Mathematics
Constructive Mathematics vs. Classical Logic in Proofs
Quick fact
In constructive mathematics, the law of excluded middle is not accepted as a general principle, meaning that a proof of 'not not P' does not count as a proof of P—it merely shows that P cannot be false.
Why this is interesting
You've probably been taught that 'if not not P, then P' is obvious. But what if rejecting that simple rule could change nearly every theorem in mathematics?