least the beginning so the most famous lower bound question the Grandmamma of them all is P equals NP okay and just to give you a very high-level idea of what P and NP are not to go in the definitions NP is the set of problems where verifying a solution to the problem is easy and P are the problems where finding a solution is easy to do okay and so by easy we mean the following technical sense of Paul meal time so there's some algorithm that on inputs of length n runs in some polynomial and an amount of steps think