The mathematical France of the 3rd Republic before the Great War (Q2789584)

This is the second edition of [Zbl 0728.01029)] from 1991 with a slightly changed title, some omissions and some additions. The new edition seems more appropriate, the main omissions consist in five articles written by different authors on specific topics, and the main additions include a vast preface of the author to the new edition, a general bibliography, and three indexes. The main part of the book remained unchanged. Although the new edition is thinner, it has retained its great informative value, the additions making the book more useful and the reading easier. NEWLINENEWLINEThe subject of the book is French mathematics between 1870 and 1914 and the main tool to its study remains the Société Mathématique de France (below SMF) founded in 1872, the main area of interest being characteristic features of mathematical activity: research, education, diffusion of ideas. NEWLINENEWLINEChapter 1 presents the SMF with its new formula (professional and not elitist but open to all people interested), its ambitions, its early structure and later changes, and its eventual success. The SMF has become an important vehicle in raising French mathematics, after a period of stagnation, up to its first-class position. NEWLINENEWLINEIn Chapter 2, the author offers an analysis of the mathematical production of the members of the SMF, both quantitative and qualitative.NEWLINENEWLINEIn Chapter 3, she analyses stimuli coming from radical institutional changes in the considered period, consisting in proliferation, an increase in the number of students of science, stress upon research etc., and their influence on the SMF. NEWLINENEWLINEChapter 4 deals with the evolution of the mathematical production in 1880--1900; after some general remarks it concentrates on granted doctorates and the contributions of members of the SMF. The author notes here an interesting series of theses devoted to the presentation of some great achievements from abroad (Fuchs, Riemann, Kronecker, Weierstrass, Lie) in French which helped to raise the level of French mathematics and led to a remarkable growth of interest in analysis. NEWLINENEWLINEChapter 5 presents the new generation of French mathematicians -- members of the SMF (Baire, Borel, Lebesgue and others) with their prevailing interest in the theory of functions, which soon has dominated the research scene. NEWLINENEWLINEChapter 6 deals with the then growing interrelations of French mathematics with the rest of world as seen in the raising number of foreign members of the SMF and its vivid relations with other mathematical societies, the participation in international congresses, and the publishing activity in foreign journals. NEWLINENEWLINEChapter 7 offers statistical tables illustrating particular topics. Of great interest is also the vast appendix containing excerpts from many great evaluations of doctoral theses presented by members of the SMF from 1870 until 1914. A valuable and stimulating book.