OpenAI claims three major scientific breakthroughs, from mathematics to quantum physics

OpenAI claims to have solved three major problems in mathematics, theoretical computer science, and physics. Independent researchers are reviewing the proofs.

Three longstanding scientific problems may have found answers through artificial intelligence. OpenAI says its internal models have produced a proof of the local smoothing conjecture, refuted a foundational hypothesis in theoretical computer science, and established mathematical existence results for certain four-dimensional quantum field theories, including quantum chromodynamics. Two of the results have already been formalized in Lean, a language that allows computers to check mathematical proofs.

The significance of these claims requires an important distinction. The proofs were generated by OpenAI's internal models, and their scientific implications remain subject to independent examination. OpenAI describes the manuscripts as research materials that require further interpretation rather than findings whose full significance has already been established. A 35-year-old conjecture in harmonic analysis

The first result concerns harmonic analysis, a branch of mathematics that studies waves, frequencies, and their propagation.

In 1991, mathematician Christopher Sogge formulated the local smoothing conjecture, which addresses how waves can become concentrated. The conjecture predicts that exceptionally strong concentration should be short-lived. Averaging the behavior of a wave over time should reveal a smoother pattern than examining its most extreme moments.

The question has implications beyond wave propagation. Establishing the conjecture would also have consequences for the Kakeya conjecture and Stein's restriction conjecture, two important problems in mathematical analysis.

Researchers had already achieved significant progress. In 2019, Larry Guth, Hong Wang, and Ruixiang Zhang proved the local smoothing conjecture in two spatial dimensions. In 2025, Hong Wang and Joshua Zahl resolved the Kakeya conjecture in three dimensions.

OpenAI now claims its models have produced a proof of local smoothing across all relevant spatial dimensions, using a novel auxiliary partial differential equation. If the argument withstands scrutiny, it would also establish the corresponding results for Kakeya and Stein's restriction conjecture.

According to OpenAI's research announcement, its models produced the result on October 18, 2026, followed by a Lean formalization the next day.

The company has released the natural-language proof and its formalized counterpart publicly, allowing mathematicians to examine the reasoning and develop their own explanations. A fundamental complexity hypothesis may be false

The second claim concerns one of theoretical computer science's central questions: how much computation is inherently required to solve certain problems?

The Exponential Time Hypothesis, or ETH, proposes that solving particular Boolean satisfiability problems, including 3-SAT, requires exponential time in the worst case. Developed in the late 1990s by Russell Impagliazzo, Ramamohan Paturi, and Francis Zane, it has informed hundreds of conditional hardness results.

The hypothesis appears across fields including graph theory, computational geometry, databases, and computational biology. Its refutation would force researchers to reconsider some widely accepted assumptions about computational difficulty.

OpenAI reports that its models generated a disproof of ETH that was subsequently formalized in Lean. Additional descriptions of the research indicate that the argument involves a deterministic algorithm capable of exactly counting satisfying assignments of certain Boolean formulas in subexponential time.

That does not establish P = NP, nor does it mean that computationally difficult problems will suddenly become easy in practical applications. An asymptotic improvement can remain computationally expensive for realistic input sizes, and its implications depend on the exact mathematical result.

The natural-language argument was generated on October 16, and its Lean formalization followed on October 17.

An external group led by Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams, researchers at UC San Diego and MIT, will coordinate the examination and explanation of the work.

Impagliazzo and Paturi were among the original proponents of ETH, making their involvement particularly significant. However, their participation is not an endorsement of the result. The researchers have explicitly called for careful, open, and independent scrutiny.

OpenAI has agreed to release the underlying materials needed for verification and to fund a conference examining the work's implications. Quantum chromodynamics and the mathematics of fundamental forces

The third claim concerns quantum field theory, the mathematical framework used to describe interactions between elementary particles.

Quantum chromodynamics, or QCD, describes the strong interaction that binds quarks inside protons and neutrons through gluons. Although QCD is central to modern particle physics and supported by extensive experimental evidence, establishing a mathematically rigorous construction of the theory in four dimensions has remained exceptionally challenging.

OpenAI claims its models have developed existence proofs for certain interacting quantum field theories containing gauge fields and fermions. These include QCD and a unified extension of the Standard Model.

The research reportedly builds on physicist Tadeusz Balaban's methods in constructive quantum field theory. According to OpenAI, it also includes an existence proof for pure Yang–Mills theory, which describes gauge-field interactions without matter fields.

That result intersects with the famous Yang–Mills existence and mass gap problem, one of the Clay Mathematics Institute's Millennium Prize Problems.

An existence proof alone should not be confused with a complete solution to the Millennium Prize Problem, which also requires proving a positive mass gap.

OpenAI says its models produced a natural-language existence proof for Yang–Mills on September 9, followed by a result involving QCD on September 18. The Lean