It's really rather disturbing.
He's just awoken from a frightfully vivid dream and he's torn between the conflicting desires that form the basis of human nature: will he forget it ever happened, or will he record everything, remember it all, preserve for whatever posterity will appreciate his works?
He's a mathematician. The choice is obvious, but as he scribbles down recollections and revelations from his noctural visions, the words seem to blur and fade. He has captured the theorem, the essential spirit of his dream, what Erdös would surely accept as an integral page of the Book; but in his haste, Fermat has forgotten the proof. He has that frustrated itchy-feeling-behind-eyes knowledge that it's right there, and everything in the room connotes an eerie sense of déjà vu as though he's awoken like this before.
Perhaps a mathematician's worst nightmare is the inability to write down the things that one knows to be true. His haste, frustration, and rage culminate in a tiny phrase chiselled in the margin of a textbook: "Cuius rei demonstrationem mirabilem sane dextei hanc marginis exiguitas non caperet". I have laid bare a truly wonderful proof of this phenomenon; which proof the paucity of the margin cannot contain, he writes, and he means it with every atom of his being. The confines of his own mind limit his understanding in a way that is more than unacceptable; it is unbearable.
In a perfectly anechoic chamber, the walls absorb all sound; none permeates. A similar sudden stillness arises in that evening as Fermat screams internally, then falls silent. He abandons the proof as a phantom lurking in the vagaries of the human mind, and he tries to move on. Slowly, the dreams with their terrifying jagged edges and their rough, alien fractal dimensions are lost. When he dreams, it is of fine French wine and women.
Fermat dies in 1665.
Some centuries later, Andrew Wiles has a secret passion within the recesses of his imagination. He has seen this miraculous assertion of Fermat; he has witnessed the grasping of straws and faulty proofs and hopelessly contradictory lemmas that Fermat has inspired.
This, his professional life's work, is practially unknown to the world; he's told his wife Nada about his fixation, but his children don't care for stories about dead French men, and he'd jeopardize his dream if he revealed his ambitions to anyone else.
He works furtively for seven years in a dark attic, voluntarily imposing upon himself the cloistered sense of entrapment that Fermat refused to confront. By the nineties he has announced his 150-page proof and has acquired international recognition.
In an interview with Nova, he asserts quite candidly that "I don't believe Fermat had a proof. I think he fooled himself into thinking he had a proof."
Wiles goes on to discover larger and more meaningful truths of mathematics, to reveal more pages of the Book for the good of humanity. His proof gradually falls through the cracks of trivialty and is only of use as an assumption in an obscure branch of elliptic curve analysis.
No one will ever pursue; no one will ever discover Fermat's lost dream; his fantastically meaningful discovery will remain a fantasy at last forgotten even by the poets and dreamers. Self-validation escapes him eternally.
Fermat will never find solace of yes.
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