the Lycée Lakana, Sceaux, Hauts-de-Seine, France
Baire won a scholarship competition for the city of Paris in 1886, he entered the Lycée Lakanal as a boarding student; there he completed his advanced classes in 1890.
the Lycée Henri IV, 23 Rue Clovis 75005 Paris, France
In 1891 Baire entered the section for special mathematics at the Lycée Henri IV.
The École normale supérieure, Paris, France
Baire presented his thesis on March 24, 1899 at the École normale supérieure and was awarded his doctorate.
In appreciation to his contribution to the firld of mathematics, Baire received the ribbon of the Legion of Honor.
(Mathematics is the study of such problems as quantity, st...)
Mathematics is the study of such problems as quantity, structure, space, and change. Mathematicians seek out and implement patterns to formulate new theories; they resolve the veracity of theories by applying mathematical proofs. When mathematical frameworks provide good replications of actual events, then mathematics can improve our predictions about natural phenomena. Using theoretical abstraction and logic, over thousands of years mathematics has developed from simple calculation and measurement, to the systematic study of the shapes and dynamics of physical objects.
Baire won a scholarship competition for the city of Paris in 1886, he entered the Lycée Lakanal as a boarding student; there he completed his advanced classes in 1890 after having won two honorable mentions in the Concours Général de Mathématiques. In 1891 Baire entered the section for special mathematics at the Lycée Henri IV, and in 1892 was accepted at both the École Polytechnique and the École Normale Supérieure. He chose the latter, and during his three years there attracted attention by his intellectual maturity.
Although he placed first in the written part of the 1895 agrégation in mathematics, Baire was ranked third because of a mistake in his oral presentation on exponential functions, which the board of examiners judged severely. In the course of his presentation, Baire realized that his demonstration of continuity, which he had learned at the Lycée Henri IV, was purely an artifice since it did not refer sufficiently to the definition of the function. This disappointment should be kept in mind because it caused the young lecturer to revise completely the basis of his course in analysis and to direct his research to continuity and the general idea of functions. While studying on a scholarship in Italy, Baire was strengthened in his decisive reorientation by Vito Volterra, with whom he soon found himself in agreement and who recognized the originality and force of his mind.
On 24 March 1899 Baire defended his doctoral thesis, on the theory of the functions of real variables, before a board of examiners composed of Appell, Darboux, and Picard.
Baire began his teaching career in the lycées of Troyes, Bar-le-Duc, and Nancy, but he could not long endure the rigors of teaching the young. In 1902, as a lecturer at the Faculty of Sciences of Montpellier, he wrote a paper on irrational numbers and limits. In 1904 he was awarded a Peccot Foundation fellowship to teach for a semester at the Collège de France. At that time this award went to young teachers to enable them to spend several months, free of routine duties, in developing their own specialties. Baire chose to work on a course in discontinuous functions, later edited by his pupil A. Denjoy and published in the Collection Borel, a series of monographs on the theory of functions.
Upon his return to Montpellier, Baire experienced the first violent attack of a serious illness that became progressively worse, manifesting itself in constrictions of the esophagus. After the crisis passed, he began drafting his paper “Sur la représentation des fonctions discontinues.” Appointed professor of analysis at the Faculty of Science in Dijon in 1905, to replace Méray, he devoted himself to writing an important treatise on analysis (1907-1908). This work revivified the teaching of mathematical analysis. His health continued to deteriorate, and Baire was scarcely able to continue his teaching from 1909 to 1914. In the spring of 1914, he decided to ask for a leave of absence. He went first to Alésia and then to Lausanne. War broke out while he was there, and he had to remain - in difficult financial circumstances - until the war ended.
Baire was never able to resume his work, for his illness had undermined his physical and mental health. He now devoted himself exclusively to calendar reform, on which he wrote an article that appeared in the Revue rose (1921). While still at his retreat on the shores of Lake Geneva, Baire received the ribbon of the Legion of Honor, and on 3 April 1922 was elected corresponding member of the Academy of Sciences. A pension granted him in 1925 enabled him to live in comparative ease, but the devaluation of the franc soon brought money worries. His last years were a struggle against pain and worry.
Thus Baire was able to devote only a few periods, distributed over a dozen years, to mathematical research. In addition to the already mentioned works, of particular importance are “Sur les séries à termes continus et tous de même signe” and “Sur la non-applicabilité de deux continus à net n+p dimensions.”
Baire’s doctoral thesis solved the general problem of the characteristic property of limit functions of continuous functions, i.e., the pointwise discontinuity on any perfect aggregate. In order to imagine this characteristic, one needed very rare gifts of observation and analysis concerning the way in which the question of limits and continuity had been treated until then. In developing the concept of semicontinuity - to the right or to the left - Baire took a decisive step toward eliminating the suggestion of intuitive results from the definition of a function over a compact aggregate. But in order to obtain the best possible results, one needed a clear understanding of the importance of the concepts of the theory stemming from aggregates.
Until the arrival of Bourbaki, his success greatly influenced the orientation of the French school of mathematics. Baire’s work, held in high esteem by Émile Borel and Henri Lebesgue, exerted considerable influence in France and abroad while its author found himself incapable of continuing or finishing the task he had set himself.
There can be no doubt that the progress of modern mathematics soon made obsolete Baire’s work on the concept of limit and the consequences of its analysis. But this work, written in beautiful French, has an incomparable flavor and merits inclusion in an anthology of mathematical thought. It marks a turning point in the criticism of commonplace ideas. Moreover, the class of Baire’s functions, according to the definition adopted by Charles de la Vallée Poussin, remains unattainable as far as the evolution of modes of expression is concerned. This model of a brief and compact work is part of the history of the most profound mathematics.
He died on July 5, 1932, at the age of 58 in Chambéry, France.
(Mathematics is the study of such problems as quantity, st...)1907
René-Louis Baire was elected a corresponding member of the Academy of Sciences on April 3, 1922.
Baire was a quiet young man who kept to himself and was profoundly introspective.
Physical Characteristics: From time to time, Baire's health would prevent him from working or studying. Consequently, the bad spells became more frequent, immobilizing him for long periods of time. Over time, he had developed a kind of psychological disorder which made him unable to undertake work which 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.