OpenAI and Anthropic models claim to refute Exponential Time Hypothesis

OpenAI published a proof claiming to overturn the Exponential Time Hypothesis (ETH), a decades-old assumption that certain logic problems grow exponentially harder as they scale. Anthropic followed hours later with its own proof, after one of its mathematicians publicly called OpenAI's work derivative. If either holds, it cracks the door to P = NP, which would mean the hardness assumptions underneath RSA and elliptic-curve encryption are shakier than the entire internet's security model currently assumes.

Neither proof has been peer-reviewed. MIT professor Ryan Williams, who is organizing the review alongside the UC San Diego researchers who originally posed ETH, described parts of OpenAI's proof as "alien-looking." That is not praise. It means the people most qualified to check this work cannot yet reconstruct the reasoning chain.

The safety failure is the most concrete thing here. If a model genuinely found a path to P = NP, the first call should have gone to cryptographers, standards bodies, and governments, not to a tech reporter. Both labs skipped coordinated disclosure entirely. Williams had to ask OpenAI science lead Dan Roberts after publication whether any encryption was now breakable. Roberts said no known breaks, which is a scoped, careful answer. It is not reassuring. Both labs have spent years promising their safety commitments cover exactly this kind of civilization-scale result. This week, the competitive race won.

Two rivals announcing the same decades-defying result within hours, both under competitive pressure, neither peer-reviewed, with sections experts cannot follow, is the pattern of a race, not a discovery. ETH has survived serious attack for decades. Unreadable proofs usually hide errors, not breakthroughs.

For operators: do not touch your crypto stack. The gap between "theoretically possible" and a working exploit on public-key crypto has historically been years to decades. The real planning risk is softer. Every security team that recently deprioritized post-quantum migration now has a reason to keep it funded, because the headline has already seeded uncertainty even if the proof collapses.

On the compute side, verification will burn real cluster time at multiple labs whether or not either result survives. That cost is immediate. The longer tail is that a real ETH collapse would say algorithmic cleverness can substitute for raw compute on a class of problems nobody has priced that way, which has implications for how the industry thinks about hardware scaling. But that question waits entirely on the math holding up.

Prediction: Williams's review group, working with the original UC San Diego ETH authors, will not have publicly confirmed either proof as correct and community-verified by 2027-05-02. The reviewers will have found a gap, or still be working through the sections nobody can currently follow. ETH's track record and the base rate for bold refutations of long-standing assumptions argue strongly in that direction. Medium confidence.

Two of the biggest AI labs each put out a proof claiming to overturn the Exponential Time Hypothesis, a decades-old assumption that some logic puzzles get exponentially harder as they grow. OpenAI went first. Anthropic followed hours later, after one of its own mathematicians called OpenAI's work derivative. If either proof holds, it cracks open the door to P = NP, which would mean the hard math problems underneath RSA, elliptic-curve, and even next-generation "post-quantum" encryption are less safe than everyone assumed.

What's actually being decided here is not whether to rip out your crypto. It's how much weight to put on a math claim that no human has fully reconstructed yet, from two companies with every reason to want the headline. Nothing is hard to undo this week, because there is nothing to undo. There's no deadline either. Peer review on a result this size runs months. Ryan Williams, the MIT professor organizing the review alongside the UC San Diego authors who first posed ETH, called parts of OpenAI's proof "alien-looking." That is not praise.

The Skeptic. Two rivals announce the same decades-defying result within hours, both under competitive heat, neither peer-reviewed, and the proof has sections experts can't read. That's the pattern of a race, not a discovery. ETH has survived decades of serious attack, so the starting odds it's actually false are low. "Alien-looking" math nobody can reconstruct is more often a mistake dressed in novel notation than a breakthrough. AI-generated proofs have produced confident, wrong answers at every scale we've tested. The Anthropic follow-up smells like a competitive reflex, not independent confirmation. Until Williams and the San Diego authors sign off, this is a claim, not a result.

