P = NP
The Clay Mathematics Institute has a standing offer of $1 million for a solution and proof to the P vs. NP problem. The relationship between the P and NP complexity classes is one of the great unsolved problems in theoretical computer science, and mathematics in general. It’s sufficiently confusing that I refer you to Google if you care for an explanation.
An apparently undaunted individual at my school stands against the common belief that P ≠ NP. While he gives no formal proof, he answers the question, prominently on the Engineering Building: