Phenomenology of Mathematical Creativity


Traditional philosophy of mathematics tends to neglect the ways in which mathematical thought emerges. Several texts dealing explicitly with mathematical invention have come to us from such practitioners of the discipline as Poincaré, Hadamard, Grothendieck and Rota, but, curiously, the professional philosopher neglects the phenomenology of mathematical creativity as something foreign to his reflection. Nevertheless, in science, and, more generally, in every area of knowledge, the way in which knowledge emerges is (at least) as important as the knowledge itself. As Valéry reminds us, ‘the interest of science lies in the art of doing science’: the art of invention and the practices associated with creativity constitute the true interest of science. This is all the more obvious in the realm of mathematics…