The Specificity of Modern and Contemporary Mathematics


It is well known that mathematics is presently enjoying something of a boom. Even conservative estimates suggest that the discipline has produced many more theorems in the last three decades than it has in its entire preceding history, a history stretching back more than two thousand years (including the very fruitful nineteenth and twentieth centuries, and all the way up to the 1970s). The great innovative concepts of modern mathematics—which we owe to Galois, Riemann and Hilbert, to cite only the three major foundational figure—have been multiplied and enriched thanks to the contributions of a veritable pleiad of exceptional mathematicians over the last fifty years. Proofs of apparently unattainable theorems—like Fermat’s Last Theorem, or the Poincaré conjecture—have been obtained, to the surprise of the mathematical community itself, thanks to the unrelenting struggle of mathematicians who knew how to carefully harness the profound explorations already undertaken by their colleagues…