René-Louis Baire
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René-Louis Baire (; 21 January 1874 – 5 July 1932) was a French
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, mathematical structure, structure, space, Mathematica ...
most famous for his
Baire category theorem The Baire category theorem (BCT) is an important result in general topology and functional analysis. The theorem has two forms, each of which gives sufficient conditions for a topological space to be a Baire space (a topological space such that th ...
, which helped to generalize and prove future theorems. His theory was published originally in his dissertation ''Sur les fonctions de variables réelles'' ("On the Functions of Real Variables") in 1899.


Education and career

The son of a tailor, Baire was one of three children from a poor working-class family in Paris. He started his studies when he entered the Lycée Lakanal through the use of a scholarship. In 1890, Baire completed his advanced classes and entered the special mathematics section of the Lycée Henri IV. While there, he prepared for and passed the entrance examination for the
École Normale Supérieure École or Ecole may refer to: * an elementary school in the French educational stages normally followed by Secondary education in France, secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing i ...
and the
École Polytechnique (, ; also known as Polytechnique or l'X ) is a ''grande école'' located in Palaiseau, France. It specializes in science and engineering and is a founding member of the Polytechnic Institute of Paris. The school was founded in 1794 by mat ...
. He decided to attend the École Normale Supérieure in 1891.René-Louis Baire
(2010). Encyclopædia Britannica on-line. Retrieved September 9, 2010
After receiving his three-year degree, Baire proceeded toward his
agrégation In France, the () is the most competitive and prestigious examination for civil service in the French public education A state school, public school, or government school is a primary school, primary or secondary school that educates all stu ...
. He did better than all the other students on the writing portion of the test but he did not pass the oral examination due to a lack of explanation and clarity in his lesson. After retaking the agrégation and passing, he was assigned to teach at the secondary school (lycée) in
Bar-le-Duc Bar-le-Duc (), formerly known as Bar, is a commune in the Meuse département, of which it is the capital. The department is in Grand Est in northeastern France. The lower, more modern and busier part of the town extends along a narrow valley, ...
. While there, Baire researched the concept of limits and discontinuity for his doctorate. He presented his thesis on March 24, 1899 and was awarded his doctorate. He continued to teach in secondary schools around France but was not happy teaching lower level mathematics. In 1901 Baire was appointed to the
University of Montpellier The University of Montpellier () is a public university, public research university located in Montpellier, in south-east of France. Established in 1220, the University of Montpellier is one of the List of oldest universities in continuous opera ...
as a "
Maître de conférences The following summarizes basic academic ranks in the France, French higher education system. Most academic institutions are state-run and most academics with permanent positions are French Civil Service, civil servants, and thus are Academic tenur ...
". In 1904 he was awarded a Peccot Foundation Fellowship to spend a semester in a university and develop his skills as a professor. Baire chose to attend the
Collège de France The (), formerly known as the or as the ''Collège impérial'' founded in 1530 by François I, is a higher education and research establishment () in France. It is located in Paris near La Sorbonne. The has been considered to be France's most ...
where he lectured on the subject of
analysis Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...
. He was appointed to a university post in 1905 when he joined the Faculty of Science at the
University of Dijon A university () is an institution of tertiary education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase , which roughly means "community of teachers and scholars". Univ ...
. In 1907 he was promoted to Professor of Analysis at Dijon where he continued his research in analysis.


Illness

Since he was young, Baire always had "delicate" health. He had developed problems with his esophagus before he attended school and he would occasionally experience severe attacks of
agoraphobia Agoraphobia is an anxiety disorder characterized by symptoms of anxiety in situations where the person perceives their environment to be unsafe with no way to escape. These situations can include public transit, shopping centers, crowds and q ...
.Dunham, William. (2005). Baire. In ''The Calculus Gallery'
pp. 183–199
Princeton, NJ: Princeton University Press .
From time to time, his health would prevent him from working or studying. The bad spells became more frequent, immobilizing him for long periods of time. Over time, he had developed a kind of psychological disorder that made him unable to undertake work that required long periods of concentration. At times this would make his ability to research mathematics impossible. Between 1909 and 1914 this problem continually plagued him and his teaching duties became more and more difficult. In 1914 he was given a leave of absence from the University of Dijon due to his poor health, after which he spent the rest of his life in
Lausanne Lausanne ( , ; ; ) is the capital and largest List of towns in Switzerland, city of the Swiss French-speaking Cantons of Switzerland, canton of Vaud, in Switzerland. It is a hilly city situated on the shores of Lake Geneva, about halfway bet ...
, Switzerland, and around
Lake Geneva Lake Geneva is a deep lake on the north side of the Alps, shared between Switzerland and France. It is one of the List of largest lakes of Europe, largest lakes in Western Europe and the largest on the course of the Rhône. Sixty percent () ...
. He retired from Dijon in 1925 and spent his last years living in multiple hotels that he could afford with his meager pension. He committed suicide in 1932.


Contributions to mathematics

Baire's skill in mathematical analysis led him to study with other major names in analysis such as
Vito Volterra Vito Volterra (, ; 3 May 1860 – 11 October 1940) was an Italian mathematician and physicist, known for his contributions to Mathematical and theoretical biology, mathematical biology and Integral equation, integral equations, being one of the ...
and
Henri Lebesgue Henri Léon Lebesgue (; ; June 28, 1875 – July 26, 1941) was a French mathematician known for his Lebesgue integration, theory of integration, which was a generalization of the 17th-century concept of integration—summing the area between an ...
. In his dissertation ''Sur les fonctions de variable réelles'' ("On the Functions of Real Variables"), Baire studied a combination of
set theory Set theory is the branch of mathematical logic that studies Set (mathematics), 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 mathema ...
and analysis topics to arrive at the
Baire category theorem The Baire category theorem (BCT) is an important result in general topology and functional analysis. The theorem has two forms, each of which gives sufficient conditions for a topological space to be a Baire space (a topological space such that th ...
and the definition of a
nowhere dense set In mathematics, a subset of a topological space is called nowhere dense or rare if its closure has empty interior. In a very loose sense, it is a set whose elements are not tightly clustered (as defined by the topology on the space) anywhere. ...
. He then used these topics to prove the theorems of those he studied with and further the understanding of continuity. Among Baire's other most important works are ''Théorie des nombres irrationnels, des limites et de la continuité'' (Theory of Irrational Numbers, Limits, and Continuity) published in 1905 and both volumes of ''Leçons sur les théories générales de l’analyse'' (Lessons on the General Theory of Analysis) published in 1907–08.


See also

*
Baire space (set theory) In set theory, the Baire space is the set of all infinite sequences of natural numbers with a certain topology, called the product topology. This space is commonly used in descriptive set theory, to the extent that its elements are often called ...


References


External links

* * {{DEFAULTSORT:Baire, Rene-Louis 1874 births 1932 deaths Scientists from Paris 19th-century French mathematicians 20th-century French mathematicians Members of the French Academy of Sciences Topologists École Normale Supérieure alumni Lycée Henri-IV alumni