View source for Émile Borel

{{Short description|French mathematician (1871–1956)}}
{{distinguish|Armand Borel}}
{{Infobox officeholder
| name                = Émile Borel
| image               = Emile Borel-1932.jpg
| image_size          = 200px
| caption             = Émile Borel (1932)
| office              = [[List of naval ministers of France|Minister of the Navy]]
| term_start          = 17 April 1925
| term_end            = 28 November 1925
| primeminister       = [[Paul Painlevé]]
| predecessor         = [[Jacques-Louis Dumesnil]]
| successor           = [[Georges Leygues]]
| office1             = Member of the [[Chamber of Deputies (France)|Chamber of Deputies]]
| term_start1         = 15 June 1924
| term_end1           = 4 June 1936
| birth_name          = Félix Édouard Justin Émile Borel
| birth_date          = {{birth date|1871|01|07|df=y}}
| birth_place         = [[Saint-Affrique]], [[France]]
| death_date          = {{death date and age|1956|02|03|1871|01|07|df=y}}
| death_place         = [[Paris]], [[France]]
| nationality         = [[French people|French]]
{{Infobox scientist | embed = yes
| fields            = Mathematics
| workplaces        = [[University of Paris]]
| alma_mater        = [[École normale supérieure (Paris)|École normale supérieure Paris]]
| thesis_title      = Sur quelques points de la théorie des fonctions
| thesis_url        = http://archive.numdam.org/ARCHIVE/ASENS/ASENS_1895_3_12_/ASENS_1895_3_12__9_0/ASENS_1895_3_12__9_0.pdf
| thesis_year       = 1893
| doctoral_advisor  = [[Jean Gaston Darboux|Gaston Darboux]]
| doctoral_students = {{unbulleted list|[[Paul Dienes]]|[[Henri Lebesgue]]|[[Paul Montel]]|[[Georges Valiron]]}}
| known_for         = [[Measure theory]] <br> [[Probability theory]] <br> [[Heine–Borel theorem]]
}}
}}

'''Félix Édouard Justin Émile Borel''' ({{IPA|fr|bɔʁɛl|lang}}; 7 January 1871 – 3 February 1956)<ref>{{DSB |first=Kenneth | last=May | title=Borel, Émile | volume=2 | pages=302–305 }}</ref> was a [[French people|French]] [[mathematician]]<ref>[http://www.univ-lille1.fr/asa_2/mathematiques/mathematiques-2.htm Émile Borel's biography] – [[Université Lille Nord de France]]</ref> and [[politician]]. As a mathematician, he was known for his founding work in the areas of [[measure theory]] and [[probability]].

== Biography ==
Borel was born in [[Saint-Affrique]], [[Aveyron]], the son of a [[Protestant]] pastor.<ref name="McElroy 2009">{{cite book |author=McElroy, Tucker |title=A to Z of Mathematicians |url=https://books.google.com/books?id=MiZIWtX9AJUC&pg=PA46 |year=2009 |publisher=Infobase Publishing |isbn=978-1-4381-0921-3 |page=46}}</ref> He studied at the [[Collège Sainte-Barbe]] and [[Lycée Louis-le-Grand]] before applying to both the [[École normale supérieure (Paris)|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.<ref name="Chang 2011">{{cite book |author=Chang, Sooyoung |title=Academic Genealogy of Mathematicians |url=https://books.google.com/books?id=4siw31DPONUC&pg=PA107 |year=2011 |publisher=World Scientific |isbn=978-981-4282-29-1 |page=107}}</ref>

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.<ref name="Chang 2011"/>

== Work ==
Along with [[René-Louis Baire]] and [[Henri Lebesgue]], Émile Borel was among the pioneers of [[measure (mathematics)|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 [[game theory|games of strategy]].<ref>[http://www.britannica.com/EBchecked/topic/74060/Emile-Borel "Émile Borel," ''Encyclopædia Britannica'']</ref> 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.<ref>{{Cite journal|last1=von Neumann|first1=J.|last2=Fréchet|first2=M.|date=1953|title=Communication on the Borel Notes|url=https://www.jstor.org/stable/1906950|journal=Econometrica|volume=21|issue=1|pages=124–127|doi=10.2307/1906950|jstor=1906950 |issn=0012-9682|url-access=subscription}}</ref> 

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 number|normal]], and with explicit constructions in terms of digits, it is quite straightforward to get numbers that are normal.<ref>{{citation
 | last = Harman | first = Glyn
 | editor1-last = Bennett | editor1-first = M. A.
 | editor2-last = Berndt | editor2-first = B. C.
 | editor3-last = Boston | editor3-first = N.
 | editor4-last = Diamond | editor4-first = H. G.
 | editor5-last = Hildebrand | editor5-first = A. J.
 | editor6-last = Philipp | editor6-first = W.
 | contribution = One hundred years of normal numbers
 | contribution-url = https://books.google.com/books?id=RWC1DwAAQBAJ&pg=PA57
 | mr = 1956249
 | pages = 57–74
 | publisher = A K Peters
 | title = Surveys in Number Theory: Papers from the Millennial Conference on Number Theory
 | year = 2002}}</ref>

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''<ref>Émile Borel (1914) [https://ebooks.library.cornell.edu/cgi/t/text/text-idx?c=math;cc=math;view=toc;subview=short;idno=04710001 Introduction Geometrique à quelques Théories Physiques], Gauthier-Villars, link from [[Cornell University]] Historical Math Monographs</ref> described [[hyperbolic rotation]]s as transformations that leave a hyperbola [[invariant (mathematics)#Invariant set|stable]] just as a circle around a rotational center is stable.

