AI Proofs Challenge a Foundational Theory in Computer Science

OpenAI and Anthropic announced this week that they have produced machine-generated proofs showing the exponential time hypothesis (ETH)—a 27-year-old conjecture about the inherent difficulty of certain computational problems—is false. The proofs were released on GitHub in both natural-language explanations and a machine-checkable Lean format. According to the companies, the work has not yet been independently verified.

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ETH posits that solving specific problems requires time that grows exponentially with input size. The hypothesis has underpinned large portions of research on algorithm design and computational complexity, guiding expectations about what can be efficiently computed. If the hypothesis is indeed false, many results that assume its truth would need to be re-examined.

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• Peter Jonsson – Professor at Linköping University, whose forthcoming paper for the IEEE Symposium on Foundations of Computer Science is now “dead” because it relies on ETH. He expects his situation to become common among peers.

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• Daniel Lokshtanov – Professor at the University of California, Santa Barbara, who helped formulate ETH. He says that confirmation of the AI proofs could render him “galactically wrong” and invalidate roughly 50 of his published papers.

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• OpenAI and Anthropic – AI firms that generated the proofs and have opened the work for community scrutiny.

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• UC Santa Barbara computer scientists – including Lokshtanov, who have been asked to coordinate a volunteer effort to unpack the AI-produced arguments.

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OpenAI has issued a public request for volunteers, distributing a Google form to gather feedback from researchers willing to examine the proofs. The company also pledged funding for a dedicated conference to discuss the implications of the result. Anthropic has made a similar call for scholarly review. Both firms have posted the proof artifacts on GitHub, inviting the broader theoretical computer-science community to verify the claims.

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If the AI-generated proofs withstand peer review, the falsification of ETH could upend a substantial body of work that assumes exponential lower bounds on problem-solving time. Researchers may need to revisit algorithmic analyses, complexity classifications, and related publications that built on the hypothesis. The situation illustrates both the disruptive potential of advanced AI in mathematical research and the challenges of rapidly validating machine-produced proofs.

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