Borel was born in Saint-Affrique, Aveyron, the son of a Protestant pastor. He studied at the Collège Sainte-Barbe and Lycée Louis-le-Grand before applying to both the École normale supérieure and the École Polytechnique. He qualified in the first position for both and chose to attend the former institution in 1889. That year he also won the concours général, an annual national mathematics competition. After graduating in 1892, he placed first in the agrégation, a competitive civil service examination leading to the position of professeur agrégé. His thesis, published in 1893, was titled Sur quelques points de la théorie des fonctions. That year, Borel started a four-year stint as a lecturer at the University of Lille, during which time he published 22 research papers. He returned to the École normale in 1897, and was appointed to the chair of theory of functions, which he held until 1941. In 1901, Borel married 17-year-old Marguerite, the daughter of colleague Paul Émile Appel; she later wrote more than 30 novels under the pseudonym Camille Marbo. Émile Borel died in Paris on 3 February 1956.
Work
Along with René-Louis Baire and Henri Lebesgue, Émile Borel was among the pioneers of measure theory and its application to probability theory. The concept of a Borel set is named in his honor. One of his books on probability introduced the amusing thought experiment that entered popular culture under the name infinite monkey theorem or the like. He also published a series of papers that first defined games of strategy. With the development of statistical hypothesis testing in the early 1900s various tests for randomness were proposed. Sometimes these were claimed to have some kind of general significance, but mostly they were just viewed as simple practical methods. In 1909, Borel formulated the notion that numbers picked randomly on the basis of their value are almost alwaysnormal, and with explicit constructions in terms of digits, it is quite straightforward to get numbers that are normal. In 1913 and 1914 he bridged the gap between hyperbolic geometry and special relativity with expository work. For instance, his book Introduction Geometrique à quelques Théories Physiques described hyperbolic rotations as transformations that leave a hyperbola stable just as a circle around a rotational center is stable. In 1928 he co-founded Institut Henri Poincaré in Paris.
Besides the Centre Émile Borel at the Institut Henri Poincaré in Paris and a crater on the Moon, the following mathematical notions are named after him:
Borel's conjecture about strong measure zero sets.
Borel also described a poker model which he coins La Relance in his 1938 book Applications de la théorie des probabilités aux Jeux de Hasard. Borel was awarded the Resistance Medal in 1950.
