Émile Borel

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Émile Borel
Émile Borel (1932)
Minister of the Navy
In office
17 April 1925 – 28 November 1925
Prime MinisterPaul Painlevé
Preceded byJacques-Louis Dumesnil
Succeeded byGeorges Leygues
Member of the Chamber of Deputies
In office
15 June 1924 – 4 June 1936
Personal details
Félix Édouard Justin Émile Borel

(1871-01-07)7 January 1871
Saint-Affrique, France
Died3 February 1956(1956-02-03) (aged 85)
Paris, France
Alma materÉcole normale supérieure Paris
Known forMeasure theory
Probability theory
Heine–Borel theorem
Scientific career
InstitutionsUniversity of Paris
ThesisSur quelques points de la théorie des fonctions (1893)
Doctoral advisorGaston 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. 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 ("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 supérieure in 1897, and was appointed to the chair of theory of functions, 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 (1921–1927) that first defined games of strategy.[5] 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.[6]

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 always normal, and with explicit constructions in terms of digits, it is quite straightforward to get numbers that are normal.[7]

In 1913 and 1914 he bridged the gap between hyperbolic geometry and special relativity with expository work. For instance, his book Introduction Géométrique à quelques Théories Physiques[8] described hyperbolic rotations as transformations that leave a hyperbola stable 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 in Paris.

Political career[edit]

In the 1920s, 1930s, and 1940s, he was active in politics. From 1924 to 1936, he was a member of the Chamber of Deputies.[9] In 1925, he was Minister of the Navy 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 that he coins La Relance in his 1938 book Applications de la théorie des probabilités aux Jeux de Hasard.[10]

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 treatise 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)
  • Probability and certainty (1950)
  • Inaccessible numbers (1952)
  • Imaginary and real in mathematics and physics (1952)
  • Emile Borel complete works (1972)


See also[edit]


  1. ^ May, Kenneth (1970–1980). "Borel, Émile". Dictionary of Scientific Biography. Vol. 2. New York: Charles Scribner's Sons. pp. 302–305. ISBN 978-0-684-10114-9.
  2. ^ Émile Borel's biographyUniversité 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. ^ von Neumann, J.; Fréchet, M. (1953). "Communication on the Borel Notes". Econometrica. 21 (1): 124–127. doi:10.2307/1906950. ISSN 0012-9682. JSTOR 1906950.
  7. ^ Harman, Glyn (2002), "One hundred years of normal numbers", in Bennett, M. A.; Berndt, B. C.; Boston, N.; Diamond, H. G.; Hildebrand, A. J.; Philipp, W. (eds.), Surveys in Number Theory: Papers from the Millennial Conference on Number Theory, A K Peters, pp. 57–74, MR 1956249
  8. ^ Émile Borel (1914) Introduction Geometrique à quelques Théories Physiques, Gauthier-Villars, link from Cornell University Historical Math Monographs
  9. ^ "Émile Borel | French mathematician | Britannica". www.britannica.com. Retrieved 2023-03-12.
  10. ^ Émile Borel and Jean Ville. Applications de la théorie des probabilités aux jeux de hasard. Gauthier-Vilars, 1938
  • Michel Pinault, Emile Borel, une carrière intellectuelle sous la 3ème République, Paris, L'Harmattan, 2017. Voir : michel-pinault.over-blog.com

External links[edit]

Political offices
Preceded by Minister of the Navy
April 17, 1925 – November 28, 1925
Succeeded by