Rene Cakes

Rene Eugene Gateaux (born the May 5th 1889 with Vitry-le-François in the the Marne - died with the combat the October 3rd 1914 with Rouvroy in the Pas-de-Calais) is a known French mathematician mainly for his definition of a directional Dérivée used in Calcul from the variations and theory of the optimal control. Paul Levy made known his work in its Leçons of functional analysis (1922).

Biography

Normalien

Rene Gâteaux was born the May 5th 1889 with Vitry-le-François (Marne), where 222 years earlier nacquit another mathematician, Abraham de Moivre, which, of huguenote family, had to flee in London following the revocation of the Edit of Nantes. The father of Rene had a small company of bourellerie-saddlery and his/her mother was dressmaker. Raise with the college of Rheims, Rene enters in 1907 to the National university, at the time uncontested center of the French intellectual life. It is pointed out soon like one of the most promising mathematicians of its promotion. During its stay with the Teacher training school, Rene Gateaux converts with Catholicism.

Professor of college

In 1910, it passes the aggregation of mathematics (it is received 11th) and is named professor with the college of Bar-le-Duc (Meuse) in 1912, after having carried out its two years of service soldier (the first like private, the second as second lieutenant as stipulated it the law of 1905 concerning the active service of the pupils of a certain number of Universities).

At the same time as it takes its station in Bar-le-Duc, Gâteaux also starts to work with its thesis on topics concerned with the functional Analyze in the spirit of work of Vito Volterra and Jacques Hadamard and his applications to the Théorie of the potential. Even if it is not known exactly why Gateaux chose this set of themes, it is plausible that it was encouraged there by Hadamard itself which had just made a series of course on the subject with the Collège de France. In addition, in 1911, Paul Levy had supported a brilliant thesis on this type of questions and in 1912, Joseph Pérès, a brilliance element of the National university of promotion preceding that by Cakes had left to Rome to work at Volterra.

Student in Rome

In 1913, Gateaux requires and obtains a purse of the foundation David Weill to go him-also to Rome. Before leaving, it exposes in a letter to Borel and Volterra, the topics on which it proposes to work in Rome. Among those integration appears on the space of infinite size of the real functional calculuses.

To Rome where it remains between October 1913 and June 1914, Gateaux follows the courses of Volterra and works like a navvy. It publishes several notes in the Rendiconti dell' Accademia dei Lincei , makes a talk with the seminar of the University of Rome. While returning to France for the summer, he thinks of setting out again as of September in Rome after having obtained a purse for a second year.

Died with the combat

Taken with deprived by the general mobilization and the declaration of war of August 1914, Gâteaux is mobilized in Toul as lieutenant of the 269ème regiment of Infantry. After the battles of the Marne, this regiment is engaged in the race with the sea and envoy in Artois. The Gateaux October 3rd, 1914 is killed on its machine-gun at the entry of the village of Rouvroy which its regiment defends. In the confusion of the massacre, the bodies are not identified and are not buried hastily. They are only a few years later that the body of Cakes will be exhumed and transported in the necropolis main road of Neuville-Saint-Vaast where Gateaux with tomb 76.

Scientific posterity

As of August 1915, Hadamard begins the steps to obtain the posthumous attribution of one of the prices of the Academy of Science to Cakes. In a letter with Picardy Emile, it mentions that “ the young man left the research extremely advanced in functional calculation (its thesis was mainly made up and partly exposed in notes presented to the Academy), research for which Mr. Volterra and I even have a great consideration ”.

In 1916, the Prix Francœur is allotted to Gâteaux. In 1918, Hadamard speaks in Paul Levy, charged to make a course on the Functional Analysis with the Collège de France, of the drafts left by Gâteaux before its departure with the face. He proposes to him to carry out of it the edition for the Bulletin of the Mathematical Company of France , which will be made in two times. The most important discovery that Levy extracted papers of Cakes relates to an outline of theory for the integration of functions in infinite dimension that it with the idea to identify in extreme cases of the median values on N first components. The importance of this work goes in fact considerable being for Levy since it will be for him the occasion to write his important book Leçons of Functional Analysis of 1922. When Levy speaks about it to the American mathematician Norbert Wiener which it meets in 1922, this last perceives immediately that it can use the definition of Cakes such as it is to format his “differential space” and to build the measurement Brownian movement (called since “measurement of Wiener”). In the article founder that it published in 1923, Wiener pays homage to Gâteaux and Levy which had made “the major studies on integration in infinite dimension”.

References

Gilbert Maheut: Routes of Mathematicians (2000), in Squaring , n°37, pp. 21-23,
Article of Laurent Mazliak: '' Phantoms of the Teacher training school: life, died and mathematical destiny of Rene Cakes ''

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