We have the word of a world known mathematician (Fermat). But yeah if he had written down the proof somewhere that he had in mind, maybe it would have turned out to have had mistakes in it, and it wouldn't have ever become such a large story/theme that it is now.

Anyways, it's important to archive the knowledge in a way that it can be understood by future humans as well. Some random website under an .edu can disappear at any moment.