French mathematician and politician, well known for his work in probability theory.
The son of a clergyman, Borel was born at St Affrique and educated at the École Normale Supérieure. After teaching at the University of Lille (1893–96) he returned to Paris, where for the following forty years he held a number of appointments at the École Normale and the Sorbonne.
In his Éléments de la théorie des probabilités (1909) Borel sought to bring probability theory into the mainstream of mathematics. His key insight was to note that rules for calculating probabilities were similar in form to those used in the calculation of areas in geometry. It was only necessary to change the term ‘set’ for ‘event’ and ‘area’ for ‘probability’. The introduction of measure theory to probability allowed the contemplation and even the solution of problems long considered too difficult. Borel also worked in analysis. In the 1920s he anticipated several results in the field of game theory, which were later published by J. von Neumann. In particular, he proved a restricted version of the mini-max theorem.
From 1924 to 1936 Borel served as a radical socialist member of the Chamber of Deputies. In 1925 he was appointed navy minister. In addition to his political activities Borel did much to change the structure of French science. He helped found the Institut Henri Poincaré, serving as its first director from 1928 until his death; he was also responsible for the founding of the Centre National de la Recherche Scientifique. With the outbreak of war in 1939 Borel was initially arrested by the Vichy government. He was released after a few months and, despite his age, served with the Resistance.
Subjects: Contemporary History (Post 1945).