Meta’s Muse Spark Helps Solve Five Open Math Problems
3 min readMeta AI says its Muse Spark model has helped mathematicians settle five previously open research problems, with the results published this week in six co-authored papers. The work was done through the regular meta.ai chat interface in Thinking Mode, with no custom research scaffold. It is one of the clearest demonstrations yet that frontier AI can contribute to original mathematics, not just competition problems with known answers.
From Olympiad gold to open questions
Earlier this year Meta’s models reached gold-medal-level performance across five high-school Olympiad competitions in mathematics, physics, and chemistry. Those contests are hard, but every problem has an answer key. Open research is a different kind of challenge. There is no guarantee an approach will work, and progress means trying ideas, failing, and starting over.
Meta spent several months partnering with working mathematicians to test whether Muse Spark 1.1 and 1.2 could help on that harder terrain. The researchers guided the work, a second group of mathematicians reviewed it, and each paper marks which passages were drafted by people and which by the AI.
What the papers solved
The five resolved problems span probability, differential equations, group theory, optimization, and non-associative algebra, according to Meta AI Research. One paper pins down the exact threshold for fitting random high-dimensional points to an ellipsoid. Another proves that certain symmetric, negative-energy waves in a laser-physics model must collapse in finite time, settling a question left open since 2015.
Two of the results are counterexamples. Muse Spark generated a search program that found a 384-element group disproving a 2024 conjecture by M. Kida, and it produced a small three-dimensional example that knocks down a proposed classification test for evolution algebras. A sixth paper connects number theory and p-adic string theory along a path first sketched by Yuri Manin in the 1980s.
Meta also acknowledged that other teams independently announced solutions to some of the same problems using different methods, including an AI agent called Nilradical that reported a separate counterexample to the Kida conjecture in September.
Why it matters
The Muse Spark math results arrive in a week dominated by AI safety worries, from OpenAI shelving a model to the FTC opening a probe into rogue agents. They are a reminder of the other side of the ledger: the same systems are starting to produce verifiable scientific knowledge. Anthropic separately described a Claude-led discovery of a possible new gene-editing mechanism, and mathematicians formalized the Poincaré conjecture proof in Lean in two weeks.
The important detail is the workflow. Humans picked the problems, steered the arguments, and checked every proof, while the model did the heavy lifting on calculations, candidate proofs, and search code. Expect more labs to publish under similar rules, and expect the question of how to credit AI contributions in peer-reviewed mathematics to get louder.
For now, Meta’s six papers set a useful bar: transparent attribution, independent review, and results other researchers can build on.