Regular folks with time machines waste their opportunity on trivial tourist activities, while mathematicians? They'd immediately hunt down Fermat to demand proof of his infamous "Last Theorem" that tormented generations of brilliant minds for over 350 years.
Fermat casually wrote in a margin that he had a "truly marvelous proof" but insufficient space to write it down—the mathematical equivalent of "my girlfriend goes to another school." Spoiler alert: he was probably bluffing, since the eventual proof required mathematical techniques not invented until centuries later.
Every mathematician fantasizes about this confrontation. "Show me your 'truly marvelous' proof, Pierre, or admit you were just showing off!"