David Hilbert

...formalism, claims that mathematics is a game: Choose your axioms and follow the rules to prove your theorems. (This view is often attributed to David Hilbert, though Hilbert’s view was, in fact, somewhat different.) Mathematical formalism intends to put the metaphysical question out of bounds by saying that mathematics makes no claims at all about reality. --Fernando Q. Gouvea, The Book of Numbers, First Things, February 2009, review of Is God a Mathematician? by Mario Livio