OpenAI’s AI has solved three longstanding problems in mathematics, computer science, and physics, according to reports from multiple outlets. The company claims its models proved the Local Smoothing Conjecture in all dimensions, disproved the Exponential Time Hypothesis, and provided mathematical evidence for 4D quantum field theories.
OpenAI’s artificial intelligence has achieved breakthroughs in three major scientific fields, according to multiple reports. The company announced that its AI models resolved decades-old challenges in mathematics, computer science, and physics, with independent verification from leading researchers.
AI Proves Theorem, Challenges Computational Assumption
In mathematics, OpenAI’s AI proved the Local Smoothing Conjecture, a problem that had remained unsolved since 1991. The conjecture relates to wave concentration phenomena and had only been proven in two dimensions prior to this development. The AI generated a proof that was formalized using the Lean theorem prover, according to Etnews.
The company also claimed to have disproven the Exponential Time Hypothesis (ETH), a foundational assumption in computer science that posits certain computational problems require exponential time to solve. This breakthrough could enable faster algorithms for complex calculations. Practical implementation would require further research, as noted by HANI.
An internal version of our next major model produced 10 new results on long-standing open problems in mathematics and theoretical computer science, using roughly $2,000 worth of tokens at GPT-5.6 Sol API rates. pic.twitter.com/4cgowmPOpY
Sam Altman spoke at the OpenAI DevDay 2026 event on October 29 in San Francisco, as reported by HANI. The AI model used a novel auxiliary partial differential equation to achieve the mathematical proofs, according to Etnews.
AI Provides Evidence for 4D Theories
In physics, OpenAI’s AI provided evidence for the mathematical existence of 4D quantum field theories, including a proof of the Yang-Mills existence and mass gap problem—a Millennium Prize problem. The work involved quantum chromodynamics (QCD) and was verified by Nobel laureate David Gross, along with other physicists, as reported by Etnews.
The company emphasized that the proofs would undergo independent review by a panel of experts, including ETH’s original proposers Russell Impagliazzo and Ramamohan Paturi, as well as MIT professor Ryan Williams. This verification process will determine the broader scientific impact of the findings, according to HANI.
The physics research also included contributions from Michael Douglas, Arthur Jaffe, and Igor Klebanov, as noted by Etnews. The team focused on unifying quantum chromodynamics and the Standard Model of particle physics. The AI generated formalized proofs using the Lean system.
Scientists Await Peer Review, Assess Impact
The scientific community awaits formal peer review, but the claims mark an important step in AI's role in advancing theoretical research. As HANI noted, If verified, these results could reshape fundamental understanding in multiple disciplines.
OpenAI’s AI-generated proofs for the Local Smoothing Conjecture, including the Kakeya and Stein restriction conjectures, were validated across all dimensions, according to Etnews. The company also addressed limitations, stating that while the ETH disproof opens new algorithmic possibilities, real-world performance improvements require additional study.
OpenAI just announced three AI-made discoveries in math, computer science and physics. Here's what you need to know.Dan Roberts of OpenAI posted it today. The three results cover harmonic analysis, complexity theory and quantum field theory. They come from OpenAI's internal… https://t.co/XdbnwVu7xI pic.twitter.com/MBRWnp6I2O
External researchers, including Nobel laureate David Gross, are conducting independent evaluations of the physics findings. The AI’s work on Yang-Mills theory and QCD was described as a “critical step” toward unifying quantum field theories, per Etnews. OpenAI has committed to transparency, with mathematical proofs and computational methods available for academic scrutiny.
More on Local Smoothing Conjecture
We are announcing three new discoveries in mathematics, computer science, and physics about harmonic analysis, complexity theory, and quantum field theory.https://t.co/9BX8HWQDTJ