Meta AI Research published six mathematics papers on October 2 in which its Muse Spark model helped human authors produce proofs, and Meta describes five of the six as answers to questions that were previously open. The post does not say that any of the six has been peer reviewed by a journal or checked by a mathematician outside the group Meta assembled. That gap decides how much weight the word “solved” can carry.
An open problem is simply a question nobody has answered yet. A competition problem has a known solution somewhere; an open one has no answer key, so a proof has to be built and then defended. According to Meta’s blog post, the mathematicians used Muse Spark 1.1 and 1.2 in Thinking Mode through the ordinary meta.ai chat window, without any special research tooling. Each paper pairs a named human author with the model, and Meta says every paper marks which passages people drafted and which the AI drafted.
The model’s role varies a lot from paper to paper. In two cases it produced counterexamples, which is the easiest kind of contribution to check because one concrete exception breaks a conjecture. Muse Spark wrote code for GAP, a software package for mathematics, and running it turned up a group with 384 elements that disproves a 2024 conjecture by M. Kida. The authors, Joseph Phillip Brennan and Milana Golich, say Golich and the people working with her checked that result and then completed the argument. In the other case, Andres Barei used the model to find a three-dimensional example that defeats a conjecture by García-Martínez and Pérez-Rodríguez about evolution algebras, then rewrote the surrounding material himself.
The proof-heavy papers lean harder on human judgment. On the ellipsoid question, which asks how many random points in a very high-dimensional space a single ellipsoid can pass through, Aykut Arslan steered the work while the model helped build and revise proof strategies. For a question about when waves in a laser-inspired model must collapse, Leonard Dinh chose the problem and the key ideas, and Meta says the model helped with calculations and revisions. Arslan also worked with the model on an optimization question, with Kien Trung Le checking the arguments. A sixth paper, by Anindya Dey, Gabriel Herczeg, An Huang, Nicolas Jaramillo Torres, and Jacob H. Swenberg, links number theory to string theory. Meta says the model drafted three of its core technical sections.
Review is where the claim is thinnest. Meta says a second group of mathematicians examined each team’s work, and the post names them. Some of them also appear elsewhere in the collaboration: Barei reviews the group theory paper, and Jaramillo Torres reviews Barei’s paper while co-authoring the string theory one. These are people Meta chose, working inside a project Meta runs, and this is the lab reporting on its own model’s results. Nothing in the post points to a referee who had no stake in the outcome.
The one outside signal is accidental. Meta says it learned, once its own work was finished, that teams outside the company had independently announced answers to overlapping problems. Three groups posted ellipsoid results in August 2026, including Misiakiewicz and Wen, who proved the same threshold. On September 16, an AI agent called Nilradical put forward its own, distinct counterexample against Kida’s conjecture, and Hu and Wen reported counterexamples against the evolution algebra conjecture. Those parallel results are not a review of Meta’s papers, but they suggest the questions were reachable by more than one route, and Meta credits them in the papers.
The post also leaves out how many problems were attempted in total. It reports six papers from several months of work, which says nothing about how many attempts produced nothing. A success rate would tell readers more than any single result does.
For anyone deciding how far to trust these papers, the counterexample results can be tested mechanically by outside mathematicians within days, while the longer proofs need journal referees. Until those referees report, treat all six as promising claims from an interested party.
Based on “Solving Open Research Problems Together,” published by Meta AI Research on its research blog on October 2, 2026.
