[pron]

> The majority of mathematicians quickly became "Formalists", holding that pure mathematics could not be philosophically considered more than a sort of elaborate game played with marks on paper (this is the theory behind Robert Heinlein's pithy characterization of mathematics as "a zero-content system").

This isn't quite what Formalism is, at least not as Hilbert -- the originator of that philosophy -- described it. In short, Formalism says that some mathematical sentences might not have an external meaning, and those are the ones that are no more than a game with symbols.

More precisely, Hilbert divided mathematical formulas to "real," those that do have external meaning, and "ideal", those that do not. The real formulas are usually finitary, while the ideal ones usually deal with infinities. Formalism is the view that mathematics is allowed to contain ideal sentences provided that they do not yield contradictions with real ones.

[chalst]

Quite so. It's also not true that formalism was ever the philosophical viewpoint that most mathematicians felt fit their views best.