Jacques Fréchet was able to find a job teaching within the new secular system.
- Maurice entered secondary education at the Lycée Buffon in Paris.
- This continued after Hadamard moved to Bordeaux, for he wrote to Fréchet setting him mathematical problems, and corrected his work with severe criticisms if there were any errors.
- The relationship was one in which Fréchet was extremely grateful for the encouragement and guidance that he was receiving, but he admitted much later that he lived in continual fear of not being able to solve the problems he was set.
- After leaving school, Fréchet undertook military service before, in 1900, entering the École Normale Supérieure in Paris.
- Even before he was awarded his Agrégation des Sciences Mathematiques in 1903, Fréchet began publishing short papers.
- Contact with several American mathematicians who were in Paris, in particular Edwin Wilson, led to Fréchet publishing some of his early papers in American Mathematical Society publications (Edwin Wilson was editor of the Transactions of the American Mathematical Society from 1903).
- Another task undertaken by Fréchet around this time was writing up Borel's lectures for publication.
- Fréchet attended these lectures while an undergraduate and wrote up the lectures during the winter of 1903-04.
- Fréchet wrote an outstanding doctoral dissertation Sur quelques points du calcul fonctionnel Ⓣ(On some points of the functional calculus) submitted on 2 April 1906.
- This parallel is drawn by Fréchet himself who requires sufficient structure on his abstract systems so that limits and continuity can be studied.
- A versatile mathematician, Fréchet served as professor of mathematics at the Lycée in Besançon (1907-08), professor of mathematics at the Lycée in Nantes (1908-09), then professor of mechanics at the Faculty of Science in Poitiers (1910-19).
- Fréchet had arranged to spend the academic year 1914-15 at the University of Illinois at Urbana in the United States and had accepted an appointment there for one year.
- There is evidence that Fréchet had arranged with some American mathematicians to publish his complete works if he did not survive the war.
- Not only did he undertake this dangerous work during the war, but Fréchet continued to produce frequent mathematics papers.
- For the period of the war Fréchet retained his post at the Faculty of Science in Poitiers despite not being able to teach there.
- As he had been in earlier times, Fréchet was able to continue to produce a large research output despite heavy duties.
- From November 1928 Fréchet held posts in Paris, but from this time on he concentrated more on statistics.
- It was Borel who encouraged Fréchet to seek positions in Paris and he supported his candidacy.
- There is also a suggestion that Fréchet had a difference of opinion with the Council of the Faculty of Science at Strasbourg which meant he was both pleased to return to Paris and not unhappy at leaving Strasbourg.
- Maurice Fréchet did not disdain contributing his own stone to the building of these mathematical foundations via his work on the notion of distance.
- In January and February of 1942 Fréchet was lecturing in Portugal.
- That the abstract theories of which Maurice Fréchet was one of the first pioneers, have allowed a major work of synthesis and clarification in the mathematical sciences to be carried out through the last thirty years.
- That the workmanship which Maurice Fréchet carried out in the most varied fields of the pure and applied mathematics is a monument to the glory of the constructive spirit of the Man.
- As we have indicated, Fréchet made major contributions to the topology of point sets, and defined and founded the theory of abstract spaces.
- Fréchet also made important contributions to statistics, probability and calculus.
- Fréchet recognised himself that he fell into the latter category.
- Finally let us mention that Fréchet was an extremely active correspondent with most of the leading mathematicians of his day.
- Among Fréchet's manuscripts are forty-eight letters of which seven were written by P S Aleksandrov and P S Urysohn and the remainder (after Urysohn's death in 1924) by Aleksandrov.
- In the earliest of these letters the young Russian scholars express their gratitude to Fréchet for having created the theory of abstract spaces on which their earliest investigations were based and cite as the source of their first published works problems posed by N Luzin in his analysis seminar at Moscow University.
- Although widely honoured, it does appear that Fréchet was more highly rated outside France than inside it.

Born 2 September 1878, Maligny, Yonne, Bourgogne, France. Died 4 June 1973, Paris, France.

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Topology

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive