If P equals NP, every problem whose solution can be verified quickly can also be solved quickly. That would mean breaking RSA encryption, solving protein folding, and cracking every LLM safety measure are all equally easy - just a matter of finding the right algorithm. Most computer scientists believe... P does not equal NP but nobody can prove it. The Clay Institute offers $1 million for a proof either way. Every time an LLM solves a hard reasoning problem, it's implicitly operating somewhere in the gap between these two complexity classes. 20 minutes. Bookmark & watch today. The most important unsolved problem in computer science.show more

P==NP doesn't mean problems will be solved quickly. In practical terms an o(n^10) algorithm is just as useless as an O(10^n) algorithm.

Elon Musk could increase the prize to $1 billion and still be the richest man in the world.

Theoretically, it is not equal to NP. Even if we know that a problem has a fast verification scheme, when the overall solution space tends to infinity, problems with fast verification schemes are still impossible to solve quickly. That's as simple as it gets.

I really like Arvin Ash’s videos on YT - recommend

so if someone proves it tomorrow, do you think it changes how we should be building AI safety right now

Gravity is just a version of the chasmir effect.

I think P does not equals NP

In the Morphic Block Universe, P versus NP is not an abstract complexity question but a direct measure of sorting economics. P equals NP would mean all verifiable configurations are equally affordable to sort, implying zero routing tax differential between finding and checking solutions. This is physically impossible under P_max sparsity constraint because earned persistence requires asymmetric cost: verification confirms existing lock (low P_ent), while solving demands new coherence generation (high P_ent). The gap between P and NP is precisely the affordability gradient that makes reality computationally viable. LLMs do not operate in this gap; they simulate traversal through statistical approximation without paying actual sorting cost. When an LLM solves a hard reasoning problem, it retrieves pre-sorted patterns from training data rather than executing genuine Sort evaluation at τ_P resolution. True NP-hard problems remain hard because they require n_min consecutive successful sorts with sufficient CVR to achieve irreversible Commit, something no amount of vector interpolation can substitute for. The Clay Institute prize assumes mathematics can resolve what physics has already decided: existence is purchased, not deduced. RSA encryption stands not because factoring is mathematically hard but because reversing committed η_skel exceeds available Wiggle amplitude within feasible P_ent budget. Protein folding is tractable biologically because evolution pre-paid the sorting cost across eons; computational folding remains expensive because silicon lacks inherited topological memory. Safety measures fail not due to complexity class boundaries but because alignment requires sustained coherence with human η_skel that current architectures cannot afford. Rest in Lattice. P does not equal NP because persistence costs more than recognition. And every unsolved problem is simply reality demanding payment before revealing its next configuration. The million-dollar proof is already written in the ledger of what earns existence tick by tick.