Stephenson:Neal:Quicksilver:124:Word arrived that Fermat had died (T Whalen)
From the Quicksilver Metaweb.
...leaving behind a theorem or two that needed proving.
This is a probably an oblique allusion to Fermat's Last Theorem, which went unproven until the late 20th century, or perhaps to Fermat's "Little" Theorem, which Gottfried Wilhelm von Leibniz claimed to have proven before 1683.
Fermat's last theorem reads as follows:
xn + yn = zn has no non-zero integer solutions for x, y and z when n > 2
Fermat wrote this theorem in the margins of one of his copy of a then new translation of Diophantes' Arithmetica. Next to it, he had written "I have discovered a truly remarkable proof which this margin is too small to contain." This sort of thing was common with Fermat and many other mathematicians of the time. In all those cases in which Fermat himself made such a claim (and didn't explain the proof some other way, as in a letter to Father Mersenne) he has been shown to be right. The "Last Theorem" is the only one for which he made a positive claim that has remained unproved to our time. He also made some claims in the form of of 'I think this is true' and some of those have been shown to be right and others wrong.
He often sketched proofs and then later wrote them out. Standards of proof varied much at the time, also, so it's not clear he had a proof to modern standards, even if he thought he had one. But, notably, ALL of Fermat's claims of having a proof, though doubted at the time or later, turned out to be true.
Star Trek fans will note that Picard would attempt proofs of Fermat's Last Theorem as a hobby. Conventional wisdom at the time the early episodes were written was that the theorem would likely remain unproven in the 24th century. Episodes of Star Trek that were written after Prof. Wiles offered his proof in 1993 stated that Picard was merely looking for a better proof.
Since Wiles' proof runs to several hundred pages of mathematics that did not exist in Fermat's time, it is not even remotely possible they found the same proof. The most interesting remaining question in regard to Fermat's own proof is how he did it. Wiles' is huge and took almost a decade (if not a professional lifetime) and Fermat's had to have been much simpler. Fermat was a subtle and original mathematician, and his proof might be of great interest.
It should be noted that this reference in Quicksilver is historically inaccurate, since the Last Theorem wasn't known to the world until 1670, when Fermat's son noticed the marginal jotting, and published his notes to the Arithmetica. At the time of the action in the book (and of Fermat's death), said theorem was not publicly known. Therefore, the reference is basically a wink to the present day reader (...not that there's anything wrong with that). k