P versus NP

Open Question
The class of problems for which an algorithm can find a solution in polynomial time is termed $P$.

The class of problems for which an algorithm can verify a solution in polynomial time is termed $NP$.

The $P$ versus $NP$ question is:


 * Are all problems in $NP$ also in $P$?

Progress
Most mathematicians and computer scientists expect the answer to the question is: no, they are not.

However, there has been no proof one way or the other so far.