Mathematics seemingly studies mathematical structures, guided by rather elusive criteria for what is worth studying, with axioms and proofs not obviously constituting the whole of its focus. In philosophy of mathematics, asserting that only formal statements and proofs make sense is known as formalism:
It has been claimed that “Formalists, such as David Hilbert, hold that mathematics is no more or less than mathematical language. It is simply a series of games...”
Mathematics seemingly studies mathematical structures, guided by rather elusive criteria for what is worth studying, with axioms and proofs not obviously constituting the whole of its focus. In philosophy of mathematics, asserting that only formal statements and proofs make sense is known as formalism: