This question is usually called the philosophy of mathematics[1] which is distinct from mathematical logic and has essentially no bearing on the actual practice

This question is usually called the philosophy of mathematics[1] which is distinct from mathematical logic and has essentially no bearing on the actual practice of mathematics. Some people are Platonists and think that mathematics exists as a sort of idealized mental realm (similar to Plato's theory of forms, but more reasonable in this context). If this is the case, we would say that mathematics is mind-independent and trans-universal; mathematical truths are true regardless of whether we exist to observe them, and they are true in all possible worlds. Others think mathematics is a linguistic "game" played by man, that it is mind-dependent and completely of our creation. Still others think mathematics is a set of derivations within a "formal system" (or formal language); this is sort of a middle ground, as it implies that mathematics is a construct of man but that it has a weaker mind-independence/trans-universal property, namely that any entity in any universe examining the same formal system comes to the same conclusions. But as I said, how you feel about this question has no effect on the real-world practice of mathematics. Most mathematicians you ask will have some opinion on the matter, but it's not like you can say "I'm a Formalist so I don't believe in that theorem." The human process of doing mathematics and the validity of theorems with respect to their assumptions has no relation to the questions of the ontological or metaphysical status of mathematics as a whole. [1] https://en.wikipedia.org/wiki/Philosophy_of_mathematics https://en.wikipedia.org/wiki/Philosophy_of_mathematics