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On October 26, 2026, OpenAI announced that its internal model produced three research results in the fields of mathematics, computer science, and physics, including a counterexample to the long-standing Exponential Time Hypothesis (ETH) in computational complexity theory. In mathematics, the model provided a proof of the local smoothing conjecture in arbitrary dimensions, and thereby resolved the Kakeya conjecture and the Stein restriction conjecture; the output was obtained on October 18 and Lean formalization was completed the next day. The computer science result was verified by a group led by Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams, and OpenAI agreed to make all raw data public and to fund related conferences; the physics result provided a rigorous existence proof for a four-dimensional quantum field theory with gauge fields and fermion interactions, and also included a pure Yang–Mills existence proof, and a group led by David Gross decided not to make the AI-produced materials public for the time being and to write up the results themselves. On October 28, AGMAI, composed of nine mathematicians and affiliated with the Institute for Advanced Study in Princeton, called on OpenAI to immediately make public the natural-language and Lean outputs of the Yang-Mills, quantum chromodynamics, and Standard Model completeness proofs, and opposed AI companies selecting the first reviewers themselves.
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Anthropic Abolishes Coding Interviews: Felix Reiseberg Says "Hunger beats tenure"Developments
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Oct 28
Latent Space
Anthropic Abolishes Coding Interviews: Felix Reiseberg Says "Hunger beats tenure"
Anthropic hiring manager Felix Reiseberg announced that the company will no longer use traditional coding interviews to evaluate candidates, citing the fact that Claude is already stronger than humans at both React challenges and assembly problems, and that truly impactful builders do not win through such tests. He advises junior engineers to pick an idea that can drive business impact, build a working prototype over the weekend, focus on just one good idea, and leverage their fresh perspective on users. On the same day, Google DeepMind released the Genie 4 world model, and Claude Opus 5.5 (58 points) topped the Artificial Analysis Intelligence Index v5.
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36Kr · AI
OpenAI and Anthropic simultaneously claim their internal models overturned the Exponential Time Hypothesis (ETH)
OpenAI and Anthropic announced almost simultaneously that their respective internal models had overturned the Exponential Time Hypothesis (ETH), which has dominated theoretical computer science for 27 years. Anthropic said its Claude research model independently found the core algorithm on October 16 with 14 million output tokens and zero human input, and that Claude is the sole named author of the paper; both companies have publicly released Lean formal proof code, and ETH proposers Russell Impagliazzo and Ramamohan Paturi are jointly conducting a line-by-line review with teams including MIT. The original article also notes that a large number of complexity lower-bound research conclusions that presuppose the truth of ETH need to be re-evaluated.
The Verge AI
The Verge: Researchers unhappy with how OpenAI publicized breakthroughs in mathematics, computer science, and physics
OpenAI announced breakthroughs in mathematics, computer science, and physics, with the three results using different disclosure strategies: the mathematics result was released directly as AI-generated output, an external research group will be formed to explain the computer science result, and the physics result has not yet been made public and will be left to external experts to decide how to release. Several researchers interviewed acknowledged the results themselves but criticized OpenAI's practice of selecting specific experts to see the results first; the Mathematics and AI advisory group AGMAI also advised AI companies not to adopt this practice of opening results to a small group of people first.
TechCrunch AISelected
Frontier AI labs claim a model has overturned the ETH. How is the computer science community responding?
OpenAI announced solutions to three mathematical problems, one of which is a refutation of the exponential time hypothesis (ETH), a long-standing assumption in computer science; Anthropic subsequently also published its own ETH rebuttal. MIT professor Ryan Williams, along with Russell Impagliazzo and Ramamohan Paturi of UC San Diego, were invited by OpenAI to help interpret the results and issued an open letter soliciting feedback and discussing norms for AI contributions. Williams said that if the conclusion holds, a large number of papers from the past decade that rely on the ETH will need to be re-examined. He also asked OpenAI science lead Dan Roberts whether existing cryptographic systems are affected, and the latter said they had checked and believed it would not lead to a break.
Numerama
Mathematicians' group AGMAI demands OpenAI immediately publish Yang-Mills theory proof
AGMAI, composed of nine mathematicians, called on OpenAI to immediately publish the natural-language and Lean versions of its claimed proofs of Yang-Mills theory, quantum chromodynamics, and the completeness of the Standard Model. OpenAI announced three mathematics, computer science, and physics results on October 26, stating that the Yang-Mills proof was completed on September 9 and its Lean formalization was completed on October 16, but the proof has only been seen by five physicists selected by OpenAI (led by 2004 Nobel Prize in Physics laureate David Gross). AGMAI is affiliated with the Institute for Advanced Study in Princeton, noted that the problem is one of the Millennium Prize Problems, and cited its October 25 statement opposing AI companies selecting the first reviewers themselves.
