Concept
René-Louis Baire (bɛʁ; 21 January 1874 – 5 July 1932) was a French mathematician most famous for his , 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. 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 and the École Polytechnique. He decided to attend the École Normale Supérieure in 1891. After receiving his three-year degree, Baire proceeded toward his agrégation. 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. 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 as a "Maître de conférences". 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 where he lectured on the subject of analysis. He was appointed to a university post in 1905 when he joined the Faculty of Science at the University of Dijon. In 1907 he was promoted to Professor of Analysis at Dijon where he continued his research in analysis. Since he was young, Baire always had "delicate" health.
