====== The 'P versus NP' problem ======

The 'P versus NP' problem is a major unsolved enigma in mathematical computer science,

It was first described in 1971 by mathematician Stephen Cook in his paper entitled [[https://dl.acm.org/doi/10.1145/800157.805047| 'The complexity of theorem-proving procedures']] //Proceedings of the Third Annual ACM Symposium on Theory of Computing//. pp. 151–158.

In simple terms :

There are some mathematical problems which can be 'solved' by a computer algorithm  - given enough time - (e.g. finding the factors for a very large prime number). [ called **P** problems ]

Some problems can be 'verified' by a computer if its provided with the answer in advance to check (also, given enough time) [ called **NP** problems ]

Are the two scenarios equivalent? In other words, if one is true for a certain problem, is the other automatically true? Or, are there some problems where a solution can be 'verified', but not 'solved' with a computing algorithm - no matter how much time is available?

To date, the P versus NP problem itself remains unsolved.

//Editor's note :// It's not easy to find an explanation of the problem in plain language. Here is a good description from [[https://danielmiessler.com/study/pvsnp/|Daniel Miessler]]