OpenAI publishes findings on 377 mathematics problems

OpenAI has released findings on 377 mathematics problems, spanning areas including algebra, theoretical computer science and mathematical logic, prompting renewed discussion among mathematicians and AI researchers about how results from advanced proprietary models should be verified and shared. The company said the release was intended to be more responsive to concerns that AI could disrupt research. ¹²

Access and oversight

The Institute for Advanced Study, an independent group of mathematical experts in Princeton, New Jersey, said it does not support frontier AI laboratories using advanced mathematical questions to test proprietary models that are not available to the wider field. It warned that such arrangements could divide mathematics between laboratories with internal systems and other researchers. ¹

The institute said AI can generate mathematical arguments that the person using the system may not be able to comprehend, check or accept responsibility for. “We believe that human understanding of mathematics remains of paramount importance,” it said. ¹

OpenAI said it planned a collaboration with the Institute for Advanced Study that would involve mathematicians in deciding the way forward. An advisory board also asked AI laboratories to offer “equitable access” to the global mathematics community. ¹

Questions about the results

According to The Guardian, OpenAI published more than 370 results across algebra, theoretical computer science and mathematical logic. The New York Times described the release as findings on 377 problems and reported that the collection does not completely resolve any of the highly prestigious open questions. ¹²

The Guardian reported that OpenAI solved the Navier-Stokes equation last month, a problem for which a $1m reward had been offered. The dossier does not establish details of the result or its independent verification. ¹

Some experts have raised concerns, according to The Guardian, about whether OpenAI has conducted enough due diligence to assess its findings. Mathematicians who prompt a model may also provide information that contributes to a result, the report said. Tristan Buckmaster, a New York University mathematician working on the Navier-Stokes problem, said: “There’s likely to be a bunch of results where they take someone’s work and then take it to completion.” ¹

Continuing debate

The New York Times reported that an earlier OpenAI solution had angered mathematicians. OpenAI characterized the latest publication as a response to concerns over AI’s potential effect on research, but The Guardian reported that the company gave no indication it would cease testing advanced problems with its models. ¹²

The central issue is not only whether AI systems can produce results, but whether researchers across the field can understand, verify and gain access to the processes behind them. The Institute for Advanced Study said proprietary internal models could allow AI laboratories to move ahead of the broader discipline and leave the mathematical community disconnected from work in its own field. ¹