Something called Edge asked a very interesting question of some of the worlds' foremost scientists and thinkers:
WHAT DO YOU BELIEVE IS TRUE EVEN THOUGH YOU CANNOT PROVE IT?
There are some pretty interesting answers, though I haven't gone through them all. I especially like Tor NØrretranders' answer.
My own answer, without taking too much time to think, is I believe Neanderthals survived until as recently as 5000 years ago, rather than going extinct 25,000 years ago as currently accepted.
So what's your answer?