I feel like it is a very "physics" motivated approach to at least "investigating" this theorem. Calculating probabilities is a line of thinking Feynman would be familiar with (quantum mechanics). Physics is often responsible for mathematical development, while they are different, they complement each other. It's nice to see different perspectives, and how ideas are connected.

> > Feynman concluded: “for my money Fermat’s theorem is true”.

> > "the main job of theoretical physics is to prove yourself wrong as soon as possible."

> Great example of the main difference between mathematicians and theoretical physicists.

Actually, I'm not sure I agree: even before Wiles's proof, almost every mathematician would have been willing to wager, at least conversationally, on the truth of FLT; and mathematicians also are in the business of proving themselves wrong as soon as possible. The only catch is that we don't count an inability to prove yourself wrong as a proof that you're right ….

The difference lies in the fact that absolute rigor to assess truths is not as fundamental in theoretical physics as it is in mathematics. Uncertainty is accepted. Physics puts a premium on empirical results and intuition over the more formal treatments common in mathematics (many important results/tools are not mathematically well-defined e.g. Feynman path-integral in d > 1).

Agreed! I didn't mean to claim that there isn't a difference, for there is a wide one; only that the two particular quotes chosen seemed (unlike most other things Feynman said!) not to illustrate them.

Fair enough. Agree that the second quote doesn’t illustrate my point, contrary to the first one. Cheers!