You really need to study your math more closely. :-) There are classes of problems which for an axiom set cannot be proven ... unknown and unknowable ... but given the correct assumptions, most anything can be proven. Ah, that word “assumptions” is critical. It is also imperative for logic (all logic starts from the a…

sigh. If you are a doctor, you failed at math. Many of the proofs in geometry are proofs “there does not exist”... one of the simplest is the proof that the square root of 2 is irrational. It proves that there are no integers A and B such that A/B = sqrt(2)