On October 2, 2026, Meta's research team published "Solving Open Research Problems Together," a post introducing six mathematics papers produced by researchers working with Muse Spark 1.1 and 1.2 in Thinking Mode. Meta says five of the six answer questions that were previously open.
The detail that makes this more than another benchmark claim is how the work was done. Meta says the researchers used the model through the standard meta.ai chat interface, with no custom research system or scaffolding. Mathematicians chose the problems, steered the exploration and checked the arguments; a separate group of mathematicians then reviewed the results. Meta writes that "each paper clearly marks which passages were primarily drafted by researchers and which were drafted by AI."
The six papers, by field, as Meta and Runtime Wire describe them:
- Probability: a sharp threshold for when random Gaussian points can be fitted by an ellipsoid.
- Differential equations: finite-time blow-up for negative-energy radial solutions of the mass-critical biharmonic nonlinear Schrödinger equation.
- Group theory: a counterexample showing that semiabelian groups need not be monomial. Runtime Wire reports the counterexample was found with GAP search code that Muse Spark wrote and the researchers then checked and completed.
- Optimization: a proof that a cycle-based relaxation is exact for a class of length-three cycle problems.
- Arithmetic physics: a result relating a string-theory two-point function to a height function on a curve.
- Non-associative algebra: a disproof of a published conjecture about solvable evolution algebras.
How people are using the model, in practice. The workflow is closer to a senior collaborator than an autonomous prover: a mathematician frames the question, the model proposes approaches, writes candidate arguments and search code, and the human decides what to keep and verifies it. The data touched is only what the researcher pastes in or the model already knows; the expensive part is human checking time.
The caveats Meta itself states. Independent teams reached some of the same results by different routes around the same time, including Gaussian ellipsoid-fitting work from August 2026 and a separate group-theory counterexample attributed to an AI agent called Nilradical on September 16. "Review" here means Meta's own panel of mathematicians, not journal peer review, and none of the six papers is reported as accepted by a journal yet.
Analysis: the useful finding for anyone outside mathematics is the interface. If an off-the-shelf chat product, with an expert in the loop, can contribute to publishable results, then the main constraint on research use is evaluation, not tooling: someone qualified has to check every step, and the papers' marking of AI-drafted passages is a practice worth copying in any team that publishes or ships model-assisted work. The concurrent independent results cut both ways -- they suggest these problems were within reach of current methods, and they mean "first" claims in AI-assisted research will need careful dating.
Meta's six Muse Spark math papers, five of which it says resolve open questions, were produced through the ordinary chat app with mathematicians directing and verifying the work and AI-drafted passages marked -- a model for expert-in-the-loop research, with the caveat that some results were reached independently at the same time and none is yet journal-reviewed.