Ou en sont les mathématiques?

The Société Mathématique de France has published the journal Gazette des mathématiciens since the 70’s. Its aim is a diffusion of mathematical knowledge. The book under review brings a sample of papers from the journal since its foundation. Papers are complemented by comments written by a contemporary specialist, describing recent evolution in the field. As a whole, it is a fascinating read. Papers (written in French) describe eighteen different topics of enormous interest, reviewed in a readable and understandable way, and designed for a general audience. The topics include classical themes (the third and the fifteenth Hilbert problems, theory of invariants, arithmetic algebraic geometry), important mathematical topics (stochastic calculus, deformation of various mathematical structures, symplectic geometry and topology, the work of M. Gromov, convex polytopes, singularities of maps, error correcting codes), very modern themes (mathematical ideas coming from quantum field theory, quantum groups and invariants of nodes, Wiles’ proof of the Taniyama-Weil conjecture), as well as some applications (image recognition, mathematics in meteorology, topology in molecular biology). It is a very nice collection, which can contribute in an essential way to the general mathematical education of any reader.

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