Geometry Becomes Special

Abstract

Let us begin with a quotation from a talk given in Cambridge by William Hodge The last thirty years (1925–1955) have seen an enormous improvement in the position of geometry as a branch of mathematics, or, rather, have seen the re-integration of geometry into the main fabric of mathematics. Indeed, one can go further and say that with the restoration of geometry to its rightful place in the mathematical scheme the process of fragmentation which had been doing so much harm to mathematics has been reversed, and we may look forward to the day in which there are no longer analysts, algebraists, geometers and so on, but simply mathematicians. Mathematical research has two aspects, motivation and technique, and when the latter gains control the result is apt to be excessive specialization. The revolution of geometrical thought, and the reinstatement of geometry as one of the major mathematical disciplines, have helped to bring about a unification of mathematics which we may justly regard as one of the major contributions of the last quarter century to the subject.

La géométrie...est une science née à propos de l’expérience...nous avons créé l’espace qu’elle etudie, mais en l’adaptant au monde où nous vivons. Nous avons choisie l’espace le plus commode...

Henri Poincaré