Ben Orlin at Math With Bad Drawings:
Every baby is born the same way (namely, as a baby).
And every mathematician is born the same way, too: as a baby as a Platonist.
It usually begins something like this: What exactly are triangles? In a cosmos where no plane is perfectly flat, no segment perfectly straight, and no corner perfectly sharp, are Euclidean triangles in any sense “real”?
Yes, says the Platonist. Tangible? No. Physical? No. But the Platonist has tasted enough of math to know, in her bones, that math is more than just human whim. Math must, in some independent sense, exist. The Platonist believes (in the grand tradition of Seinfeld) that mathematical objects are real, and they’re spectacular.
Other philosophies may come later. Structuralists evolve, like birds from dinosaurs. Formalists are trained, like soldiers in boot camp. Intuitionists emerge, like neo-reactionaries from economic recessions.
But every mathematician begins in the same sweet swaddle of Platonism.
More here.
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