**René Eugène Gateaux** was a French mathematician who worked in the calculus of variations.

- Another very famous mathematician was born 222 years before Gateaux in the same small town, Abraham de Moivre, who had to leave for London where he spent all his outstanding scientific career.
- Not much is known about René's parents.
- We do not know precise details of the school career of René Gateaux.
- On 24 February 1906, Gateaux signed a letter to the Ministry of Education to get permission to sit for the examination for admission to the École Normale Supérieure (science division) in 1906, though he had not attained the regular minimum age of 18 (he was to be 17 in May 1906).
- In October 1907, Gateaux entered the École Normale Supérieure, which was in these years the very centre of intellectual life in France.
- It is without noise that Gateaux's personality blossomed, following the way he judged to be the best possible, and his personality unceasingly and smoothly strengthened.
- During his second year at the École Normale, Gateaux became a member of the Roman Catholic Church.
- A strong Catholic group attended the École Normale in these days (let us only mention Pierre Poyet, one of Gateaux's comrades among the 1907 pupils, who took orders and became a Jesuit) and Gateaux had certainly the occasion to move in these circles.
- In 1910, Gateaux passed the agrégation of mathematical sciences.
- On July 8th , 1912 a ministerial decree appointed Gateaux as Professor of Mathematics at the Lycée of Bar-le-Duc, the main town of the département of Meuse, 250 km east of Paris, and not very distant from his native Vitry-le-François.
- Nevertheless, before taking up this post, Gateaux had the boring but necessary task to fulfil his military obligations.
- On October 10th , 1910 Gateaux joined the 94th Infantry regiment where he was a basic 'second class' soldier.
- Then Gateaux had to follow some special training for officers, and the comments made by his superiors on the military dossier indicate that the supposed military training at the École Normale had (not surprisingly) been more virtual than real.
- On 4 October 1912, Gateaux, freed from the active army, began his lectures at the Lycée of Bar-le-Duc.
- We did not find precise details about how Gateaux chose this subject for his researches, but it is plausible that he was advised to do so by Hadamard himself who had just delivered lectures at the Collège de France and entered the Academy of Science in 1912.
- There were good reasons for Gateaux to be attracted by this new and hardly explored domain.
- And also, a young French normalien of the year before Gateaux, Joseph Pérès, had in 1912-1913 benefited from a grant offered by the David Weill foundation to work for a one-year period in Rome with Volterra.
- A David Weill grant was awarded to Gateaux for the year 1913-1914.
- As he exposed them in a letter to Volterra, we know precisely what were the mathematical aims of Gateaux when he went to Rome.
- Gateaux considered two main points of interest for his future researches.
- In a last paragraph, Gateaux mentions the possible applications of such an integration of functionals, such as the residue theorem ...
- About Gateaux's stay in Rome, we do not have many details.
- An interesting document, found among the documents of the Académie des Sciences in Paris, is the draft of a report Gateaux had to write at the end of his visit, probably for the David Weill foundation.
- Gateaux seems to have worked quite actively in Rome.
- Moreover, on the postcard sent by Borel to Volterra on 1 January 1914 with his best wishes for the new 1914 year (a sentence which sounds strange to the ears of one knowing what was going to happen soon ...), Borel mentioned how he was glad to learn that Volterra was absolutely satisfied with Gateaux in Rome.
- On 14 February 1914, Gateaux delivered a lecture at Volterra's seminar; his lecture notes were kept among his papers.
- Gateaux mainly dealt with the notion of functional differentiation.
- Gateaux probably came back to France at the beginning of the summer, in June 1914.
- Gateaux seems to have been caught napping by the beginning of the war.
- Gateaux was mobilized in the reserve as lieutenant of the 269th Infantry regiment, a member of the 70th infantry division.
- The quartering of Gateaux's regiment took place in Toul.
- General Joffre decided to withdraw from the eastern part of the front (precisely where Gateaux was) a large number of divisions and to send them by rail to places in Picardie, then to Artois, and finally to Flandres, to try to outrun the Germans.
- On 3 October, Gateaux's regiment was in Rouvroy, a small village, 10 km south-east of Lens, and Gateaux was killed at 1 o'clock in the morning, while trying to prevent the Germans from entering the village.
- Gateaux's body was buried near the St Anne Chapel in Rouvroy, a simple cross without inscription marking the place.
- Only long after, Gateaux's corpse was exhumed and formally identified, and finally transported to the necropolis of the military cemetery of Bietz-Neuville St Vaast where Gateaux's grave is number 76.
- As soon as August 1915, Hadamard began the necessary steps to obtain the attribution of one of the prizes of the Academy of Science to Gateaux.
- Volterra answered both letters on January 15th , telling Lévy that none of Gateaux's publications concerned integration.
- From this sentence, we may infer that it is Fréchet who firstly wrote to Lévy about Gateaux's papers, and certainly because he had an idea of what they contained.
- On 12 February, Lévy began to describe to Fréchet the content of what he had precisely found in Gateaux papers, namely a first theory of harmonic functionals.
- Gateaux's interest in infinite dimensional integration originated in the extension of Cauchy's formula.
- Gateaux seems to have been the first to propose a natural way to bypass the problem by considering the integral as an asymptotic mean value.

Born 5 May 1889, Vitry-le-François, Marne, France. Died 3 October 1914, Rouvroy, near Lens, France.

View full biography at MacTutor

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