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Rohan Paul
Math and AI advisory group calls on OpenAI to disclose Yang-Mills proof
The Mathematics and Artificial Intelligence Advisory Group publicly called on OpenAI to release its undisclosed Yang-Mills proof, requesting the related natural-language and Lean output. OpenAI says its model proved Yang-Mills existence on September 9 and proved quantum chromodynamics on September 18, with Lean completing the first check on October 16. Its Kakeya and exponential-time hypothesis results were published directly to GitHub, while the physics-related documents remain held by reviewers led by David Gross.
Oct 27
36Kr · AISelected
OpenAI says its model disproved the Exponential Time Hypothesis (ETH) and presents three interdisciplinary results in mathematics and physics
On October 26, OpenAI announced that its internal model had achieved new results in three fields—mathematics, computer science, and physics: disproving the Exponential Time Hypothesis (ETH), which has been used in theoretical computer science for nearly 30 years; proving the local smoothing conjecture in all dimensions; and establishing a rigorous existence proof for a four-dimensional quantum field theory involving quantum chromodynamics. In the ETH part, the model constructed a deterministic algorithm for fixed-width CNF Boolean formulas, giving a subexponential running-time bound of 2^{O(n/√log n)}, and on October 16 generated a natural-language disproof, completing Lean formalization the next day; OpenAI has invited Impagliazzo and Paturi, the original proposers of ETH, and Ryan Williams of MIT to organize an independent review. In the mathematics part, it says the model found a new auxiliary partial differential equation, advancing the 2019 two-dimensional local smoothing conjecture to all dimensions, with the proof obtained on October 18 and Lean formalization completed on October 19; the physics part was organized by a working group led by Nobel laureate in physics David Gross, and the original AI-generated proof will not be made public for now.
The DecoderSelected
OpenAI asks external experts to verify proofs generated by its AI in mathematics, computer science, and physics
OpenAI says its internal models produced proofs in three fields—mathematics, computer science, and physics—including refuting the Exponential Time Hypothesis (ETH) in computational complexity theory, proving that the local smoothing conjecture holds in all dimensions, and proving the existence of four-dimensional quantum field theory. The company has translated the mathematics and computer science proofs into Lean and asked external experts to serve as independent verification shepherds, with the physics portion handled by a team led by David Gross, winner of the 2004 Nobel Prize in Physics. OpenAI says it does not claim authorship of scientific discoveries and has committed to releasing the raw data and investing $5 million in the Simons Foundation to fund related workshops.
MIT Tech Review
Anthropic Files IPO Prospectus, MIT Tech Review Roundup of the Day's Tech News
Anthropic has filed its IPO prospectus, a document totaling 335 pages, of which about 100 pages focus on risks, and which disclosed safety failures and a training pause lasting one month. Concurrent headlines also include OpenAI announcing three new scientific discoveries in mathematics, computer science, and physics, and Microsoft offering buyout packages to about 60,000 employees while planning to invest $190 billion in AI this year.
36Kr · AI
OpenAI claims to have proven the mathematical existence of Yang-Mills field theory, filling in half of Yang Zhenning's regret from back then
OpenAI published a post claiming that its internal model proved the mathematical existence of Yang-Mills field theory in four-dimensional space, and also claimed to have solved the Kakeya conjecture and the Stein restriction conjecture, overturned the Exponential Time Hypothesis (ETH), and provided a mathematical existence proof for QCD and a grand unification completion containing all gauge fields and fermions of the Standard Model. The article sorts out the two remaining problems of Yang-Mills field theory, pointing out that OpenAI has only solved existence; the mass gap required by the Clay Mathematics Institute's Millennium Prize Problems has not been solved, gravity has not been included, and the physics-related materials have not been made public, with the conclusions not yet verified.
NumeramaSelected
OpenAI says its model proved the existence of Yang-Mills theory, but only five physicists can see it
On October 26, OpenAI said its internal model had produced a mathematical proof of the existence of four-dimensional Yang-Mills theory, covering the first of the two parts of the Millennium Prize Problem, but the proof has so far been given only to five physicists, including David Gross, for review. OpenAI said the proof has been verified in Lean, with verification completed on October 16, and that it concerns only Yang-Mills rather than QCD, and that Lean also does not guarantee that the formalized translation matches the physical formulation. The same batch of announcements also included a proof of the local smoothing conjecture in harmonic analysis and a refutation of the exponential time hypothesis; the Clay Institute said it will not award a prize for now, and that journal publication and two years of peer recognition are required first.
