A

grateful

[Shaun Fosmark @Shaun_Fosmark]

Im not convinced people actually know what the P=NP problem is.

Lets break it down.

Before the 1960s, computers were getting faster every year, so engineers just assumed that if a problem was too hard for a computer to solve then, all had to do was just wait a few years for a faster computer, boom, problemo solved.

But then, they ran into a wall with a specific group of problems. No matter how powerful the computers got, they would freeze up, overheat, or take billions of years to solve them.

So these were super hard theoretical physics or black hole topography, right? Nope, they were everyday things like designing a high school schedule where a teacher is never in two places at the same time, or like, draw a trace on a circuit board that's as short as possible without overlapping other traces.

Heres the kicker, once the problem was solved, the computer could VERY quickly go back over and be like "Yup, no scheduling conflicts!". Once the problem was solved, verifying the solution was easy. It would be like you walking up to a lock someone left on a door and trying to figure out the code, and then someone else coming up behind you "Hey, the code is 26-42-36-10. Pop in the code and boom! Problem solved, solution verified.

Computer scientists grouped all of these problems into a category called "NP". Aww now if makes sense. And you know what ALLLLLLL of these problems have in common? They were exponential. Meaning if you only had 5 classes, your computer could solve thay in a MILISECOND. But if your schedule had like 100 classes, the possible combinations went insane like, more atoms than in the known universe numbers.

So by putting these problems into this "NP category", scientists were basically telling software developers "Stop wasting billions of dollars on trying to get your computers to solve these problems" and do something heuristic like, draw a line first, then verify it sux and iterate on it quickly until its good enough and move on.

So then they realized something terrifying. If you could figure out a trick to solving ANY of these problems, you could solve ALL of them, no matter what it was as long as it was an NP problem.

Ok so whats the big deal then!?! What do people mean why they say "If AI solves P=NP, thats the end game!". They are essentially saying that if its easy to verify a solution to a problem that was solved, then there must be a hidden trick to solve it as easily from scratch and if you could find that trick, all the hard problems could be solved instantly. Some of this is good like medicine or cosmology, some of it bad like cryptography which rides on assumptions that these problems are extremely difficult to solve from scratch.

Thats the entire breakdown on the P=NP or P≠NP debate you see floating around X these days.

Thanks for reading.

[𝖬𝖺𝗁𝖽𝗂 𝖢𝗁. (bluesky:@mahdi.ch) @mahdi_tcs_]

If AI solves P vs NP, then I think the chance that it will kill us all in 10 years will be 100%.

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