OpenAI and Anthropic say AI may have cracked a famed complexity assumption — and computer scientists are scrambling

OpenAI and Anthropic said on Oct. 27, 2026 that their models found algorithms that may refute the Exponential Time Hypothesis, a long-standing assumption in computer science that helps define which problems are thought to stay hard as inputs grow. If the claims survive review, they could ripple through complexity theory and raise fresh questions about the foundations of cryptography.

The announcement has already triggered an unusually public response from researchers, including MIT professor Ryan Williams, who is helping organize the field’s pushback and scrutiny. The episode is also forcing a broader debate about how frontier AI labs should present major scientific claims when the evidence comes from model-generated mathematics rather than from a conventional research pipeline.

What OpenAI and Anthropic claimed

According to TechCrunch, OpenAI first released solutions to three major math problems on Oct. 26, 2026, including a claim that appears to reject the Exponential Time Hypothesis, or ETH. Anthropic later put out its own ETH refutation after questioning OpenAI’s work, escalating what began as a single lab’s proof dump into a cross-lab dispute over one of theoretical computer science’s most closely watched assumptions.

TechCrunch reported that the claims center on algorithms said to run in sub-exponential time. That matters because ETH is a foundational assumption about how hard certain problems are supposed to be: if input size grows, some problems are expected to require exponential time to solve. A credible refutation would not merely be a neat result. It would potentially reshape a wide stretch of complexity theory.

How did the labs present the work?

OpenAI used different release formats depending on the discipline, according to TechCrunch: GitHub for the mathematics material, and working groups for computer science and physics. That split suggests the lab was trying to match the disclosure method to the audience and the type of proof involved, while also exposing the work to specialists who could examine it more quickly.

Researchers familiar with the episode, as described by TechCrunch, asked OpenAI to share the proofs publicly and to fund a conference devoted to discussing them. The request reflects how unusual the moment is: instead of a quiet preprint-and-peer-review cycle, the field appears to be negotiating public norms in real time.

Why it matters

The immediate significance is theoretical, but the downstream implications could be practical. ETH is one of the assumptions that supports a large amount of modern thinking in computer science. If it turns out to be wrong, a body of published work built on it may need to be revisited.

Ryan Williams told TechCrunch that the result could force revisions to many papers that relied on ETH. That is a strong statement, but it points to the scale of the issue: assumptions in complexity theory are not just abstract philosophizing. They shape how researchers classify problems, frame lower bounds, and reason about what is feasible.

There is also a cryptography angle. Complexity assumptions often underpin the design and analysis of modern cryptographic systems. TechCrunch reported that Williams said OpenAI checked whether the result broke crypto systems and believed it did not. Even so, the possibility that a new algorithmic result could weaken some assumptions is enough to draw intense attention from researchers who work at the boundary between theory and security.

Finally, the episode matters because it exposes a growing governance problem for AI labs. If models can generate mathematically sophisticated claims that arrive faster than the traditional review process can absorb them, the research world needs ways to decide what counts as evidence, how to share it, and who is responsible for validating it.

Background: What is the Exponential Time Hypothesis?

ETH was first published in 1999 by Russell Impagliazzo and Ramamohan Paturi, according to the timeline described by TechCrunch. In broad terms, it says that certain hard problems are not expected to have substantially faster algorithms than exponential time as the size of the input grows.

That idea sits in the same family of questions as P versus NP, the classic computer-science problem asking whether every problem whose answer is easy to verify is also easy to solve. Ryan Williams referenced that distinction in comments to TechCrunch, saying:

“P = NP is asserting that this is true for every single problem you can verify quickly”

ETH is narrower than P versus NP, but it has broad influence because complexity theory often builds from such assumptions. In practice, these assumptions help researchers organize their understanding of hardness and guide the search for algorithms, lower bounds, and limits on efficient computation.

TechCrunch also noted that frontier AI labs have recently been releasing mathematical results that attract close scrutiny from researchers. That context helps explain why this latest announcement immediately became a public test case: it is not just about whether the proof is correct, but about how AI-generated research should enter the scientific record.

What Ryan Williams and other researchers are saying

Ryan Williams, a computer scientist at MIT, appears to be at the center of the field’s response. TechCrunch said he is organizing the computer-science community’s reaction, and that he co-signed an open letter seeking feedback and norms for AI-assisted research contributions.

Williams has also been publicly skeptical of OpenAI’s proof release before this latest development. TechCrunch said he criticized an earlier proof dump in October 2026, and the newer dispute appears to have sharpened his concerns rather than eased them.

In comments reported by TechCrunch, Williams said parts of the proof looked routine but that a few sections looked unusual. He also said he doubted OpenAI’s algorithm was the best possible, suggesting the result may be valid but not necessarily final or optimally sharpened. That distinction matters in mathematics, where a claim can be interesting, correct, and still leave room for better formulations or cleaner proofs.

