Feynman on Fermat's Last Theorem
Using way simpler math, the probability that an even number is prime is zero. One cannot conclude from that that there are no even primes (in fact, many mathematicians think the smallest prime is even (https://cs.uwaterloo.ca/journals/JIS/VOL15/Caldwell2/cald6.h... ))Mathematicians do use this kind of back of the envelope calculations to get a feeling for whether a statement may be true, but they can never prove something.