Pierre Cartier

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The axioms of set theory are inconsistent, but the proof of inconsistency is too long for our physical universe.
Quoted by Ruelle, Chance and Chaos
Nowadays, one of the most interesting points in mathematics is that, although all categorical reasonings are formally contradictory, we use them and we never make a mistake. Grothendieck provided a partial foundation in terms of universes but a revolution of the foundations similar to what Cauchy and Weierstrass did for analysis is still to arrive. In this respect, he was pragmatic: categories are useful and they give results so we do not have to look at subtle set-theoretic questions if there is no need. Is today the moment to think about these problems? Maybe . . .
Interview in Newsletter of the European Mathematical Society, January 2010.