OpenAI Claims AI Model Disproved Exponential Time Hypothesis and Solved Major Math, Physics Problems

OpenAI Announces Three Major AI Scientific Discoveries

OpenAI announced three AI scientific discoveries in computer science, mathematics, and physics, less than a month after releasing hundreds of manuscripts containing solutions to long-standing mathematics questions1

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. The company claims its internal AI model has disproved the Exponential Time Hypothesis, resolved the Kakeya conjecture across all dimensions, and produced a rigorous proof for certain interacting quantum field theories2

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. This time, OpenAI introduced external experts as shepherd experts to guide verification, though this approach has sparked debate about academic credit and access.

AI Model Breakthroughs Challenge Exponential Time Hypothesis

The most significant claim involves disproving the Exponential Time Hypothesis, which has been widely believed to be true in computer science. According to OpenAI, its model found the disproof on 16 October and verified it in Lean proof assistant the next day2

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. Hundreds of computer science papers rest on this conjecture, which concerns Boolean satisfiability problems closely tied to P versus NP2

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. Researchers have used it to demonstrate that problems in graph theory, computational biology, databases, and other fields are hard to solve quickly.

Russell Impagliazzo and Ramamohan Paturi of UC San Diego, who originally proposed the Exponential Time Hypothesis with Francis Zane in 1999, will lead the verification process alongside Ryan Williams of MIT1

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. The group emphasized in an open letter that their involvement should not be taken as certification of the claim, stating that a result of this significance requires careful, independent scrutiny2

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. Williams confirmed the group signed no non-disclosure agreements and will not be paid, and they asked OpenAI to release all raw data and fund a conference for the research community, which OpenAI agreed to2

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. OpenAI released the model's writeup and Lean proof on GitHub1

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Mathematics Breakthrough Resolves Local Smoothing Conjecture

In mathematics, OpenAI claims its models proved the local smoothing conjecture, proposed by Christopher Sogge in 1991, in every dimension2

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. This would also settle the Kakeya conjecture and Stein's restriction conjecture in all dimensions1

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. Mathematicians had previously proved local smoothing in two dimensions in 2019, and just months ago, NYU professor Hong Wang was awarded a prestigious Fields Medal by the International Mathematical Union for resolving the Kakeya conjecture in three dimensions1

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. OpenAI released the model's writeup and a Lean proof for this discovery as well2

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Quantum Field Theory Proof Includes Standard Model Completion

The physics discovery involves a mathematically rigorous existence proof of certain interacting quantum field theories containing gauge fields and fermions in four dimensions, including Quantum Chromodynamics and a unified completion of the Standard Model of particle physics1

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. The work includes a proof that pure Yang-Mills theory exists, which is part of one of the Clay Mathematics Institute's Millennium Prize problem2

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. OpenAI said in September it would not claim the prize for its Navier-Stokes proof2

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. Nobel laureate David Gross will lead a group including Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov that will shepherd this work1

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. Unlike the other discoveries, this group chose not to release the AI-produced material for now and will write up the work themselves2

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Controversy Over Shepherd Approach and Academic Credit

OpenAI's approach of designating shepherd experts to receive AI-assisted scientific discovery outputs first has drawn criticism. The AGMAI panel of math advisers OpenAI assembled recommended just yesterday that AI companies do not adopt these practices, citing unequal access, borrowed reputation, and biased selection as key issues1

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. Instead, they recommended that AI labs release output on scholarly repositories with Lean-formalized proofs, information on how problems were chosen, funding for people working on understanding the results, and other details1

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. OpenAI acknowledges in its blog post that choosing initial shepherds necessarily shapes who gets involved first and creates asymmetry of information3

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OpenAI states it does not seek academic credit for the discoveries and says researchers in each group should get recognition for the explanations they write2

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. The company has given $5m to the Simons Foundation for workshops and conferences on AI-produced results2

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. However, the three computer scientists working on the Exponential Time Hypothesis verification process ask in their letter how credit should work when AI finds results first, warning that recognition may go to those who publish first or have the most powerful tools, while checking and explaining the work gets less credit2

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