Séminaire Lotharingien de Combinatoire, B44d (2000), 71 pp.
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
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
Received: June 21, 2000; Accepted: August 5, 2000; Final Version: October 27, 2000.
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