Séminaire Lotharingien de Combinatoire, B44d (2000), 71 pp.

Pierre Cartier


Abstract. The implicit philosophical belief of the working mathematician is today the Hilbert-Bourbaki formalism. Ideally, one works within a closed system: the basic principles are clearly enunciated once for all, including (that is an addition of twentieth century science) the formal rules of logical reasoning clothed in mathematical form.

My thesis is: there is another way of doing mathematics, equally successful, and the two methods should supplement each other and not fight. This other way bears various names: symbolic method, operational calculus, operator theory ...

In this article I make a case for this "other method" of doing mathematics, by discussing several instances where it has led to, respectively will (hopefully) lead to, fruitful insights and developments.

Received: June 21, 2000; Accepted: August 5, 2000; Final Version: October 27, 2000.

The following versions are available: