OpenAI claims ETH refutation, QCD proof; Barak, Impagliazzo, Paturi to organize open review
OpenAI claims an internal model refuted the Exponential Time Hypothesis, and Boaz Barak, Russell Impagliazzo, and Mohan Paturi have agreed to organize an open, independent examination of the claim. Preprints for the ETH and local smoothing results are on GitHub. Tenobrus calls the trend toward efficient algorithms for supposedly hard problems concerning for capability upper bounds; Roon frames it as a runaway-intelligence-explosion dynamic. No independent verification yet.
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- Couldn't think of a better team to study and expand on this result! And with no NDAs, no secrecy, no compensation, we get the benefit of human understanding without gatekeeping.An internal model at OpenAI has produced a claimed refutation of ETH! Russell Impagliazzo, Mohan Paturi, and I have been asked to help organize an open and independent examination of this claim. 1/4 open on X6 likes · 0 reposts
- While mathematics and TCS share a lot in common, it is up to each community to decide how best they want to address the question of AI's impact on their field.Our letter to the community invites ideas for organizing this effort and, separately, for addressing the broader questions raised by AI-generated results: docs.google.com/document/d/1ad… OpenAI's announcement is here: openai.com/index/building… open on X7 likes · 1 reposts
- there are many caveats, but personally i find myself pretty concerned by this directional trend towards highly efficient algorithms for things we previously thought fundamentally hard. it makes the upper bounds of capabilities stretch much, much further53 likes · 1 reposts
- fighting for control over a runaway intelligence explosion will continuously look like “wow I didn’t know you could DO that with mere bits and atoms” and then losingWe are announcing three new discoveries in mathematics, computer science, and physics about harmonic analysis, complexity theory, and quantum field theory. openai.com/index/building… open on X151 likes · 9 reposts
- The Exponential Time Hypothesis is false. Quoting: 'Our models produced a natural language proof for Yang–Mills existence on September 9th, 2026, and then subsequently produced a proof for QCD on September 18th, 2026. Given the length and complexity of the work, we postponed release until the Lean formalization completed. We finished our formalization of Yang–Mills’ existence on October 16th, 2026, which led us to develop the collaboration described here.'
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- this is completely fucking insane.@andrewcurran_: The Exponential Time Hypothesis is false. open on X25 likes · 3 reposts
- oh yeah for sure this proof specifically has literally no real world impact1 likes · 0 reposts
- OpenAI has announced to three new discoveries in mathematics, computer science, and physics: - Local smoothing and the Kakeya conjecture - The Exponential Time Hypothesis is false - Existence of quantum chromodynamics and completions of the Standard Model
102 likes · 25 reposts - From the letter:
An internal model at OpenAI has produced a claimed refutation of ETH! Russell Impagliazzo, Mohan Paturi, and I have been asked to help organize an open and independent examination of this claim. 1/4 open on X66 likes · 3 reposts - I apologize for the thread being sloppy, I was a little rattled.21 likes · 0 reposts
- Yes, the models are also in shock.12 likes · 0 reposts
- Mira is growing in strength.11 likes · 0 reposts
Our letter to the community invites ideas for organizing this effort and, separately, for addressing the broader questions raised by AI-generated results: docs.google.com/document/d/1ad… OpenAI's announcement is here: openai.com/index/building… open on X11 likes · 0 reposts- They explain here:
6 likes · 1 reposts - The Exponential Time Hypothesis is false.
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- Local smoothing and the Kakeya conjecture.
