I'm reading Chihara's: Constructibility and Mathematical Existence. It says:
An even more radical view rejects the assumption that mathematics is true—at least in the straightforward way that mathematics is believed to be true by the Literalist philosophers. At one point, Hilary Putnam espoused such a view of mathematics. Making use of some ideas of the early Bertrand Russell, Putnam argued that “pure mathematics consists of assertions to the effect that if anything is a model for a certain system of axioms, then it has certain properties” (Thesis, p. 294).
According to this, rejecting that mathematics is true has something to do with using if-then. But at least intuitively, I don't see the use of if-then as something not being true, but as something that could be true or something that could be false. So what would be truth? I guess that the idea of truth would have something to do with tautologies (in which it could not be false).