André Joyal

André Joyal has made profound contributions to four branches of mathematics using elegant categorical methods. He revolutionalized 'combinatorics' by letting coefficients of power series be finite sets. In 'topology', he replaced spaces by locales, dispensing with Euclid's points, and developed a categorical treatment of "braids", preparing for an attack on "knots" and "strings" in physics. In 'algebra', he significantly improved and generalized Grothendieck's Galois theory. In 'logic', he pioneered categorical models of type theory and is linked with the American philosopher in "Kripke-Joyal semantics" for intuitionistic higher order logic.