The new results are likely to expand AI controversy roiling the mathematics community.
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 from an unreleased ChatGPT pioneer model, confirmed by a OpenAI’s new advisory group, are likely to expand the Navier-Stokes AI controversy roiling the mathematical community.
The results were expected, as OpenAI said last month that its models had resolved “more than 100 long-standing open problems across most areas of mathematics.” As part of the release, OpenAI included the model’s reasoning, compute estimates and information about the number of problems attempted. The company said the “average result” required around three hours of ChatGPT Pro use.
OpenAI said it followed guidelines for release of the papers as recommended by its independent Advisory Group on Mathematics and Artificial Intelligence (AGMAI). Those included a prompt release of results through traditional academic channels, plus details like the name of the model used, prompts, and compute costs.
“For this release, we’re publishing the results in a GitHub repository, with protocols for paper revisions and citations,” the company wrote. “We’re continuing to explore other community-hosted alternatives for this release which meet the committee’s guidelines. For future releases, we are committed to further improving the quality of the papersthe results for better understanding.”
OpenAI did ignore some of board’s suggestions, though. The company didn’t release specific compute times for problems or which prompts it used.
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 toward the hyper-challenging Riemann hypothesis. Nearly every paper was produced in a response to a single prompt given to a single AI agent, OpenAI told <a href="https://www.scientificamerican.com/article/openai-unleashes-hundreds-more-math-results-upon-a-field-already-in-shock/” rel=”nofollow noopener” target=”_blank”>Scientific American.
The results still need to be assessed by mathematicians before their impact can be understood. And following the Navier-Stokes imbroglio (read more about that here) there is still a lot of skepticism among scientists. “Until and unless they release the model and people can replicate their results, I think you should treat any claims about one-shotting problems with a single agent as unverified,” MIT mathematician Andrew Sutherland told SciAm.
