René Gateaux

René Eugène Gateaux (ʁəne øʒɛn ɡɑto; 5 May 1889 – 3 October 1914) was a French mathematician. He is principally known for the Gateaux derivative, used in the calculus of variations and in the theory of optimal control. He died in combat during World War I. Paul Lévy produced a posthumous edition of his works, extending them considerably, in his Leçons d'analyse fonctionnelle of 1922. Gateaux was born on at Vitry-le-François, Marne, 222 years after another mathematician, Abraham de Moivre, was born there (de Moivre, being of Huguenot ancestry, fled to London after the Edict of Fontainebleau of 1685). His father had a small saddlery and upholstery business, and his mother was a seamstress. He was schooled at Reims, and in 1907 entered the École normale supérieure (ENS) on the rue d'Ulm. He was well regarded as one of the most promising mathematicians among his peers. During his time at ENS, Gateaux converted to Roman Catholicism. In 1910, he sat the mathematics examination (being placed 11th of 16 in his year, a somewhat unimpressive result perhaps due to his being so young, according to the ENS's deputy head Émile Borel). He became a teacher at the lycée in Bar-le-Duc, Meuse in 1912, having completed his two years' military service (the first as a private soldier, and the second as a sub-lieutenant, as was required by a 1905 law concerning the service of students from some Grandes Écoles). At the same time as he took the post at Bar-le-Duc, he started to work on his thesis about functional analysis, following the work of Vito Volterra and Jacques Hadamard, and its applications to potential theory. Even though it is unknown why Gateaux chose this subject, he may have been encouraged by Hadamard himself, who had just completed a course on the subject at the Collège de France. Among others, in 1911 Paul Lévy had undertaken a brilliant thesis on this type of question, and in 1912 Joseph Pérès, an alumnus of the ENS in the year before Gateaux, had left for Rome to work under Volterra.