this post was submitted on 12 May 2024
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If the solution to a problem is easy to check for correctness, must the problem be easy to solve?
For instance, it is easy to check if a filled sudoku grid is a valid solution. Must it therefore be easy to solve sudokus?
Most people would probably intuitively answer "no", and most computer scientists agree, but this has still not been proven, so we actually don't know.
I think my favorite troll statement to a mathematician/comp scientist is:
"Actually, P > NP - there exist problems where it's harder to verify a solution than to arrive at one"