Indiscrete Variations on Gian-Carlo Rota's Themes

In M. Pitici (ed.), The Best Writings on Mathematics 2010, pp. 311-329. Princeton University Press (2011)
I never met Gian-Carlo Rota but I have often made references to his writings on the philosophy of mathematics, sometimes agreeing, sometimes disagreeing. In this paper I will discuss his views concerning four questions: the existence of mathematical objects, definition in mathematics, the notion of proof, the relation of philosophy of mathematics to mathematics.
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