Meta says it wanted to see whether its AI model could help with open research math, not just contest problems. On Friday, Oct. 2, the company published six math papers written by mathematicians working with its Muse Spark model, and says five present answers to previously open research questions. Two of the papers disprove conjectures other mathematicians had proposed. Meta says this is a different kind of test from its earlier gold-medal-level results on high-school Olympiad competitions, since contest problems already have a known solution and open problems do not.
Meta says the mathematicians used Muse Spark 1.1 and 1.2 in Thinking Mode through the regular meta.ai chat interface, with no custom research setup. Meta says a team of mathematicians guided the research and a second group reviewed it, though its post names no reviewers for one of the six papers. Each paper marks which passages researchers drafted and which the AI drafted.
The model's role varied. In a group theory paper, Muse Spark wrote the search program that found a group with 384 elements that breaks a conjecture by mathematician M. Kida, Meta says. In a paper linking number theory and a version of string theory, Meta says, it drafted three core technical sections that the researchers then checked and corrected. Other papers cover random data fitting, when a wave equation must collapse, an optimization problem, and a type of algebra inspired by evolutionary biology. The data fitting paper leaves open what happens exactly at the cutoff it finds.
At least two of the results were not first. Meta says it learned after finishing that outside teams had independently announced solutions to some of the same problems. Theodor Misiakiewicz and Garrett G. Wen posted a proof of the same data fitting result, the point past which random points almost certainly can't all be fitted to an ellipsoid, on Aug. 10, one of three outside papers from August that Meta acknowledges. An AI agent called Nilradical reported a different counterexample to Kida's conjecture on Sept. 16, and Meta says researchers Hu and Wen separately reported counterexamples to the conjecture in the evolution algebra paper; Meta's post does not say when.
It is not yet known how many problems the mathematicians tried with Muse Spark without success, or whether the papers will go through journal peer review. The reviewers are part of Meta's collaboration, and Meta's post does not say whether the papers have been submitted to journals.