For an epistemology of mathematical contents: Albert Lautman

Albert Lautman was an attentive observer of modern mathematics from Riemann to the Bourbakist movement in the 1930s and developed his thought within that unique thread of philosophy of science that was the philosophie mathématique in France during the early twentieth century. He gave a coherent form to the philosophical concerns of mathematicians such as Hilbert, Weyl and Gödel, highlighting the unity of mathematics and their dynamic and creative character. He developed a philosophy of mathematics that differed from standard 1930s philosophy of science, and focussed on the analysis of the “contents” of mathematical thought, not considered only as a formal language. Thanks to this historical-epistemological choice, as claimed by Jean Dieudonné who knew him personally, Lautman was able to anticipate the themes and problems of the subsequent mathematical thought, and to provide some tools that allow us to better understand the complex figure of Grothendieck. His “epistemology of mathematical contents” also represents an important moment in French philosophy of the sciences, which even today in France does not receive adequate critical attention.