P vs NPNicholas Bulinski

Informally it is the question of if a computer can quickly verify that a solution to a problem is true then can the computer solve that problem quickly as well?

This is one of the seven millennium prize problems

What is P vs NP?

When we say “quickly” we mean any algorithm that runs in polynomial time.

The class of problems that can be solved in polynomial time is known as class P or just P.

An example of a problem that is in P would be finding the determinant of an n by n matrix.

What is P and What is NP?

However there are some problems that (so far) can not be solved quickly but the answer to that problem can be verified in polynomial time.

The class of problems where the solution can be verified in polynomial time is known as NP.

An example of a problem in NP is the subset sum problem. The problem asks given a set of integers is there a non-empty subset that sums to 0?

What is P and What is NP?

If this is proven to be true this would have an huge impact on just about every field of science.

The reason why is that programmers frequently encounter NP problems and by extension any field that uses computers (which is almost all of them) would benefit greatly (or suffer) from such a proof.

This range's from the multiple sequence alignment problem in biology to the factoring integers (used in the RSA encryption system)

Why is this cool?