A student comes up with what appears to be a proof of Fermat's Last Theorem. So, she gives it to her professor hoping that he will find a mistake in it (see below). It turns out that the professor is a member of an elite club of seven worldfamous mathematicians called The Marginalia, and the student's proof garners her an invitation to join as well...on the condition that the proof remains secret.
Note that Fermat's Last Theorem (the statement that there are no positive, whole number solutions to the equation x^{n}+y^{n}=z^{n} when n>2) is famous for being a mathematical statement that is very simple to make but notoriously difficult to prove or disprove. In fact, it was an open problem for hundreds of years until Andrew Wiles finally completed a proof in 1994. It is a common popular belief that there must be some elementary proofs of the theorem out there (either waiting to be discovered or known in secret as the story suggests). However, Wiles' proof is quite complicated (depending on advanced mathematical knowledge of elliptic curves and modular functions which are not available to a casual puzzle solver) and it seems likely that the statement cannot be proved in a much more elementary way at all.
Some things about the math in the story work well. The relationship between the students and the professors is interesting and not unbelievable. (Perhaps I'll try smashing my finger with a tomato juice can to impress my students like the character in this story....On second thought, no I won't.) I appreciate the remark pointing out that even though FLT is a sort of ``puzzle'' with no immediate application, many important discoveries have grown out of investigating it. And, I liked the following exchange that occurs near the beginning:
(quoted from Fermat's Best Theorem)
"I'll find your mistake, if it's there."
"It had better be," Laurie said, grinning back at him.
Peter's grin broadened. "Why?"
She hadn't stopped to consider that. That certainty was the way she was behaving. Not as if she'd solved something but as if she'd let some cat out of some bag. It took her a minute to pin the feeling down.
"Oh." She could feel her grin turn sheepish. "That's why."
"Why?" he asked again.
"That was the problem that lured me into mathematics as a major. Something that looks so easy and yet has remained unsolved for so long. Something you could sovle with pencil and paper  none of this fourteen days' worth of computer time. Something romantic..."
"Romantic? That's not a word i hear applied to math very often!"
"Romantic, Peter, the man scribbles this in the margin of his book then he goes off and gets himself killed in a duel, and the solution dies with him? If that's not romantic, I don't know what is."

Still, there are some misconceptions here.
"Killed in a duel"?! I think the author is confusing Fermat with Galois. Fermat had plenty of time to tell us his "proof" if he wanted to, and died peacefully . Speed is not measured in g's. And it is a bit disappointing to me that absolutely no hint is given as to what sort of proofs these researchers have found: are they purely arithmetic or do they involve heavier tools like analysis and projective geometry? In the end, however, the idea for the story is cute, it is executed well enough, and deserves to be read by any fan of "mathematical fiction"...if you can find a copy!
Originally published in Absolute Magnitude magazine in 1995, it was reprinted in their 1997 ``best of'' anthology.
(Thanks to Tony Nance for bringing it to my attention!)
Contributed by
Dr Meghashri Dalvi
Hi.
Was reading your amazing collection and came across "Fermat's Best Theorem".
If you want to add to this page, the story is available online here.
Thanks for a great read!
Meghashri

