OpenAI claims AI models solved 30-year math conjecture and disproved core theory

OpenAI announced on Monday that its artificial intelligence models have produced three distinct scientific breakthroughs across mathematics, computer science, and physics.

The company stated that its systems proved the local smoothing conjecture in every spatial dimension, a result that had remained unsolved for decades.

Harmonic analysis studies how complex signals decompose into elementary waves, and researchers had previously only established the theory in three dimensions.

Alex Iosevich, a mathematics professor at the University of Rochester who specializes in this field, described the development as historic.

Iosevich noted that the conjecture was originally formulated by his doctoral advisor, Chris Sogge, making the result personally resonant.

“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 he now feels joy and optimism regarding the impact of AI on the scientific enterprise.

“Now I am filled with joy and optimism, because the scientific enterprise as a whole is going to make giant leaps as a result of the AI revolution, and we have the chance to be a part of this historic development,” Iosevich said.

Iosevich acknowledged a sense of sadness among theoretical mathematicians regarding how the discipline may change.

“I feel a twinge of sadness as a result,” Iosevich said.

“Many theoretical mathematicians I know feel the same way, but I firmly believe that these feelings will soon give way to the realisation that there is so much we can now accomplish.”

Beyond the harmonic analysis proof, OpenAI reported that its models disproved the Exponential Time Hypothesis, a central assumption in computational complexity theory concerning the time required to solve complex problems. The company also said its models provided mathematically rigorous proof of the existence of quantum chromodynamics, the theory describing interactions between quarks and gluons. OpenAI, valued at 852 billion dollars, contacted scientists outside the company to convert raw research data into scientific understanding. The firm consulted three expert groups to determine how to release the findings. The groups working on mathematics and computer science chose to publish the data immediately. The physics group decided to delay the release to write their own interpretation of the results. OpenAI stated that these approaches involve tradeoffs, noting that initial collaboration shapes who gets involved first and creates asymmetry of information. The company said it welcomes feedback on how to broaden participation in the process. This announcement follows a similar claim last month by Anthropic, the creator of Claude, which reported the discovery of a new enzyme resembling CRISPR, a gene editing mechanism used to treat conditions such as cancer and sickle cell disease. Reactions to the Anthropic announcement were mixed, with some researchers calling the finding exciting while others suggested the company had exaggerated its significance.