But, then, Picard would have known that too if he was interested in that problem and its history. So if we are almost certain, why isn't he ?
I'd argue the point is that Picard would never stand a chance of understanding Wiles' proof, or improving upon it, let alone achieving something all-new and useful in the field of mathematics - but as an amateur mathematician, he would be qualified at finding
Fermat's proof if it indeed did exist. It's a romantic pursuit, but it's not 100% impossible the way inventing a perpetual motion machine is. (Although with TNG tech, even the latter could probably easily be devised by somebody of Picard's standing!)
Everybody on the Enterprise (And most aliens) seems to have an encyclopedic knowledge of 20th century culture and art but no knowledge at all between the 21st and 23rd century.
On the other hand, nobody on the
Voyager knows anything about the 20th century but Tom Paris - and what he knows is more often incorrect than not.
Kirk had absolutely no clue on that century, either, despite apparently knowing a lot about the 19th century, at least as pertained to the United States. Gangsters, Nazis, the Recession, the eighties - it all went flying over his head. (Spock knew about the Giants, but then again, he knows about pretty much everything, except the difference between WWIII and Eugenics Wars.)
As for 20th century culture, Archer's crew watches the movies. But Picard quotes Shakespeare and Kirk quotes Melville, Milton and the like. It's "20th century" only in the sense of "everything
up to 20th century, perhaps with a slight bias for what is still considered pretty cool in the 20th century".
It's just DS9 that has this actual 20th century bias despite being in the TNG rather than the more proximal ENT era, and perhaps mainly because Sisko has this racist fixation. (The three prominent holoscenarios that take Bashir and O'Brien to that century, Vic's, Secret Agent and Battle of Britain, are just a narrow slice of their broader holo-interests, which include the Alamo and the Viking age.) Then again, DS9 also gives us a
real mathematician, Tobin Dax, who actually worked on realistic, professional solutions to Fermat's proof problem...
Timo Saloniemi