OpenAI And Anthropic Claim AI Disproved ETH Hypothesis

OpenAI and Anthropic claim their AI systems disproved the 27-year-old Exponential Time Hypothesis and published Lean proofs on GitHub, but neither result is independently verified. OpenAI posted 722 manuscripts on 400 problems, and Lokshtanov expects around 50 of his papers may need revisiting; encryption is not directly broken.

What Happened

OpenAI and Anthropic each say their AI systems have disproved the Exponential Time Hypothesis (ETH), a 27-year-old assumption that underpins large parts of theoretical computer science. NDTV and WIRED reported the claims.

ETH was proposed in 1999 by Russell Impagliazzo and Ramamohan Paturi at the University of California, San Diego. It holds that 3-SAT — deciding whether a logical formula can be made true — has no sub-exponential time algorithm.

In practical terms, that means certain problems cannot be solved significantly faster than existing mathematical estimates predict. Researchers have leaned on the idea to explain why some computations become brutally hard as they scale.

Key figures in the ETH dispute
Key fact	Detail
Age of the hypothesis	27 years
Proof formats published by both firms	Natural language and Lean
Manuscripts OpenAI posted to GitHub	722 manuscripts on 400 problems
Papers Lokshtanov expects to revisit	Around 50 published papers

Both companies published their proofs on GitHub in ordinary language and in Lean, a proof assistant that lets computers check mathematical arguments formally. Neither result has been independently verified.

OpenAI has asked the UC San Diego computer scientists who originally proposed the hypothesis, plus an MIT academic who has refuted a version of ETH, to help unpack the proofs.

That effort includes a Google form for volunteers and a commitment from OpenAI to fund a conference on the topic.

The human fallout is already visible. Linköping University professor Peter Jonsson says much of his work, due to be presented in two weeks at the IEEE Symposium on Foundations of Computer Science, is now “dead.”

He expects the same scene in talk after talk: “People will start the talks: ‘ETH is false, half of my paper does not work.’”

He added that researchers still learn a lot from the shift, and “this is what science is about.”

UC Santa Barbara professor Daniel Lokshtanov estimates the result, if confirmed, will render him “galactically wrong” and leave around 50 of his published papers either “pointless” or in need of a revisit.

“It’s just a giant bomb dropped into the middle of the field,” he told WIRED. “It’s really cool and terrible at the same time.”

Thore Husfeldt, head of the algorithms research group at the IT University of Copenhagen, spent most of this year on a single problem in his subfield. “As far as I can tell, it’s now all irrelevant,” he said.

He still calls the finding “fantastic” and a “once-in-a-generation result,” describing mathematicians as people stumbling about in a completely dark room. “It’s like somebody just illuminated an entire subfield in floodlights of knowledge,” he said.

Not everyone is celebrating.

Husfeldt said the last few months have been “really tough,” with AI results every week or second week that “annihilate the ongoing research projects of many people.”

His department has considered hiring an occupational psychologist because “some people are really depressed and really sad.”

Volume is part of the strain. OpenAI earlier this month posted 722 manuscripts on 400 problems to GitHub, annoying academics, and several documents contained errors, WIRED reported.

36kr reported that Anthropic’s paper credits Claude with independently deriving the core algorithm under zero human intervention, with Claude listed as sole author.

OpenAI researcher Sebastien Bubeck, a former vice president at Microsoft AI, called it “the biggest surprise I have seen in 20 years,” according to 36kr.

NDTV reported that the breakthrough does not directly break existing encryption systems. Cryptography relies on certain problems staying hard, so any wider security impact depends on the proofs’ details.

What This Means For You

For researchers and students: OpenAI has asked researchers to help review the proofs and committed to funding a conference. If ETH falls, conditional results built on it may need revision.

For developers and engineers: The reports describe a theoretical debate. YourStory noted that even if ETH is overturned, it would not mean every difficult computing problem suddenly becomes easy.

For security teams: NDTV reports no direct break to encryption. Any wider impact would depend on the details of the proofs and their relevance to cryptographic methods.

Why It Matters

The deeper shift is about who produces mathematics and how fast it is absorbed. Husfeldt’s subfield went from a year of focused work to “all irrelevant” in a single result.

Because the proofs are published in Lean, they allow formal checking of mathematical arguments. Formal verification can expose logical gaps, but it does not automatically settle whether the wider claim is correctly framed, as YourStory noted.

There is also a structural point about the field. In 1999 the hypothesis was a description of collective intuition; it later became load-bearing for hundreds of papers.

This suggests the cost of overturning an assumption grows with the number of results that quietly depend on it.

One logical detail matters for how far the damage spreads. As 36kr noted, if ETH holds then P≠NP follows, but if ETH is overturned you cannot conclude that P=NP.

Key Takeaway

OpenAI and Anthropic both claim their AI systems disproved the Exponential Time Hypothesis, and both published Lean-checkable proofs on GitHub.
No independent verification exists yet; OpenAI has asked the hypothesis’s original UC San Diego proposers and an MIT critic to organize review.
Named researchers expect real damage to published work — Lokshtanov cites around 50 papers and Jonsson calls his forthcoming conference material “dead.”
The result does not directly break encryption, though it could raise questions about the hardness assumptions cryptography rests on.

Frequently Asked Questions

What is the Exponential Time Hypothesis?

It is a 1999 assumption, proposed by Russell Impagliazzo and Ramamohan Paturi, that 3-SAT cannot be solved in sub-exponential time. Researchers have used it to set limits on how fast algorithms for many other problems could ever become.

Has anyone confirmed the proofs?

Not yet. WIRED reports that researchers have not independently verified, let alone fully understood, the AI-produced proofs published by OpenAI and Anthropic.

Does this mean encryption is broken?

No. NDTV reports the claimed breakthrough does not directly break existing encryption systems, and any wider impact would depend on the details of the proofs.

Sources

This report is based on coverage from NDTV, wired.com, yourstory.com and eu.36kr.com. Figures and quotes were checked against these reports before publication.