Numerama
OpenAI claims its AI has overturned the exponential time hypothesis; results await expert review
On October 26, 2026, OpenAI announced that its AI had overturned an important hypothesis in computer science, the exponential time hypothesis (ETH), which holds that the hardest cases such as 3-SAT cannot be solved by subexponential-time algorithms. OpenAI said the AI produced a refutation on October 16 and completed formalization in Lean the next day, and that the manuscript and formal proof have been published on GitHub. The results will be reviewed by experts including Russell Impagliazzo, Ramamohan Paturi and Ryan Williams, the first two of whom are the originators of the hypothesis; OpenAI also acknowledged that turning this result into practical improvements still requires further research.
ScienceNetSelected
OpenAI announces three AI-generated results in mathematics, computer science, and physics
OpenAI announced that its model has made new discoveries in three areas—harmonic analysis, complexity theory, and quantum field theory—concerning respectively the local smoothing conjecture and the Kakeya conjecture, the Exponential Time Hypothesis (ETH), and the existence of Yang–Mills theory. The mathematical proof was obtained as AI output on October 18 and formalized in Lean the next day, and will be made public on GitHub as recommended by experts; the ETH counterproof was generated on October 16 and verified in Lean. All three results await independent verification by the academic community; Russell Impagliazzo and others involved in the review said their participation should not be regarded as certification of the claim, and OpenAI has decided not to release the AI-generated output of the quantum field theory project for now.
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Latent SpaceSelected
Anthropic Files S-1 for IPO: $16.3 Billion in First-Half Revenue, $974 Million in Q2 Operating Profit
Anthropic publicly filed its S-1 on Monday, planning to list on Nasdaq under the ticker ANT, with revenue growing from $41 million in 2023 to $16.3 billion in the first half of 2026, including $11.6 billion in Q2 alone, up 1368% year over year. Q2 operating profit was $974 million, first-half operating cash flow was positive at $3.9 billion, while the $80.7 billion net loss mainly came from $81.1 billion in non-cash financial instrument expenses. About 48% of first-half revenue (roughly $7.8 billion) flowed through Bedrock, Vertex, and Azure Marketplace; the S-1 also disclosed that pretraining of a frontier model was recently delayed, and listed NVIDIA compute commitments of up to $120.5 billion.
Phoenix TechnologySelected
OpenAI says its model disproved ETH and proved the local smoothing conjecture in all dimensions
OpenAI announced that its internal models achieved results in three fields—mathematics, computer science, and physics—including disproving the Exponential Time Hypothesis (ETH), which had been used in theoretical computer science for nearly 30 years, proving the local smoothing conjecture in all dimensions, and establishing a rigorous existence proof for a four-dimensional quantum field theory involving quantum chromodynamics. The ETH portion produced a subexponential-time algorithm of the form 2^{O(n/√log n)}, and on October 16 generated a natural-language counterproof, completing Lean formalization the next day. OpenAI invited Impagliazzo and Paturi, the original proposers of ETH, along with MIT's Ryan Williams, to organize an independent review; for the physics portion, a working group led by David Gross first organized the materials.
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cnBetaSelected
OpenAI announces three mathematics and physics results, inviting external experts to lead interpretation
OpenAI announced three scientific results, concerning respectively a local smoothing conjecture in harmonic analysis, the refutation of the Exponential Time Hypothesis (ETH), and a proof of the existence of a four-dimensional quantum field theory containing gauge fields and fermions, among which the mathematics and physics results have been formalized in Lean. Regarding the release strategy, the computer science and physics results were interpreted by teams organized under the leadership of external experts, while the mathematics results were released directly as AI output for researchers to interpret themselves; OpenAI says it does not yet know which approach is most useful. The physics working group is led by David Gross, and the computer science working group is responsible for verification by Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams; OpenAI also put forward four principles: transparency, not seeking academic credit, acknowledging contributions, and independence.
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English text is being prepared.Selected
OpenAI announces AI model achieves three scientific breakthroughs, involving the local smoothing conjecture, ETH, and the existence of quantum field theory
OpenAI announced that its AI model has achieved three breakthroughs in the fields of mathematics, computer science, and physics. The mathematics and computer science results have been formally verified through Lean and the proof materials have been made public, while the physics results are being reviewed by experts including Nobel Prize laureates in physics. In mathematics, the model provided a proof of the local smoothing conjecture in all dimensions, and thereby resolved the Kakeya conjecture and the Stein restriction conjecture in all dimensions; in computer science, the model provided a proof that the Exponential Time Hypothesis (ETH) is false. OpenAI has invited external experts to lead the verification and interpretation of the results, and has uploaded the natural-language proofs and Lean proofs to a public GitHub repository.
