There was a great editorial in the Notices of the American Mathematical Society by someone who was asked by a senator to explain his research. Finally he went into a speech about chaos theory and felt guilty later. That's a problem with defining a mathematican's ability by what they are able to do with proofs. It's not for anything. It's the truth.
Statements are only true relative to a system.
She won't tell you that her math books are wrong. Mathematicans don't have problem with multiple systems, each with their own rules of what is true and false. Not only is the concept of truth shaken by the existence of multiple equally correct answers to the same question, but the very nature of truth itself is a questionable concept mathematically. If the statement is unprovable with those axioms, then there's a true statement about that system that the system can't deduce. That's the reason I let myself get so longwinded here.