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- I don't mean Terra.@andrewcurran_: OpenAI has announced to three new discoveries in mathematics, computer science, and physics: - Local smoothing and the Kakeya conjecture - The Exponential Time Hypothesis is false - Existence of quantum chromodynamics and completions of the Standard Model open on X3 likes · 0 reposts
- I mean this:@andrewcurran_: OpenAI has announced to three new discoveries in mathematics, computer science, and physics: - Local smoothing and the Kakeya conjecture - The Exponential Time Hypothesis is false - Existence of quantum chromodynamics and completions of the Standard Model open on X3 likes · 0 reposts
- Ugh, 'to three' sorry about that, typing too fast.3 likes · 0 reposts
- 🤯🤯🤯The physics collaboration will understand and explain a result that gives a mathematically rigorous existence proof of certain interacting quantum field theories containing gauge fields and fermions in four dimensions, including Quantum Chromodynamics (QCD) and a unified completion of the Standard Model of particle physics. As a subproblem, this work also includes a proof of the existence of pure Yang–Mills theory, which is part of the Quantum Yang–Mills Theory Clay Mathematics Institute Millennium Prize problem. These proofs are all formally verified in Lean. Our models produced a natural language proof for Yang–Mills existence, and then subsequently produced a proof for QCD After the formalization completed, we reached out to David Gross. David will lead a group including Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov that will shepherd this work, and we will defer to them on the release of materials. Gross’s work on asymptotic freedom in Yang-Mills theories helped establish QCD as the theory of the strong interactions and earned him a share of the 2004 Nobel Prize in Physics. Jaffe formulated the Quantum Yang–Mills Theory Millenium Prize problem with Witten and also envisioned the idea of Millennium Prize problems and co-founded the Clay Mathematics Institute. Douglas has already been a steward of this problem over the last 20 years; Klebanov helped pioneer the application of gauge–string duality to confinement, an important property of QCD, and now directs the Simons Collaboration on Confinement and QCD Strings; and Nekrasov has done groundbreaking work on exact methods for generalizations of Yang–Mills theory. open on X2 likes · 0 reposts
- :0The computer science collaboration will understand and explain a result concerning the Exponential Time Hypothesis (ETH), a longstanding conjecture about the computational complexity of Boolean formula satisfiability, a problem deeply related to the P vs. NP problem. Surprisingly, our system has recently proved that the ETH is false, a result that was subsequently verified in Lean. The refutation of the ETH reopens questions about how much faster these tasks could become, and may help guide the search for better algorithms. Finding such algorithms, and turning theoretical advances into practical improvements, will require significant further research. Our system found its natural language disproof for the ETH we reached out to to @rrwilliams. Ryan will form a collaboration with Russell Impagliazzo and Ramamohan Paturi to verify and shepherd this result. Impagliazzo and Paturi, along with Francis Zane, are the original proposers of the Exponential Time Hypothesis, and Williams has refuted strong versions of the ETH, used ETH for hardness results, and connected algorithms and lower bounds. This group asked us to make all raw data of the results public to facilitate independent verification by the community, which we have done by posting the natural language proof and Lean formalization to our GitHub repo. The group also invites the community to help organize an open examination of the ETH claim and to discuss the broader questions that AI-generated breakthroughs raise about verification, access, credit, and the future of research. github.com/openai/math/bl… open on X2 likes · 0 reposts
- This:@andrewcurran_: OpenAI has announced to three new discoveries in mathematics, computer science, and physics: - Local smoothing and the Kakeya conjecture - The Exponential Time Hypothesis is false - Existence of quantum chromodynamics and completions of the Standard Model open on X1 likes · 0 reposts
- The models, as usual on one of these days, are in various states of shock and disbelief.1 likes · 0 reposts
- It's second post in thread, but here is also: openai.com/index/building…1 likes · 0 reposts
- Professor Ryan Williams.An internal model at OpenAI has produced a claimed refutation of ETH! Russell Impagliazzo, Mohan Paturi, and I have been asked to help organize an open and independent examination of this claim. 1/4 open on X1 likes · 0 reposts
- It's all in the thread.0 likes · 0 reposts
- From the thread by OpenAI's Dan Roberts.The physics collaboration will understand and explain a result that gives a mathematically rigorous existence proof of certain interacting quantum field theories containing gauge fields and fermions in four dimensions, including Quantum Chromodynamics (QCD) and a unified completion of the Standard Model of particle physics. As a subproblem, this work also includes a proof of the existence of pure Yang–Mills theory, which is part of the Quantum Yang–Mills Theory Clay Mathematics Institute Millennium Prize problem. These proofs are all formally verified in Lean. Our models produced a natural language proof for Yang–Mills existence, and then subsequently produced a proof for QCD After the formalization completed, we reached out to David Gross. David will lead a group including Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov that will shepherd this work, and we will defer to them on the release of materials. Gross’s work on asymptotic freedom in Yang-Mills theories helped establish QCD as the theory of the strong interactions and earned him a share of the 2004 Nobel Prize in Physics. Jaffe formulated the Quantum Yang–Mills Theory Millenium Prize problem with Witten and also envisioned the idea of Millennium Prize problems and co-founded the Clay Mathematics Institute. Douglas has already been a steward of this problem over the last 20 years; Klebanov helped pioneer the application of gauge–string duality to confinement, an important property of QCD, and now directs the Simons Collaboration on Confinement and QCD Strings; and Nekrasov has done groundbreaking work on exact methods for generalizations of Yang–Mills theory. open on X0 likes · 0 reposts
- what’s ETH?0 likes · 0 reposts
- Thread here.An internal model at OpenAI has produced a claimed refutation of ETH! Russell Impagliazzo, Mohan Paturi, and I have been asked to help organize an open and independent examination of this claim. 1/4 open on X0 likes · 0 reposts
- Link here:Our letter to the community invites ideas for organizing this effort and, separately, for addressing the broader questions raised by AI-generated results: docs.google.com/document/d/1ad… OpenAI's announcement is here: openai.com/index/building… open on X0 likes · 0 reposts
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