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Jun 8, 2013 at 15:30 comment added Joël This is an interesting quote. Yet the idea that definitions are the most important "vehicles" of mathematical rigor is very old, and has been perfectly expressed already by Pascal in "l'art de persuader". A more original idea is the one of Grothendieck, that definition may have an even higher role in mathematics, as vehicle not only of rigor, but of mathematical creativity itself. That is, the creative work of a mathematicians is not mainly to prove good theorems, it is to "invent" good definitions. His works are a sufficient illustration of this new maxim.
Jun 8, 2013 at 14:33 history answered Carlo Beenakker CC BY-SA 3.0