Félix Édouard Justin Émile Borel (; 7 January 1871 – 3 February 1956) was a

French French (french: français(e), link=no) may refer to: * Something of, from, or related to France ** French language, which originated in France, and its various dialects and accents ** French people, a nation and ethnic group identified with Franc ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and

politician A politician is a person active in party politics, or a person holding or seeking an elected office in government. Politicians propose, support, reject and create laws that govern the land and by an extension of its people. Broadly speaking, ...

. As a mathematician, he was known for his founding work in the areas of measure theory and

probability Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, ...

Biography

Borel was born in Saint-Affrique,

Aveyron Aveyron (; oc, Avairon; ) is a department in the region of Occitania, Southern France. It was named after the river Aveyron. Its inhabitants are known as ''Aveyronnais'' (masculine) or ''Aveyronnaises'' (feminine) in French. The inhabitan ...

, the son of a

Protestant Protestantism is a Christian denomination, branch of Christianity that follows the theological tenets of the Reformation, Protestant Reformation, a movement that began seeking to reform the Catholic Church from within in the 16th century agai ...

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 In France, the ''agrégation'' () is a competitive examination for civil service in the French public education system. Candidates for the examination, or ''agrégatifs'', become ''agrégés'' once they are admitted to the position of ''profe ...

, 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'' ("On some points in the theory of functions"). That year, Borel started a four-year stint as a lecturer at the

University of Lille The University of Lille (french: Université de Lille, abbreviated as ULille, UDL or univ-lille) is a French public research university based in Lille, Hauts-de-France. It has its origins in the University of Douai (1559), and resulted from th ...

, during which time he published 22 research papers. He returned to the École normale supérieure 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 Henri Léon Lebesgue (; June 28, 1875 – July 26, 1941) was a French mathematician known for his theory of integration, which was a generalization of the 17th-century concept of integration—summing the area between an axis and the curve of ...

, Émile Borel was among the pioneers of measure theory and its application to

probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set ...

. The concept of a

Borel set In mathematics, a Borel set is any set in a topological space that can be formed from open sets (or, equivalently, from closed sets) through the operations of countable union, countable intersection, and relative complement. Borel sets are na ...

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 The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type any given text, such as the complete works of William Shakespeare. In fact, the monkey would ...

or the like. He also published a series of papers (1921–1927) that first defined games of strategy. John von Neumann objected to this assignment of priority in a letter to ''Econometrica'' published in 1953 where he asserted that Borel could not have defined games of strategy because he rejected the minimax theorem. With the development of

statistical hypothesis testing A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters. ...

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 always In probability theory, an event is said to happen almost surely (sometimes abbreviated as a.s.) if it happens with probability 1 (or Lebesgue measure 1). In other words, the set of possible exceptions may be non-empty, but it has probability 0. ...

normal, 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 In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The law ...

with expository work. For instance, his book ''Introduction Géométrique à quelques Théories Physiques'' described hyperbolic rotations as transformations that leave a hyperbola

stable A stable is a building in which livestock, especially horses, are kept. It most commonly means a building that is divided into separate stalls for individual animals and livestock. There are many different types of stables in use today; the ...

just as a circle around a rotational center is stable. In 1922, he founded the Paris Institute of Statistics, the oldest French school for statistics; then in 1928 he co-founded the

Institut Henri Poincaré The Henri Poincaré Institute (or IHP for ''Institut Henri Poincaré'') is a mathematics research institute part of Sorbonne University, in association with the Centre national de la recherche scientifique (CNRS). It is located in the 5th arrond ...

in Paris.

Political career

In the 1920s, 1930s, and 1940s, he was active in politics. From 1924 to 1936, he was a member of the

Chamber of Deputies The chamber of deputies is the lower house in many bicameral legislatures and the sole house in some unicameral legislatures. Description Historically, French Chamber of Deputies was the lower house of the French Parliament during the Bourbon R ...

. In 1925, he was

Minister of the Navy Minister of the Navy may refer to: * Minister of the Navy (France) * Minister of the Navy (Italy) * Minister of the Navy (Japan) * Minister of the Navy (Netherlands) * Minister of the Navy (Spain) * Minister of the Navy (Turkey) * Minister of ...

in the cabinet of fellow mathematician

Paul Painlevé Paul Painlevé (; 5 December 1863 – 29 October 1933) was a French mathematician and statesman. He served twice as Prime Minister of the Third Republic: 12 September – 13 November 1917 and 17 April – 22 November 1925. His entry into politic ...

. During the

Second World War World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposi ...

, he was a member of the

French Resistance The French Resistance (french: La Résistance) was a collection of organisations that fought the German occupation of France during World War II, Nazi occupation of France and the Collaborationism, collaborationist Vichy France, Vichy régim ...

Honors

Besides the ''Centre Émile Borel'' at the

in Paris and a crater on the Moon, the following mathematical notions are named after him: *

Borel algebra In mathematics, a Borel set is any set in a topological space that can be formed from open sets (or, equivalently, from closed sets) through the operations of countable union, countable intersection, and relative complement. Borel sets are name ...

