This series of conversations between three mathematicians is also confronts three points of view on mathematics, reflecting three types of mathematicians: the “physicist” mathematician (Connes); the “formalist” or “Bourbakist” mathematician (Lichnerowicz); and the “applied” mathematician (Schützenberger). The conversations are centred around four main topics: the nature of mathematics; the application of mathematics to the real world; the interpretation of quantum mechanics and its relation to relativity; and mathematical time versus human time. In these pages, Alain Connes develops his philosophy of mathematics, which had been previously presented in his dialogue with Jean-Pierre Changeux in Matière à Pensée.

Triangle à Pensée offers an unprecedented description of the current transition from modern mathematics, a subject that has been traditionally withdrawn from reality, and post-modern mathematics, which is resolutely open to the world.

Alain Connes teaches at the Collège de France and is a member of the Institut des Hautes Etudes Scientifiques in Bures-sur-Yvette, near Paris. He was awarded the Fields Medal for Mathematics. André Lichnerowicz previously taught at the Collège de France, and Marco Schützenberger has taught at the University of Paris-VI.