OpenAI has posted hundreds of solutions and progress toward 372 major math problems in a release of 722 manuscripts on GitHub, the company announced. The breakthroughs of an undisclosed ChatGPT pioneering model, confirmed by OpenAI’s new advisory group, are likely to expand the Navier-Stokes AI controversy that is sweeping the mathematical community.
The results were expected, as OpenAI said last month that its models had “solved more than 100 long-standing open problems in most areas of mathematics.” As part of the release, OpenAI includes the rationale of the model, calculated estimates and information on the number of problems attempted. The company said that the “average result” requires about three hours of ChatGPT Pro use.
OpenAI said it followed guidelines for publishing the work, as recommended by its independent Advisory Group on Mathematics and Artificial Intelligence (AGMAI). These include prompt publication of results through traditional academic channels, plus details such as the name of the model used, queries and computational costs.
“For this publication, we publish the results in a GitHub repository, with protocols for paper versions and citations,” the company wrote. “We continue to explore other community-hosted alternatives for this publication that meet the committee’s guidelines. For future publications, we are committed to further improving the quality of papers regarding citations, mathematical exposition and presentation of results for better understanding.”
However, OpenAI ignored some of the board’s suggestions. The company hasn’t released specific computing times for problems or what queries it uses.
Some of the key results claimed by OpenAI are a solution to the four-dimensional Kakeya conjecture, along with improvements to key computer algorithms and progress towards the hyper-challenging Riemann hypothesis. Almost every paper was produced in response to a single query to a single AI agent, OpenAI said Scientific Americans.
The results still need to be evaluated by mathematicians before their impact can be understood. And after the Navier-Stokes imbroglio (read more about it here) there is still a lot of skepticism among scientists. “Until and unless they publish the model and people can replicate their results, I think you should treat any claims about one-shooting problems with a single agent as unverified,” said MIT mathematician Andrew Sutherland SciAm.