OpenAI Models Prove Long-Standing Math Conjecture in All Dimensions

OpenAI announced on Monday that its artificial intelligence models have generated new scientific results in mathematics, computer science, and physics. The release marks a shift in how major AI companies present their technical capabilities to the public and academic communities.

The most detailed result involves harmonic analysis, a branch of mathematics that studies how complex signals break down into elementary waves. The AI models proved the local smoothing conjecture in every spatial dimension. Researchers had previously managed to prove this specific theory only in three dimensions, leaving higher dimensions unresolved for decades.

Alex Iosevich, a mathematics professor at the University of Rochester, confirmed that the AI appeared to have cracked the conjecture. Iosevich noted that the conjecture was formulated by his PhD adviser, Chris Sogge, making the result personally significant to him. He described the initial news as a shock before expressing joy and optimism about the potential of the AI revolution to drive scientific progress.

Iosevich stated that he expects theoretical mathematics to change drastically due to these new tools. He acknowledged a twinge of sadness for theoretical mathematicians but believes those feelings will give way to the realization of what can now be accomplished. He added that many problems in pure mathematics originated from concrete physical considerations, connections that can now be explored rapidly and decisively.

Beyond mathematics, OpenAI said its models disproved the Exponential Time Hypothesis. This hypothesis relates to the time required to solve complex computational problems. The company also reported that its systems provided mathematically rigorous proof of the existence of quantum chromodynamics, a field that studies the interaction of quarks and gluons.

OpenAI stated it reached out to scientists outside the company to transform raw research data into scientific understanding. The San Francisco-based company consulted with three expert groups acting as shepherds to determine how to release the findings. The groups handling mathematics and computer science opted to publish the data immediately. The physics group chose to defer the release to write up their own interpretation of the results.

The $852 billion start-up acknowledged that different release methods involve tradeoffs. OpenAI said the collaborations empower experts to contextualize the results within the academic community. However, the company noted that choosing initial shepherds shapes who gets involved first and creates information asymmetry. The company said it welcomes feedback on how to broaden participation in this process.

This announcement follows a similar claim by Anthropic last month. The Claude creator announced the discovery of a new enzyme resembling CRISPR, a gene-editing mechanism used in treating conditions like cancer and sickle cell disease. That release drew mixed reactions from scientists, with some praising the development and others suggesting the company had exaggerated its significance.