Muse Spark has co-authored six mathematics papers with researchers: Meta claims to have solved five open problems

Probability, wave equations, group theory: Meta has published six articles written using its Muse Spark model, which is used in Meta AI’s simple chat interface.

Meta published on October 2 six mathematical research papers produced by mathematicians working with Muse Spark 1.1 and 1.2 in "Thinking" mode, from Meta AI's consumer chat interface and not a bespoke search system. The areas covered range from probability to optimization, partial differential equations, group theory, arithmetic physics and evolutionary algebras. According to Meta, five of the six texts answer previously open questions.

Concrete results

Aykut Arslan identifies a net threshold, around n = d²/4, beyond which high-dimensional random Gaussian points can no longer be placed on the same centered ellipsoid. Leonard Dinh demonstrates the explosion in finite time of a class of radial solutions of a wave equation, a question left unanswered since 2015. In group theory, GAP research code written by the model unearthed a group of 384 items that refutes a 2024 conjecture about semi-abelian groups. The researchers chose the problems, guided the model, corrected its errors, and took responsibility for the proofs; each paper points out passages written mostly by AI.

The picture is less clear than it seems: other teams have announced solutions to some of these same problems, including a counterexample in group theory found by the agent Nilradical in mid-September. Meta also gives no indication of the cost, the number of attempts or the failure rate: six documented articles do not say how often the model produces valid research.