The ghosts of the Ecole Normale. Life, death and legacy of Ren\'e Gateaux

TL;DR

This paper explores the life and scientific legacy of René Gateaux, a young mathematician whose pioneering work on infinite-dimensional integrals significantly influenced the development of probability theory and functional analysis.

Contribution

It highlights Gateaux's early contributions to infinite-dimensional integration and their impact on later developments by Paul Lévy and the Wiener measure.

Findings

Gateaux introduced early ideas on infinite-dimensional integrals.

Lévy extended Gateaux's concepts within a probabilistic framework.

Gateaux's work influenced the foundation of the Wiener measure.

Abstract

The present paper deals with the life and some aspects of the scientific contributions of the mathematician Ren\'e Gateaux, killed during World War 1 at the age of 25. Though he died very young, he left interesting results in functional analysis. In particular, he was among the first to try to construct an integral over an infinite dimensional space. His ideas were extensively developed later by Paul L\'evy. Among other things, L\'evy interpreted Gateaux's integral in a probabilistic framework that later contributed to the construction of the Wiener measure. This article tries to explain this singular personal and professional destiny in pre- and postwar France.