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The PaperSelected
OpenAI Announces Three New Discoveries in Mathematics, Computer Science, and Physics, Including the Kakeya Conjecture and Yang–Mills Theory
OpenAI announced new discoveries in three directions—harmonic analysis, complexity theory, and quantum field theory—claiming that its model proved the local smoothing conjecture and thereby solved the Kakeya conjecture and the Stein restriction conjecture in all dimensions, also provided a counterproof that the Exponential Time Hypothesis (ETH) is false, and rigorously proved a four-dimensional interacting quantum field theory containing gauge fields and fermions. All three results await independent verification by the academic community; the mathematics and computer science results have been made public on GitHub per expert recommendations, while the physics result will not have AI-generated artifacts released for now due to the opinions of the external expert team.
Phoenix TechnologySelected
OpenAI Says AI Solved the Kakeya Conjecture in One Shot, Disproved ETH, and Proved the Existence of Yang-Mills
OpenAI announced that its model achieved three mathematical and theoretical physics breakthroughs in one shot: proving the local smoothing conjecture in all dimensions, from which it follows that the Kakeya conjecture and the Stein restriction conjecture hold in all dimensions; proving that the Exponential Time Hypothesis (ETH) is false; and constructing existence proofs for quantum chromodynamics and Yang-Mills theory. The relevant proofs have been formalized using Lean and uploaded to a public GitHub repository. OpenAI has also invited external teams, including Russell Impagliazzo and Paturi, the original proposers of ETH, and Nobel laureate David Gross, to participate in the review, and is not seeking academic authorship.
Electronic Technology ApplicationSelected
OpenAI announces three breakthroughs by its model in mathematics, computer science, and physics
OpenAI announced that its AI model has achieved three breakthroughs in the fields of mathematics, computer science, and physics, claiming that the model can independently discover and prove complex scientific theories. The mathematics and computer science results have been formally verified through Lean, and the proof materials and natural-language proofs have been uploaded to a public GitHub repository; the physics result is being reviewed by experts including Nobel laureates in physics. In mathematics, the model provided a proof of the local smoothing conjecture in all dimensions, and thereby solved the Kakeya conjecture and the Stein restriction conjecture in all dimensions; in computer science, the model provided a proof that the Exponential Time Hypothesis (ETH) is false. OpenAI stated that the relevant results still require further independent confirmation by the academic community.
The Verge AISelected
OpenAI announces three discoveries in mathematics, computer science, and physics, and brings in external experts to vet them
OpenAI announced three "major" discoveries in mathematics, computer science, and physics. In computer science, it claims to have proven that ETH (the Exponential Time Hypothesis), long widely believed to be true, is in fact false, and the related AI output and Lean proof have been published on GitHub. The physics result has not yet been fully disclosed; OpenAI describes it as a rigorous existence proof for an interacting quantum field theory in four dimensions containing gauge fields and fermions, covering a unified completion of QCD and the Standard Model, and says David Gross and others will lead the vetting. In mathematics, its model produced a proof of the local smoothness conjecture in arbitrary dimensions, and thereby resolved the Kakeya conjecture and the Stein restriction conjecture in all dimensions; OpenAI also published an open letter soliciting opinions on how to test these conclusions.
Rohan PaulSelected
OpenAI claims AI produced proofs for multiple mathematics and complexity problems
Rohan Paul, relaying OpenAI's claims, said its AI proved that the Exponential Time Hypothesis (ETH) is false, an assumption that has underpinned related research for about 25 years. It also claims to have cracked the 35-year-old local smoothing conjecture and thereby solved the Kakeya conjecture, and in physics to have proven with full mathematical rigor that the foundations of quantum chromodynamics are sound, covering half of the $1 million Yang-Mills existence and mass gap Millennium Prize Problem.
Unite.AISelected
OpenAI Says Its Model Produced Results in Three Research Areas: Mathematics, Computer Science, and Physics
On October 26, 2026, OpenAI announced that its internal model had produced three research results in the fields of mathematics, computer science, and physics, including a counterexample to the long-standing Exponential Time Hypothesis (ETH) in computational complexity theory. In mathematics, the model provided a proof of the local smoothing conjecture in arbitrary dimensions, and thereby resolved the Kakeya conjecture and the Stein restriction conjecture; the output was obtained on October 18 and Lean formalization was completed the next day. The computer science result was verified by a group led by Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams, and OpenAI agreed to disclose all raw data and fund related conferences; the physics result provided a rigorous existence proof for a four-dimensional quantum field theory with gauge fields and interacting fermions, and also included a pure Yang–Mills existence proof, with the group led by David Gross deciding to temporarily not disclose the AI-produced materials and to write up the results themselves.
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