OpenAI models verify 30-year math conjecture and disprove complexity theory assumption

OpenAI announced on Monday that its AI models solved a mathematical problem that has eluded researchers for three decades and disproved a core assumption in computer science. The company stated that the models achieved these results across three distinct scientific fields: harmonic analysis, complexity theory, and quantum field theory.

The first finding involves the local smoothing conjecture, a central proposition in harmonic analysis. OpenAI reported that its models proved this conjecture in every spatial dimension for the first time. Prior to this announcement, researchers in the field had only been able to prove the theory in three dimensions. Harmonic analysis is a branch of mathematics that examines how complex signals and functions can be decomposed into elementary waves.

Alex Iosevich, a mathematics professor at the University of Rochester who specializes in harmonic analysis, described the development as historic. He noted that the conjecture was formulated by his doctoral advisor, Chris Sogge. Iosevich told Al Jazeera that the news was initially a shock. He said, “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.” Iosevich also expressed a twinge of sadness, expecting theoretical mathematics to change drastically due to AI influence.

In computer science, OpenAI stated that its models disproved the Exponential Time Hypothesis. This hypothesis relates to the time required to solve complex computational problems. The company further claimed that its models provided mathematically rigorous proof of the existence of quantum chromodynamics. This branch of physics studies the interaction of quarks and gluons.

OpenAI said it reached out to external scientists to transform its raw research data into scientific understanding. The company consulted with three expert groups, which it designated as shepherds, to determine how to release the findings. The groups collaborating on the mathematics and computer science problems chose to make the AI-produced data public immediately. In contrast, the physics group decided to defer the release to write their own interpretation of the findings first.

The company acknowledged that these different release strategies involve tradeoffs. OpenAI stated that the collaborations empower experts to unpack the results and contextualize them in the academic community. However, the company noted that choosing initial shepherds shapes who gets involved first and creates an asymmetry of information. The $852 billion startup added that it welcomes feedback on how to broaden participation and make the process more useful.

This announcement follows a series of claimed scientific breakthroughs credited to AI. Last month, Anthropic, the creator of Claude, announced the discovery of a new enzyme. Anthropic said the enzyme resembles CRISPR, a gene editing mechanism used to treat conditions such as cancer and sickle cell disease. Scientists responded to the Anthropic news with mixed reactions. Some researchers hailed the finding as an exciting development, while others suggested the company exaggerated its significance.