OpenAI and Anthropic Claim Refutations of Exponential Time Hypothesis

OpenAI and Anthropic have both released candidate proofs claiming to refute the Exponential Time Hypothesis (ETH)—a foundational 1999 assumption in computational complexity theory—sparking intense scrutiny across theoretical computer science and mathematics over both the algorithms themselves and how frontier AI labs release scientific claims, according to The Verge and TechCrunch.

Three Frontier Claims Across Complexity Theory, Geometry, and Physics

OpenAI announced that its latest reasoning models produced major advances on three long-standing problems across three disciplines:

1. Theoretical Computer Science: A purported refutation of the Exponential Time Hypothesis (ETH), which posits that 3-SAT and related NP-complete problems cannot be solved in sub-exponential time.
2. Mathematics: A new result advancing the Kakeya conjecture in geometric measure theory, released directly to GitHub.
3. Theoretical Physics: A new calculation in quantum chromodynamics (QCD) modeling strong nuclear force interactions, currently under review by a physics working group.

Hours after OpenAI’s announcement—and after Anthropic mathematician Levent Alpöge suggested on social media that OpenAI’s approach built heavily on pre-existing literature—Anthropic published its own model-generated refutation of the Exponential Time Hypothesis.

MIT’s Ryan Williams and ETH Founders Coordinate Community Verification

To avoid what MIT Professor Ryan Williams had previously criticized earlier in October as a “DDOS attack on mathematicians” when unvetted AI proofs flooded researchers, OpenAI asked Williams—alongside UC San Diego computer scientists Russell Impagliazzo and Ramamohan Paturi, who formulated the ETH in 1999—to help organize the computer science community’s response and request funding for a dedicated conference.

“Some parts [of OpenAI’s proof] are, maybe you could say routine, but then yes, there are two or three alien-looking parts, and it’s exactly these parts that I saw that made me think, wow, this is something that the whole community needs to work on together,” Williams told TechCrunch.

Because a sub-exponential algorithm for hard NP problems could theoretically affect cryptographic assumptions, Williams immediately asked OpenAI science lead Dan Roberts whether the lab had checked for cryptographic breaks; Roberts’ team reported they were reasonably confident existing cryptographic systems were not compromised.

AGMAI Criticizes Closed "Expert Shepherd" Gatekeeping

Even as computer scientists welcomed a more structured working-group review, members of the Advisory Group on AI and Mathematics (AGMAI)—including Johns Hopkins University mathematician Emily Riehl and Fields Medalist Terence Tao—raised concerns to The Verge that handpicking closed groups of “expert shepherds” under non-disclosure agreements creates a new form of corporate gatekeeping in academic mathematics.