I had a dream last night that about 10 years ago, I had done up a one-page proof of Fermat's Last Theorum, which was far more elegant and straightforward than the proof that actually exists. In my dream, I was scrambling to find where I had written it down (checking old email addresses, etc.).
The dream was so vivid that when I woke up, for about 10 minutes, I tried recollecting whether this had in fact been true, and whether I might have actually done this at some point.
I guess I can't prove that I never did this, but at this point, I'm certain that it was just a dream, not based in any reality.