we are Hilbert’s children; when we have beers with the philosophers on the weekend, and the philosophers hassle us about the status of the objects we study,* we retreat into our formalist redoubt, protesting: sure, we use our geometric intuition to figure out what’s going on, but the way we finally know that what we say is true is that there’s a formal proof behind the picture. In the famous formulation of Philip Davis and Reuben Hersh, “The typical working mathematician is a Platonist on weekdays and a formalist on Sundays.” Hilbert didn’t want to destroy Platonism; he wanted to make the
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