Émile Borel

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Émile Borel
Emile Borel-1932.jpg
Émile Borel (1932)
Born (1871-01-07)7 January 1871
Saint-Affrique, France
Died 3 February 1956(1956-02-03) (aged 85)
Paris, France
Nationality French
Alma mater École Normale Supérieure Paris
Known for Measure theory, Probability theory
Scientific career
Fields Mathematics, politics
Institutions University of Paris
Thesis Sur quelques points de la théorie des fonctions (1893)
Doctoral advisor Gaston Darboux
Doctoral students

Félix Édouard Justin Émile Borel (French: [bɔʁɛl]; 7 January 1871 – 3 February 1956)[1] was a French mathematician[2] and politician. As a mathematician, he was known for his founding work in the areas of measure theory and probability.


Borel was born in Saint-Affrique, Aveyron, the son of a Protestant pastor.[3] He studied at the Collège Sainte-Barbe and Lycée Louis-le-Grand before applying to both the École normale supérieure and the École Polytechnique. Although he qualified for both, he chose to attend the former institution in 1889. That year he 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 ("On some points in the theory of functions"). 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 function, which he held until 1941.[4]

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.[4]


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 (1921–27) that first defined games of strategy.[5]

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[6] described hyperbolic rotations as transformations that leave a hyperbola stable just as a circle around a rotational center is stable.

Political career[edit]

In the 1920s, 1930s, and 1940s, he was active in politics. In 1922, he founded Paris Institute of Statistics, the oldest French school for statistics. From 1924 to 1936, he was a member of the French National Assembly. In 1925, he was Minister of Marine in the cabinet of fellow mathematician Paul Painlevé. During the Second World War, he was a member of the French Resistance.


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 also described a poker model which he coins La Relance in his 1938 book Applications de la théorie des probabilités aux Jeux de Hasard.[7]

Borel was awarded the Resistance Medal in 1950.[4]


  • 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 (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 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 treaty on probability calculation and its applications (1924-1934)
  • Application of probability theory 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 (1943)
  • Paradoxes of the infinite (1946)
  • Elements of set theory (1949)
  • Inaccessible numbers (1952)
  • Imaginary and real in mathematics and physics (1952)
  • Emile Borel complete works (1972)



  1. ^ May, Kenneth (1970–80). "Borel, Émile". Dictionary of Scientific Biography. 2. New York: Charles Scribner's Sons. pp. 302–305. ISBN 978-0-684-10114-9. 
  2. ^ Émile Borel's biography - Université Lille Nord de France
  3. ^ McElroy, Tucker (2009). A to Z of Mathematicians. Infobase Publishing. p. 46. ISBN 978-1-4381-0921-3. 
  4. ^ a b c Chang, Sooyoung (2011). Academic Genealogy of Mathematicians. World Scientific. p. 107. ISBN 978-981-4282-29-1. 
  5. ^ "Émile Borel," Encyclopædia Britannica
  6. ^ Émile Borel (1914) Introduction Geometrique à quelques Théories Physiques, Gauthier-Villars, link from Cornell University Historical Math Monographs
  7. ^ Émile Borel and Jean Ville. Applications de la théorie des probabilités aux jeux de hasard. Gauthier-Vilars, 1938

External links[edit]