# P vs NP

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 $$P\subseteq NP$$. However, we still do not know whether the reverse implication, $$P \supseteq NP$$, holds.

A positive, constructive result would have profound implications through all the fields of science and math, not to mention the whole of society.

Children:

Parents:

• Mathematics

Mathematics is the study of numbers and other ideal objects that can be described by axioms.

• Complexity theory

Study of the computational resources needed to compute something