For thousands of years, mathematicians searched for a set of axioms from which all mathematical truths could be derived. Their dreams were shattered when Kurt Gödel published his incompleteness theorem. He proved that there can be no set of axioms from which all other mathematical facts can be derived. The result is there will always be truths that cannot be proven. We are then left with questions that may or may not have answers such as the Collatz Conjecture, Goldbach Conjecture and many other unproven mathematical conjectures. We may be disappointed that we'll never have a single set of axioms for mathematics, but Gödel's proof leaves us with the extra challenge of proving these conjectures knowing such proof may or may not exist.
Also see recent article:
https://bigthink.com/surprising-science/kurt-godel-foundations-mathematics-unproven
