Cannot be proved.

[Chrissi]

In my geometry & discrete math textbook, there is a sidenote in our proofs unit about a theorem that some dead dude says he proved. The theorem is something along the lines of:

"This theorem cannot be proved."

Huhwhat, you ask? I didn't quite understand at first. What theorem? It took me awhile to understand it was the sentence itself that cannot be proved. But he says he proved it. Huhwhat?

If you try to dig into this, you find that it's a paradox. He says he proved it, but it can't be proved. So he proved that it couldn't be proved? How'd he do that? By not proving it... but if he proved it, the theorem is false! So is the theorem false? No, it can't be proved.

HUHWHAT?

This is the type of stuff that hurts my brain. I haven't looked for this on the internet yet, but here's my theory about how it can be proved.

If you haven't heard of the theory, you needn't worry about whether it can be proven or not. So if he erases his memory.... you get the picture. He can prove it by having never heard of it. Maybe that doesn't make sense. But wouldn't it be damn cool to be able to erase your memory for the sole purpose of proving a theorem that can't be proved?

Okay, seriously.. does this hurt anyone else's brain? I'm feeling it right now.