Obituary of René-Louis Baire by Henri Lebesgue

The following obituary of René-Louis Baire, Correspondent of the Geometry Section of the Paris Academy of Sciences was delivered by Henri Lebesgue. It was published in L'Enseignement Mathématique (2) 3 (1) (1957), 28-30.

Obituary of René-Louis Baire by Henri Lebesgue.

M René-Louis Baire, born in Paris on 21 January 1874, entered the École Normale Supérieure in November 1892; he graduated with an agrégé in mathematical sciences in July 1895. After a short stint at the high schools of Troyes, Bar-le-Duc and Nancy, having become a doctor of science in 1899, he began teaching in higher education as a lecturer at the Faculty of Science of the University of Montpellier. The Faculty of Science of Dijon then chose him as professor of mathematical analysis. It was in Dijon that his brilliant and short career as a researcher and professor ended. Ill from his adolescence, he soon had to give up all activity; his life from then on passed on the shores of Lake Geneva, in Lausanne, then in Thonon. Transported to Bassens, near Chambéry, he died there on 5 July 1932.

René Baire was barely able to devote to scientific research other than a few periods of better health spread over a dozen years. However, he achieved such success in his work that our Academy, of which he was a prize-winner several times, elected him correspondent for the Geometry Section on 3 April 1922.

After the Ecole Normale, René Baire was sent to Italy as a scholarship holder. There he met our colleague M Vito Volterra, who immediately discerned the originality and vigour of his mind. The influence of M Volterra, added to that exercised by Jules Tannery, definitively oriented Baire's thoughts towards the theory of functions of real variables.

For his first attempt, he solved a problem more general than all those that had dared to be approached in this way: the search for a characteristic property of the limit functions of continuous functions. The function must be point-wise discontinuous on any perfect set.

To guess this statement, it was necessary to have real gifts of observation at the service of a rich imagination and a solid critical sense. To legitimise it, it was necessary to be capable of using the transfinite; that is to say, to profoundly modify a mode of reasoning that had only been used once before and moreover in a completely different domain.

This first research led Baire to be the first to pose, and to approach a crucial question: the integration of partial differential equations when the solution is not subjected to any condition other than that of satisfying the given equation.

Other studies more directly required the attention of René Baire: that of functions of several variables and of class 1, that of functions of several variables separately continuous with respect to each of the variables on which they depend, and especially that of functions that can be formed from functions of class 1 as these were formed from continuous functions. That is to say, the study of functions, called class 2, limits of functions of class 1. Then that of functions of class 3; and so on. Baire obtained fundamental results on functions of classes 1, 2 and 3; he found a property common to functions of all classes. If we add that Baire was interested in the analysis situs (topology) as well as in all the general principles of analysis, on which he wrote a beautiful book, this may suffice to explain the universal notoriety that Baire enjoyed, but it cannot give rise to suspicion of the feeling of personal mourning that will grip those who have made the theory of functions of real variables the principal object of their meditations, at the news of the death of the one for whom they had veneration.

If, before Baire, many scholars had been interested in real variables it was incidentally and with a view to the complex variables with which we had been occupied almost exclusively since the beginning of the 19th century. Baire was the first to devote all his scientific activity to the theory of functions of real variables. He did more, he taught us to devote our activity to it in a fruitful way.

First of all, he provided us with the material to study. The set of functions of class 1, 2, 3, Baire functions as they are now called following the example of M de La Vallée Poussin, is the framework, provisional certainly but immense, of the new theory.

Baire then shows us how to study this subject; what problems to pose, what notions to introduce. He teaches us to look at the world of functions, to discern the true analogies, the real differences. By repeating the observations that Baire was able to make, we become a perceptive observer, we learn to analyse banal notions, to break them down into more hidden, more subtle, but also more effective notions.

Little by little, Baire's teachings will bear fruit; appreciating more exactly all that we owe to him, we will understand better that the one we have just lost was a mathematician of the highest class.

Last Updated March 2025