In 1915 he was appointed head of the technical cabinet for the newly formed [[Directorate of Inventions for National Defense]] which aimed to coordinate French laboratories for the war effort in the [[First World War]].

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 ==
In the 1920s, 1930s, and 1940s, he was active in politics. From 1924 to 1936, he was a member of the [[Chamber of Deputies (France)|Chamber of Deputies]].<ref>{{Cite web |title=Émile Borel {{!}} French mathematician {{!}} Britannica |url=https://www.britannica.com/biography/Emile-Borel |access-date=2023-03-12 |website=www.britannica.com |language=en}}</ref> In 1925, he was [[List of Naval Ministers of France|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]].
[[File:1918 E Borel.jpg|thumb|[[Autochrome Lumière|Autochrome]] portrait by [[The Archives of the Planet|Auguste Léon]], 1918]]

== Honors ==

Besides the ''Centre Émile Borel'' at the [[Institut Henri Poincaré]] in Paris
and a [[Borel (crater)|crater on the Moon]], the following mathematical notions are named after him:
{{div col|colwidth=25em}}
*[[Borel algebra]]
*[[Borel's lemma]]
*[[Borel's law of large numbers]]
*[[Borel measure]]
*[[Borel–Kolmogorov paradox]]
*[[Borel–Cantelli lemma]]
*[[Borel–Carathéodory theorem]]
*[[Heine–Borel theorem]]
*[[Borel determinacy theorem]]
*[[Borel right process]]
*[[Borel set]]
*[[Borel summation]]
*[[Borel distribution]]
*[[Strong measure zero set|Borel's conjecture]] about [[strong measure zero set]]s (not to be confused with [[Borel conjecture]], named for Armand Borel).
{{div col end}}

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''.<ref>Émile Borel and Jean Ville. Applications de la théorie des probabilités aux jeux de hasard. Gauthier-Vilars, 1938</ref>

Borel was awarded the [[Resistance Medal]] in 1950.<ref name="Chang 2011"/>

== Works ==
{{div col|colwidth=25em}}
{{refbegin}}
* ''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)
{{refend}}
{{div col end}}

=== Articles ===

* {{in lang|fr}} [http://amshistorica.unibo.it/diglib.php?inv=7&int_ptnum=51&term_ptnum=107&format=jpg "La science est-elle responsable de la crise mondiale?"], ''[[Scientia (Italian journal)|Scientia : rivista internazionale di sintesi scientifica]]'', 51, 1932, pp.&nbsp;99–106.
* {{in lang|fr}} [http://amshistorica.unibo.it/diglib.php?inv=7&int_ptnum=31&term_ptnum=231&format=jpg "La science dans une société socialiste"], ''Scientia : rivista internazionale di sintesi scientifica'', 31, 1922, pp.&nbsp;223–228.     
* {{in lang|fr}} [http://amshistorica.unibo.it/diglib.php?inv=6&int_ptnum=6&term_ptnum=29&format=jpg "Le continu mathématique et le continu physique"], ''[[Scientia (Italian journal)|Rivista di scienza]]'', 6, 1909, pp.&nbsp;21–35.

== See also ==
*[[Borel right process]]

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

== External links ==
* {{MathGenealogy|id=39071}}
*{{Wikiquote-inline}}
*{{wikisourcelang-inline|fr|Auteur:Émile Borel}}
*{{Commons category-inline}}
* {{Internet Archive author |sname=Émile Borel |sopt=w}}
* {{MacTutor Biography|id=Borel}}
* [https://zbmath.org/authors/?q=ai:borel.emile Author profile] in the database [[Zentralblatt MATH|zbMATH]]

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{{succession box
| title  = [[List of naval ministers of France|Minister of the Navy]]
| years  = April 17, 1925 &ndash; November 28, 1925
| before = [[Jacques-Louis Dumesnil]]
| after  = [[Georges Leygues]]
}}
{{s-end}}
<!-- {{Université Lille – Nord de France}} -->

{{Authority control}}

{{DEFAULTSORT:Borel, Emile}}
[[Category:1871 births]]
[[Category:1956 deaths]]
[[Category:People from Saint-Affrique]]
[[Category:French Calvinist and Reformed Christians]]
[[Category:Radical Party (France) politicians]]
[[Category:Republican-Socialist Party politicians]]
[[Category:Ministers of marine]]
[[Category:Members of the 13th Chamber of Deputies of the French Third Republic]]
[[Category:Members of the 14th Chamber of Deputies of the French Third Republic]]
[[Category:Members of the 15th Chamber of Deputies of the French Third Republic]]
[[Category:Members of Parliament for Aveyron]]
[[Category:19th-century French mathematicians]]
[[Category:20th-century French mathematicians]]
[[Category:French probability theorists]]
[[Category:Measure theorists]]
[[Category:Intuitionism]]
[[Category:Lycée Louis-le-Grand alumni]]
[[Category:École Normale Supérieure alumni]]
[[Category:Academic staff of the Lille University of Science and Technology]]
[[Category:Members of the French Academy of Sciences]]
[[Category:French military personnel of World War I]]
[[Category:French Resistance members]]
[[Category:Grand Cross of the Legion of Honour]]
[[Category:Recipients of the Croix de Guerre 1939–1945 (France)]]
[[Category:Recipients of the Resistance Medal]]