The creation of the French mathematical society in 1872 comes at the beginning of a period of radical change in the French system of higher education. During the most part of the XIXth century, the dominant institution for mathematics was the Ecole polytechnique, while universities and the Ecole normale supérieure played no significant role, particularly for training research mathematicians. However, starting in the 1850's, Polytechnique graduates became less and less interested in the advancement of science, while the Ecole normale supérieure, under the impulse of Louis Pasteur who became its director of studies in 1857, became the preferred option for those students who would become mathematicians.

The bitter defeat in the war against Prussia in 1871, after which France lost Alsace and part of Lorraine, led public intellectuals to the conclusion that the defeat was due to the inferiority of French universities compared with their German counterparts. As a result, French national government invested large amounts to bring universities to life, through new constructions and the creation of professorial chairs.

The combination of public policies and a push for renovation coming from within Academia turned the situation of French universities around ; in mathematics this manifested itself by the emergence of a spectacular new generation of mathematicians : Darboux, Poincaré, Picard, Hadamard, Cartan, Borel, Lebesgue to name but a few ; all of of them are "normaliens" except Poincaré.

When the Société mathématique de France (SMF) is created in 1872, the older generation of "polytechniciens" is still at the helm. Michel Chasles (1793-1880), a graduate of the Polytechnique, and still a professor at the Sorbonne becomes the first president of the new society. Remembering that the Polytechnique is an engineering school (several of the most distinguished research mathematicians who are graduates of the Polytechnique hold engineering rather than academic positions) it is not surprising that the weight of engineers and teachers in the membership of SMF is strong. By 1900, the weight of frontier researchers, graduates of the Ecole normale, in the society has become dominant.