The 50-year-old P-NP problem that eludes theoretical computer science
I have low hopes for P=NP. I really don’t see how you can solve for example the TSP exactly to guaranteed optimality without utilizing all of the useful available information. Approximation approaches show that by discarding information you give up optimality guarantees.<p>There must be something in information theory to help with proving that to construct a solution to an NP hard problem you need at least that much information.