# [$P=NP$](https://stackoverflow.com/questions/111307/whats-p-np-and-why-is-it-such-a-famous-question)

Let me tick the list:

1. Most likely false, because, as Scott Aaronson said *"If $P = NP$, then the world would be a profoundly different place than we usually assume it to be."*

2. Yes, it's The Open Problem in computational complexity theory

3. Yes, it's old

4. It's important, again quoting Scott: *"[because if it were true], there would be no special value in "creative leaps," no fundamental gap between solving a problem and recognizing the solution once it's found. Everyone who could appreciate a symphony would be Mozart; everyone who could follow a step-by-step argument would be Gauss..."*

5. It's an equality rather than a negation