There is a theorem proved by Kurt Godel in 1931, which is the Incompleteness Theorem for mathematics. The theorem says that if you have any finite formulation of mathematics, that is, a finite set of equations and a finite set of rules of logical inference, then you can write down statements within the language that is defined that way, and you can prove that they cannot be proved and that they cannot be disproved.

So given any finite system of mathematics, there are statements within the system that you can't decide whether they are true or untrue by using the rules, which is a very powerful and profound result. It means that any formulation of mathematics is incomplete; there are always questions that you can't answer within the system.