Borel's lemma In mathematics, Borel's lemma, named after Émile Borel, is an important result used in the theory of asymptotic expansions and partial differential equations. Statement Suppose ''U'' is an open set in the Euclidean space R''n'', and suppose th ...

* Borel's law of large numbers * Borel measure * Borel–Kolmogorov paradox * Borel–Cantelli lemma *

Borel–Carathéodory theorem In mathematics, the Borel–Carathéodory theorem in complex analysis shows that an analytic function may be bounded by its real part. It is an application of the maximum modulus principle. It is named for Émile Borel and Constantin Carathéodor ...

* Heine–Borel theorem *

Borel determinacy theorem In descriptive set theory, the Borel determinacy theorem states that any Gale–Stewart game whose payoff set is a Borel set is determined, meaning that one of the two players will have a winning strategy for the game. A Gale-Stewart game is a poss ...

* Borel right process *

Borel summation In mathematics, Borel summation is a summation method for divergent series, introduced by . It is particularly useful for summing divergent asymptotic series, and in some sense gives the best possible sum for such series. There are several va ...

* Borel distribution * Borel's conjecture about

strong measure zero set In mathematical analysis, a strong measure zero set is a subset ''A'' of the real line with the following property: :for every sequence (ε''n'') of positive reals there exists a sequence (''In'') of intervals such that , ''I'n'', < ε_{''n' ...}

s (not to be confused with Borel conjecture, named for Armand Borel). Borel also described a poker model that he coins ''La Relance'' in his 1938 book ''Applications de la théorie des probabilités aux Jeux de Hasard''.Émile Borel and Jean Ville. Applications de la théorie des probabilités aux jeux de hasard. Gauthier-Vilars, 1938 Borel was awarded the Resistance Medal in 1950.

Works

* ''On a few points about the theory of functions'' (PhD thesis, 1894) * ''Introduction to the study of number theory and superior algebra'' (1895) * ''A course on the theory of functions'' (1898) * ''A course on

power series In mathematics, a power series (in one variable) is an infinite series of the form \sum_^\infty a_n \left(x - c\right)^n = a_0 + a_1 (x - c) + a_2 (x - c)^2 + \dots where ''an'' represents the coefficient of the ''n''th term and ''c'' is a con ...

'' (1900) * ''A course on divergent series'' (1901) * ''A course on positive terms series'' (1902) * ''A course on meromorphic functions'' (1903) * ''A course on growth theory at the Paris faculty of sciences'' (1910) * ''A course on functions of a real variable and polynomial serial developments'' (1905) * ''Chance'' (1914) * ''Geometrical introduction to some physical theories'' (1914) * ''A course on

complex variable Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebra ...

uniform monogenic functions'' (1917) * ''On the method in sciences'' (1919) * ''Space and time'' (1921) * '' Game theory and left symmetric core integral equations'' (1921) * ''Methods and problems of the theory of functions'' (1922) * ''Space and time'' (1922) * ''A treatise on probability calculation and its applications'' (1924–1934) * ''Application of

to games of chance'' (1938) * ''Principles and classical formulas for probability calculation'' (1925) * ''Practical and philosophical values of probabilities'' (1939) * ''Mathematical theory of contract bridge for everyone'' (1940) * ''Game, luck and contemporary scientific theories'' (1941) * ''Probabilities and life'' (1943) * ''Evolution of

mechanics Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objec ...

'' (1943) * ''Paradoxes of the infinite'' (1946) * ''Elements of

set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concern ...

'' (1949) * ''Probability and certainty'' (1950) * ''Inaccessible numbers'' (1952) * ''Imaginary and real in mathematics and physics'' (1952) * '' Emile Borel complete works'' (1972)

Articles

*
"''La science est-elle responsable de la crise mondiale?''"
Scientia : rivista internazionale di sintesi scientifica, 51, 1932, pp. 99–106. *
"''La science dans une société socialiste''"
Scientia : rivista internazionale di sintesi scientifica, 31, 1922, pp. 223–228. *
"''Le continu mathématique et le continu physique''"
Rivista di scienza, 6, 1909, pp. 21–35.

References

* Michel Pinault, ''Emile Borel, une carrière intellectuelle sous la 3ème République'', Paris, L'Harmattan, 2017. Voir : michel-pinault.over-blog.com

External links

* * * * *
Author profile
in the database zbMATH {{DEFAULTSORT:Borel, Emile 1871 births 1956 deaths People from Aveyron Politicians from Occitania (administrative region) Radical Party (France) politicians Republican-Socialist Party politicians Ministers of Marine Intuitionism Members of the 13th Chamber of Deputies of the French Third Republic Members of the 14th Chamber of Deputies of the French Third Republic Members of the 15th Chamber of Deputies of the French Third Republic 19th-century French mathematicians 20th-century French mathematicians Probability theorists Measure theorists Lycée Louis-le-Grand alumni École Normale Supérieure alumni Lille University of Science and Technology faculty Members of the French Academy of Sciences French military personnel of World War I French Resistance members Grand Croix of the Légion d'honneur Recipients of the Croix de Guerre 1939–1945 (France) Recipients of the Resistance Medal