It is known that axioms are the building blocks of mathematics. Differents sets of axioms different "games". What I don't understand is how do we know that we pick axioms that are consistent? . Does this mean that some day we may find a theorem that is true and false at the same time? Then what is the point trying to prove theorems if we can't know that our starting points are consistent? The word "proof" also doesn't make sense in that case.