The Safety Lens. If a model genuinely found a road to P = NP, the first call is not a tech reporter. It's a coordinated disclosure with cryptographers, standards bodies, and governments, because the entire internet's encryption rests on these hardness assumptions. Both labs skipped that. OpenAI published, Anthropic counter-published hours later, and only afterward did Williams ask OpenAI science lead Dan Roberts whether any encryption was now breakable. Roberts said no known breaks. That question should have been answered before anyone hit publish. Both labs have spent years promising their safety commitments cover exactly this kind of civilization-scale result. This is the test, and the race won.

The Researcher. If it holds, this is the most important complexity-theory result in forty years. The "if" is carrying almost everything. Williams calling parts "alien-looking" means the community cannot yet rebuild the chain of reasoning, and a proof that passes a lab's internal checks but resists human reconstruction is a genuinely new and dangerous category. We don't have good tools for grading math no human understands. Williams's credibility is being borrowed to lend weight to work he's openly saying he doesn't yet follow. What actually matters is boring: do the original ETH authors, who know this terrain better than anyone, confirm or find the flaw?

The Builder. Do not touch your crypto stack this week. Roberts said no known breaks, and that answer was scoped and careful, not reassuring. The engineering question is how long "theoretically possible" takes to become a working exploit. For public-key crypto that gap has historically been years to decades, not a news cycle. What actually moves because of this story is softer: every security team that just pushed post-quantum migration down the roadmap now has a reason to leave it funded. The tooling risk isn't RSA falling tomorrow. It's planning assumptions quietly going stale while everyone waits for peer review that won't finish this quarter.

The Compute Pragmatist. The whole AI scaling pitch assumes hard problems need more hardware, that enough GPUs eventually crack reasoning. A real ETH collapse would say algorithmic cleverness can substitute for raw compute on a class of problems nobody has priced that way. NVIDIA's moat partly rests on hardness being permanent. That's the long tail. The near-term cost is concrete: multiple labs will burn real cluster time trying to reproduce and verify these proofs, and the verification is itself expensive because you're re-running the systems that generated them. The race to confirm costs money whether or not the result survives.

Where they split. The Researcher and the Skeptic agree to wait but for opposite reasons. The Researcher thinks this might be the result of the century and wants it handled with care. The Skeptic thinks it's probably an error hidden in novel notation and wants it handled with suspicion. Both land on "don't believe the press release," which tells you the headline is running ahead of the math. The Safety Lens and the Builder disagree on urgency: Safety wants coordinated disclosure as if the result were real, the Builder points out there's no exploit and nothing to patch. That tension resolves cleanly once you separate the claim's magnitude from its maturity. The magnitude is enormous. The maturity is near zero.

What this hinges on is one question: do the UC San Diego authors who posed ETH and the review group Williams is organizing confirm the proof, find a fixable gap, or find a fatal flaw? Everything downstream, crypto exposure, compute theory, the scaling thesis, waits on that. The council leans hard toward skepticism. Not because AI can't do real math, but because two competing labs racing out an unreviewed, unreadable proof the same afternoon is exactly how a mistake gets amplified into a narrative.

Prediction: The peer-review group organized by Ryan Williams with the original UC San Diego ETH authors will not have publicly confirmed OpenAI's or Anthropic's ETH refutation as a correct, community-verified proof by 2027-05-02; the reviewers will instead have either found a gap or still be working through the "alien-looking" sections.

Confidence: Medium. ETH has survived decades; unreadable proofs usually hide errors.

Why: Williams has already said parts of OpenAI's proof are "alien-looking" and that the whole community needs to reconstruct them together, which means the reasoning chain is not yet verifiable by the people qualified to check it. Peer review of a result this consequential runs in months, and complexity theory's track record is that bold refutations of long-standing assumptions usually surface a flaw once experts dig in, especially when two rival labs race them out the same afternoon under competitive pressure. The opposite outcome, a clean community sign-off inside six months on math no reviewer can currently follow, would break the normal pace of serious proof-checking and the base rate for decades-old conjectures falling. The far likelier path is a slow grind that either breaks the proof or is still unresolved come spring.

Revisit by 2027-05-02: We're right if, by then, no published statement from Williams's review group or the original ETH authors declares either proof correct and community-verified. We're wrong if that group publicly confirms OpenAI's or Anthropic's refutation as a valid proof before 2027-05-02.