OpenAI Claims Proofs in Math and Physics That Stumped Humans for Decades

The intersection of artificial intelligence and fundamental science has produced a series of high-profile claims in recent months, shifting the debate from algorithmic capability to specific mathematical and physical results. On Monday, OpenAI announced that its models have generated three distinct scientific discoveries spanning mathematics, computer science, and physics.

The central claim involves the local smoothing conjecture, a proposition within harmonic analysis that has eluded a general proof for approximately 30 years. OpenAI stated that its models proved the conjecture holds in every spatial dimension. Prior to this announcement, researchers in the field had only successfully demonstrated the theory in three dimensions. Harmonic analysis is a branch of mathematics dedicated to decomposing complex signals and functions into elementary waves.

Alex Iosevich, a mathematics professor at the University of Rochester specializing in harmonic analysis, described the development as "historic." He noted that the conjecture was originally formulated by his PhD adviser, Chris Sogge. "It is near and dear to my heart, and the news was a shock at first," Iosevich said. He added that he is now "filled with joy and optimism," citing the potential for the scientific enterprise to make "giant leaps" as a result of the AI revolution.

Iosevich expressed that he expected the field of theoretical mathematics to "change drastically." While he acknowledged a "twinge of sadness" shared by many theoretical mathematicians, he argued that these feelings would soon give way to the realization of new capabilities. "Problems in pure mathematics did not arise in a vacuum," he said. "Many of them came out of concrete physical considerations, and these connections can now be explored rapidly and decisively."

Beyond harmonic analysis, OpenAI said its models disproved the Exponential Time Hypothesis. This hypothesis relates to the time required to solve complex computational problems. The company also claimed to have provided "mathematically rigorous [proof of the] existence" of quantum chromodynamics, a theory that studies the interaction of quarks and gluons.

OpenAI stated it reached out to external scientists to translate its "raw research data into scientific understanding." The San Francisco-based company consulted with three expert groups, which it termed "shepherds," to determine how to release the findings. The groups handling the mathematics and computer science problems opted to make the AI-produced data public immediately. Conversely, the physics group decided to defer the release to allow time for them to write their own interpretation of the findings.

The company, which is valued at $852 billion, acknowledged that these different release strategies involve tradeoffs. "On the one hand, the collaborations empower experts to foster unpacking the results and contextualizing them in the broader academic community," OpenAI said. "On the other hand, choosing initial shepherds necessarily shapes who gets involved first and creates asymmetry of information. We welcome feedback on how to broaden participation and make this process more useful."

This announcement follows a similar claim made last month by Anthropic, the creator of Claude. Anthropic announced the discovery of a new enzyme that it said resembles CRISPR, a gene-editing mechanism used in treating conditions such as cancer and sickle cell disease. That announcement received mixed reactions from the scientific community, with some researchers praising the finding and others suggesting the company had exaggerated its significance.