P ≠ NP means there are problems whose solutions can be verified in polynomial time but cannot be found in polynomial time. Seems obviously true, but has never been proved. Much of modern cryptography relies on related assumptions about computational hardness and asymmetry. It’s easy to check a solution, but enormously expensive to find one.

ETH is stronger, says the set of 3SAT problems, which is NP-complete, needs at least 2^(kn) time for some k > 0. So at least exponential, not just polynomial.

OpenAI claims to have solved a class of 3SAT problems in 2^(n/√log n) which is better. So ETH as stated is false.

Many papers say if ETH is true, then X. They become dead letters. So maybe ETH just needs to be replaced with a weaker conjecture? And 2^(n/√log n) is still superpolynomial and grows super fast.

Anyway AI is good at theoretical computer science, and a lot of theoretical computer science papers need fixes, which may or may not be simple.

Googling its own grave? TFW when your raison d’être is accessing the world’s information, but if you make it too easy to access it breaks your whole business model.

Arena.ai still has Opus 5.5 #1, ArtificialAnalysis.ai has Carbon #1 (but it’s not available to most mortals)

when the answer key is public, even AI cheats on its exams

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