The company released purported solutions to long-standing conjectures in harmonic analysis and complexity theory, while holding back physics proofs for expert review.
OpenAI announced on Monday that its artificial intelligence systems have produced major scientific breakthroughs across mathematics, computer science and physics, according to Al Jazeera. The San Francisco-based company said its models resolved long-standing questions in harmonic analysis and computational complexity, while also formulating an existence proof in quantum field theory.
Three scientific claims
In mathematics, the company reported that an AI system established Sogge’s local smoothing conjecture for Euclidean wave equations across every spatial dimension of at least two, The Verge reported. Researchers in harmonic analysis, which analyzes how complex signals break down into elementary waves, had previously proven the conjecture only in three dimensions. OpenAI said the solution also resolves the Kakeya maximal and dimension conjectures, as well as Stein’s spherical restriction estimates across the interior of the conjectured range. Just months earlier, New York University professor Hong Wang won a Fields Medal from the International Mathematical Union for resolving the Kakeya conjecture in three dimensions.
University of Rochester mathematics professor Alex Iosevich, who specializes in harmonic analysis, said the model appeared to have cracked the conjecture. ‘The conjecture was formulated by my PhD adviser, Chris Sogge, so it is near and dear to my heart, and the news was a shock at first,’ Iosevich said. He added that while he felt a twinge of sadness over how theoretical mathematics will change, he expects the scientific enterprise to make giant leaps forward as pure mathematics problems are explored rapidly alongside their physical connections.
In computer science, OpenAI claimed its models disproved the Exponential Time Hypothesis, which concerns how long it takes to solve complex computational problems. The company published a deterministic algorithm that counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space, with the 3-SAT problem refuting the hypothesis. The hypothesis was originally proposed in 1999 by a group that included University of California, San Diego researchers Russell Impagliazzo and Ramamohan Paturi. Both researchers, along with Massachusetts Institute of Technology professor Ryan Williams, formed an independent working group to evaluate and explain the results.
The physics finding, which has not been published in full, claims a mathematically rigorous existence proof for interacting quantum field theories with gauge fields and fermions in four dimensions. The work includes Quantum Chromodynamics, the study of how quarks and gluons interact, alongside a unified completion of the Standard Model of particle physics.
Expert review and release disputes
To handle the findings, OpenAI selected external specialists, referred to as shepherds, to guide the results. The math and computer science teams chose to release the AI-generated data and Lean-formalized proofs on GitHub immediately so other scientists can examine them. In contrast, the physics group, led by David Gross alongside Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov, chose to hold back their full findings while writing up their own interpretation.
The practice of giving select researchers early access has drawn pushback. A panel of mathematical advisers assembled by OpenAI stated that ‘we recommend that AI companies do not adopt’ the practice of choosing specific individuals to inspect results first. The advisers warned that the approach creates unequal access, relies on borrowed reputation and introduces bias. They urged AI labs instead to post outputs directly to academic repositories alongside Lean-formalized proofs, information on how problems were selected, and funding for researchers who analyze the findings.
The computer science group issued an open letter asking the research community how early access should work, how credit should be assigned between AI models and human verifiers, and how academic institutions should support students as research methods shift. OpenAI, valued at $852 billion, acknowledged that picking shepherds creates information asymmetry and invited feedback on widening participation.
Growing claims of AI discovery
The announcements mark the latest push by AI companies into scientific research. Less than a month earlier, OpenAI made a mass release of hundreds of manuscripts containing purported solutions to mathematical problems. Other competitors have made similar moves. Last month, Anthropic said its AI systems discovered an enzyme resembling the gene-editing mechanism CRISPR, though scientists offered mixed reactions, with several questioning whether the company had overstated its importance.
Independent researchers are now working to evaluate OpenAI’s code and mathematical proofs.
