# Golden Ticket: Chapter 7

## For Your Enjoyment

## Proving P ≠ NP

- To prove P = NP, a polynomial algorithm that solves an NPC
problem suffices.
- To prove P ≠ NP, a proof is needed that shows that
no possible algorithm exists.
- Negative proofs can be quite difficult. For example, Fermat posed
his last theorem in 1637 (e.g. a
^{n} + b^{n} ≠
c^{n} for distinct natural numbers a, b, c
and n > 2) but it wasn't until 1995 that British mathematician
Andrew Wiles proved it.