P versus NP problem
Since the best efforts of scientists and mathematicians have not found general, easy methods for solving NP problems yet, many people believe that there are NP problems other than P problems (that is, that P ≠ NP is true). Most mathematicians also believe this to be true, but currently no one has proven it by rigorous mathematical analysis. If it can be proven that NP and P are the same (P = NP is true), it would have a huge impact on many aspects of day-to-day life. For this reason, the question of P versus NP is an important and widely studied topic.