Artificial Intelligence

OpenAI and Anthropic Claim AI Refuted Key Math Hypothesis

Frontier AI labs OpenAI and Anthropic claim their models have generated sub-exponential algorithms that refute the Exponential Time Hypothesis. Computer scientists led by MIT professor Ryan Williams are organizing an academic response.

Radwan AbdulhadiEditor and technology writer

Published: October 28, 2026 · Updated: October 28, 2026 · 4 min read

OpenAI and Anthropic Claim AI Refuted Key Math Hypothesis — Image: TechCrunch

AI Breakthroughs Challenge Core Mathematical Assumptions

OpenAI published solutions to three major mathematics problems, including a surprise rejection of the Exponential Time Hypothesis (ETH), a fundamental assumption in computer science that helps define computational difficulty. The announcement sparked immediate debate within the scientific community. Anthropic mathematician Levent Alpöge suggested that OpenAI was basing its solutions on pre-existing work. Hours after that claim, Anthropic released its own refutation of the hypothesis, escalating competition between the frontier research laboratories.

The release reflects a changing distribution strategy for OpenAI. Rather than issuing a single unified release, OpenAI structured its releases differently across disciplines. Pure mathematicians received proof files on GitHub, while physicists formed a working group to manage their results. Meanwhile, computer scientists established a working group that requested public access to the proofs and asked OpenAI to fund a dedicated conference to discuss the findings.

Organizing the Scientific Response

MIT professor Ryan Williams is leading the computer science community's response to the findings. Williams, whose research focuses on computational complexity, previously voiced criticism of OpenAI's communication methods, calling its proof drop earlier in October a "DDOS attack on mathematicians." Despite those earlier concerns, Williams agreed to collaborate with frontier labs to evaluate ideas that are vital to the field, telling TechCrunch that the work requires broad scientific review.

OpenAI invited Williams to help interpret the solution alongside UC San Diego computer scientists Russell Impagliazzo and Ramamohan Paturi, who originally published the ETH in 1999. The researchers initiated their evaluation by publishing an open letter requesting community feedback and sparking dialogue on norms surrounding AI contributions. Williams noted that while some portions of OpenAI's proof appear routine, two or three "alien-looking parts" require collective scrutiny from researchers worldwide.

Understanding ETH and the P Versus NP Problem

The Exponential Time Hypothesis is closely linked to P versus NP, a central open problem in computer science that explores whether problems with easily verified solutions (NP) can also be solved easily (P). A common illustration is Sudoku: verifying a completed puzzle is fast, but finding the solution from scratch is time-consuming. This principle also forms the basis of modern cryptography, where holding a key allows fast decryption, but cracking an encoded message without one takes far too long to be practical.

Because scientists have not proven whether fast verification guarantees fast resolution, most assume P does not equal NP. The ETH supported this view by postulating that even the fastest computer algorithm requires exponentially more time as variables grow in specific logic puzzles. OpenAI and Anthropic now claim their AI models generated algorithms that solve these puzzles in "sub-exponential" time, potentially disproving the ETH and opening potential paths toward P equaling NP.

Theoretical and Security Implications

If verified, refuting the ETH will require researchers to revisit numerous academic papers published over the past decade that relied on the hypothesis. Williams noted that while the AI algorithms may not represent the final theoretical answers, they challenge long-standing intuitions regarding the tractability of complex computational problems and necessitate updates to foundational computer science theories.

Beyond theoretical mathematics, an improved algorithm raises potential cybersecurity questions, as cracked assumptions could theoretically render certain encryption key sizes insecure. Williams stated he asked OpenAI science lead Dan Roberts whether existing cryptographic systems were compromised. Roberts responded that OpenAI had evaluated the potential impact and was reasonably confident the finding does not imply active security breaches.

Adapting to AI-Driven Discoveries

The emergence of AI models solving complex mathematical problems presents new challenges for scientific training and academic workflows. Williams expressed optimism about the evolving paradigm despite concerns regarding how the next generation of researchers will be trained. He observed that AI capabilities are pushing scientists to be more ambitious and re-examine their focus as routine tasks become low-hanging fruit for automated models.