Williams used a vivid phrase to describe how the field may feel about the flood of AI-produced claims:

“DDOS attack on mathematicians”

His remark captures the strain on human reviewers. If multiple labs and models can generate credible-looking advances at speed, researchers may be forced to triage an incoming stream of results that are too technical to dismiss but too numerous to validate quickly.

What makes this claim different from a normal preprint?

This is not a typical paper-then-peer-review story. The result reportedly emerged from AI models at two major labs, with one lab’s announcement prompting the other to produce its own refutation of the same assumption. That sequence turns the episode into a live demonstration of AI-assisted research competition.

There is also an epistemic issue. TechCrunch reported that parts of the proof looked routine to Williams, but some sections looked alien enough to merit skepticism. He even used the phrase:

“there are two or three alien-looking parts”

Those “alien-looking” sections matter because a proof can contain familiar scaffolding and still hinge on a subtle leap that needs independent checking. That is especially true in complexity theory, where the difference between an elegant proof and a flawed one may rest on a delicate construction or an overlooked assumption.

By the numbers

The reported facts show how quickly this discussion escalated. Here is a compact summary of the key timeline and quantities involved.

How could this affect cryptography and complexity theory?

The most serious potential consequences lie in the assumptions beneath entire areas of theory. TechCrunch reported that if validated, the claims could weaken assumptions underlying cryptography and broader complexity theory. That does not mean cryptography would suddenly collapse, but it does mean researchers would need to check whether any security arguments lean on the same hardness intuitions ETH supports.

Williams said OpenAI checked whether the result broke crypto systems and believed it did not. That nuance is important. A refutation of ETH would not automatically invalidate all cryptographic systems, but it would force a careful audit of any arguments that depend, directly or indirectly, on the same family of complexity assumptions.

For complexity theorists, the larger concern is the paper trail. Williams said the result could force revisions to many papers that relied on ETH. If a foundational assumption is weakened, prior work may need to be reclassified, reinterpreted, or rewritten. That is a slow, difficult process, and it only begins if the claim survives independent verification.

How are the AI labs handling disclosure?

The lab behavior may be as important as the result itself. According to TechCrunch, OpenAI chose different release channels by discipline, using GitHub for math and working groups for computer science and physics. That suggests the company is experimenting with how to package frontier results for different academic communities.

At the same time, researchers have asked for more transparency. They want the proofs shared publicly and, in at least one case, want a conference funded to focus on the claims. Those requests point to a familiar tension: faster disclosure can speed up scrutiny, but it can also create confusion if the underlying material is incomplete, difficult to parse, or still evolving.

Williams’ open letter, co-signed with others, calls for feedback and norms around AI-assisted research contributions. That is a small but telling sign that the field is trying to build a rulebook while the game is already in motion.

Timeline of the dispute

The pace of the story is part of what makes it notable. The sequence below reflects the events described in the fact sheet and in TechCrunch’s reporting.

1. 1999: Russell Impagliazzo and Ramamohan Paturi first publish ETH.
2. Earlier in October 2026: Ryan Williams criticizes an earlier OpenAI proof release.
3. Oct. 26, 2026: OpenAI releases solutions to three major math problems, including an ETH rejection.
4. Oct. 27, 2026: TechCrunch reports OpenAI and Anthropic claims that models may have refuted ETH.
5. Afterward: Researchers seek public proofs, feedback, and a conference devoted to the claims.

What happens next

The central question is whether the ETH refutation holds up under independent review. That is the first test, and it is the one that matters most. Until outside researchers examine the proofs, the claim remains provocative rather than settled.

Several open questions remain. TechCrunch identified uncertainty over whether the algorithms are genuinely novel or partly based on prior work, how the physics and computer-science working groups will release or vet the material, and whether any broader cryptography implications emerge. Each of those threads could move in different directions.

There is also the broader cultural question. If AI labs can generate frontier mathematical claims that are serious enough to prompt counterclaims from rival labs, the research community may need new norms for disclosure, attribution, and validation. Williams’ open letter suggests that process has already begun.

For now, the safest way to read the story is as a major but unverified challenge to a classic complexity assumption. If the claims are confirmed, the implications would extend well beyond a single theorem. If they fail, the episode will still likely shape how the next wave of AI-generated research is introduced to the world.

Bottom line

OpenAI and Anthropic have each said their models found algorithms that may refute ETH, a major computer-science assumption first published in 1999. The claims are not yet established, but they have already prompted scrutiny from leading researchers and a wider debate over cryptography, complexity theory, and the norms for AI-assisted scientific discovery.