P problems are problems that can be solved quickly regardless of size, sometimes called "easy" problems.

NP problems are "hard": The time it takes to solve them grows with the size of the problem extremely quickly, but once you *see* a solution, you can verify it easily.

Breaking passwords is an NP problem, and this xkcd shows you how fast they grow. With 28 inputs, it takes **3 days** to break a password at 1000 guesses/second; Add just 16 more inputs, and it takes **550 years**. Yet, in either case it's extremely fast for the server to verify that your password is correct. So fast that it doesn't even notice the difference between a 3-days-to-crack password and a 550-years-to-crack password.

The P=NP? problem asks, "How can it be possible to verify that a solution is correct so quickly, without having the ability to *find* a correct solution quickly? What is *happening* to that extra information?"

Any time you think, "I couldn't make it myself, but I know it when I see it," that's the P=NP? problem. Humor is a perfect example. It's harder to write a funny joke, than it is to hear a joke and know whether or not it was funny. *Why?* Is there a way to harness the ability to recognize humor and turn it into a way to *create* humor? If so, then P=NP. If not, then it doesn't.

I once got high with a mathematician friend and I asked him, "Do you ever have that nightmare where the complexity of NP-complete problems is the Lovecraftian horror underlying the universe?"

And he said, "Well, I *didn't*."

So the P=NP? problem is the question of whether these two groups of problems are actually the same. In other words, Is there something deep in the nuts and bolts of reality that would allow us to solve NP problems quickly?

If not, *why is it possible to recognize solutions quickly*? Why is it possible to write an algorithm that verifies a password that would take 3 days to crack, and a password that would take 550 years to crack, in basically the same number of milliseconds?

When dozens of people recognize that a joke is funny, but none of them could write the joke themselves, *how is that possible?* What knowledge are they tapping into that they can all independently laugh at the same funny joke in its final form, but apparently none of them could access when they were trying to write the joke from scratch? *What is happening to that extra information?*