CHARLES HERMITE'S STROLL THROUGH THE GALOIS FIELDS

Although everything seems to oppose the two mathematicians, Charles Hermite's role was crucial in the study and diffusion of Evariste Galois's results in France during the second half of the nineteenth century. The present article examines that part of Hermite's work explicitly linked to Galois, the reduction of modular equations in particular. It shows how Hermite's mathematical convictions-concerning effectiveness or the unity of algebra, analysis and arithmetic-shaped his interpretation of Galois and of the paths of development Galois opened. Reciprocally, Hermite inserted Galois's results in a vast synthesis based on invariant theory and elliptic functions, the memory of which is in great part missing in current Galois theory. At the end of the article, we discuss some methodological issues this raises in the interpretation of Galois's works and their posterity.