OpenAI Announces Three Major Discoveries in Math, CS, and Physics

OpenAI dropped a bombshell yesterday: three new AI-produced discoveries spanning harmonic analysis, computational complexity, and quantum field theory. All three were formalized in Lean, the proof assistant, before release. And in a notable shift from their previous approach, they partnered with academic experts before going public [1].

The announcement hit the top of Hacker News with over 700 points and 300 comments within hours. The related paper on the Exponential Time Hypothesis collected another 500. This is the kind of story that makes you stop and recalibrate your expectations for what AI can do [2].

The math: local smoothing and Kakeya in all dimensions

The first result concerns the local smoothing conjecture, proposed by Sogge in 1991. The conjecture deals with how waves behave when they become focused: the most extreme focusing must be short-lived, and the worst-case scenario is always more dramatic than what you observe after averaging over time. Because this phenomenon is so fundamental, the conjecture implies two other major open problems: the Kakeya conjecture and Stein's restriction conjecture [3].

Progress on this has been slow and hard. Guth, Wang, and Zhang proved the local smoothing conjecture in two dimensions in 2019. In 2025, Wang and Zahl proved the Kakeya conjecture in three dimensions, a result significant enough to earn Wang a Fields Medal. Now OpenAI's models have produced a proof of the local smoothing conjecture in every dimension, which simultaneously resolves the Kakeya conjecture and Stein's restriction conjecture in all dimensions. The proof uses a novel auxiliary partial differential equation [4].

The AI output was produced on October 18, 2026, formalized in Lean the next day, and released publicly on GitHub along with the Lean proof. For this result, OpenAI followed the same strategy as their October 6 release: just put the AI output out there and let researchers organize themselves [5].

The computer science: ETH is false

The second result is the one that got the most attention on Hacker News, and for good reason. The Exponential Time Hypothesis (ETH) is a longstanding conjecture in computational complexity theory, proposed by Impagliazzo, Paturi, and Zane in 1999. It states that there is no subexponential-time algorithm for solving k-SAT (Boolean formula satisfiability where each clause has at most k literals). ETH has been widely believed to be true and has been used in hundreds of papers to derive conditional hardness results across graph theory, computational biology, databases, computational geometry, and many other fields [6].

OpenAI's system proved that ETH is false. The algorithm it produces runs in time roughly 2 to the power of n divided by the square root of log n, which is subexponential but still superpolynomial. This does not mean P equals NP. But it does mean that a boundary that researchers treated as a wall is actually permeable, and hundreds of hardness results that assumed ETH now need to be reexamined [7].

The disproof was found on October 16, formalized in Lean on October 17, and released publicly. OpenAI has formed a collaboration led by Russell Impagliazzo and Ramamohan Paturi, the original proposers of ETH, and Ryan Williams, who has previously refuted strong versions of ETH. The group requested that all raw data be made public for independent verification, and that OpenAI fund a conference to understand the implications. Both requests were accepted [8].

As one Hacker News commenter put it: "2026 is weird." Another, who had taken a graduate complexity course, recalled spending time philosophizing about ETH with their professor. "I am very chuffed to see this result" [9].

The physics: Yang-Mills existence and QCD

The third result is the most ambitious. OpenAI's models produced a mathematically rigorous existence proof for 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. As a subproblem, this includes a proof of the existence of pure Yang-Mills theory, which is part of the Clay Mathematics Institute Millennium Prize problem [10].

The Standard Model describes three of the four fundamental forces, excluding gravity. QCD describes the strong force, the interactions of quarks and gluons. Pure Yang-Mills theory describes only the self-interactions of gluons. The existence of these theories as mathematically rigorous objects has been a major open problem for decades [11].

The AI produced a natural language proof for Yang-Mills existence on September 9, 2026, and a proof for QCD on September 18. Given the length and complexity, OpenAI postponed release until the Lean formalization of Yang-Mills existence was completed on October 16 [12].

For this result, the physics collaboration group has chosen to hold back the AI-produced artifacts and write it up themselves. The group is led by David Gross, who won the 2004 Nobel Prize for his work on asymptotic freedom in Yang-Mills theories, and includes Michael Douglas, Arthur Jaffe (who formulated the Millennium Prize problem with Witten), Igor Klebanov, and Nikita Nekrasov [13].

A new release process

What makes this announcement different from OpenAI's previous math drops is the collaboration framework. After backlash from the math community over their last release, OpenAI is now experimenting with three different strategies: release AI output directly and let researchers self-organize (math), form an external group while making everything public (CS), and defer to external experts on release timing (physics) [14].

The collaborations follow four principles: transparency (no NDAs), no academic credit for OpenAI, recognition for the working groups, and independence. Participants are unpaid and their conclusions are their own. OpenAI has also committed to a $5 million contribution to the Simons Foundation to support workshops and conferences for researchers navigating AI-generated results [15].

The approach is not without criticism. On Hacker News, some commenters noted that choosing initial shepherds creates asymmetry of information, and that the physics group, which keeps results private, could disadvantage researchers working on adjacent problems. Others pointed out that this is still fundamentally a publicity strategy, even if a more responsible one [16].

Why this matters

Three results, three fields, all formalized in Lean before release. The ETH disproof alone would be a major story. A proof of the Kakeya conjecture in all dimensions, coming just a year after the three-dimensional case won a Fields Medal, is staggering. And an existence proof for Yang-Mills and QCD touches a Millennium Prize problem [17].

The question of whether AI is "doing real mathematics" or "parasitically remixing human work" is going to get a lot louder. But the formalization in Lean matters here: these are not plausible-sounding arguments that might have subtle errors. They are machine-checked proofs. The mathematical content is verified, even if the human understanding of why they work is still catching up [18].

For the ETH specifically, the practical implications are unclear but potentially significant. The algorithm OpenAI found runs in subexponential time, which is better than exponential but not polynomial. Finding actual faster algorithms for the problems that were assumed hard under ETH will require more work. But the door is now open, and hundreds of complexity results that leaned on ETH as an assumption need footnotes [19].

As one commenter on Hacker News noted: "It is amazing what you can accomplish if you do not care who gets the credit." Whether OpenAI truly does not care about credit remains to be seen. But the structure of this release, with external experts shepherding the work and OpenAI explicitly disclaiming academic credit, is a meaningful shift [20].