[summary: Are problems with solutions easy to check also easy to solve? ]
The greatest currently open problem in complexity theory and computer science in general, which talks about the relationship between the class of efficiently solvable problems, [ P], and the class of problems with easily checkable solutions, [ NP].
It is a basic result that [ P⊆NP]. However, we still do not know whether the reverse implication, P⊇NP, holds.
A positive, constructive result would have profound implications through all the fields of science and math, not to mention the whole of society.