The Pulse
Meta Says Muse Spark Helped Answer Five Open Math Questions
Meta says mathematicians working with Muse Spark produced six research papers, five of which answer previously open questions. The papers include a counterexample to a conjecture about evolution algebras, while another connects p-adic strin
AI.info Team ·
“We resolve an open question of Boulenger–Lenzmann.”
Leonard Dinh, author of the paper
Meta says its Muse Spark models helped mathematicians answer five previously open research questions, describing the work in six papers published October 2. Researchers used Muse Spark 1.1 and 1.2 in Thinking Mode through the standard meta.ai chat interface, the company said, without a custom research scaffold. The results span probability, differential equations, group theory, optimization and mathematical physics.
Meta’s claim is about collaboration, not a model independently producing five finished proofs. The company says mathematicians guided the investigations, developed arguments with the model and reviewed the work; each paper marks passages drafted primarily by researchers or by AI. The papers also credit earlier scholarship they build on.
Five questions, six papers
The six papers do not map one-to-one onto the five open questions Meta highlights. Among the reported results, one establishes a threshold for fitting random Gaussian points in high dimensions with an ellipsoid: below the threshold, a fit exists with high probability; above it, one almost certainly does not. Meta says the exact behavior at the threshold remains unresolved.
In a result on a nonlinear Schrödinger equation, the paper by Leonard Dinh proves that radial solutions with negative energy in two or more dimensions collapse in finite time. Meta describes it as resolving a question left open in 2015 and confirming a prediction from computer simulations in 2002. In group theory, researchers found a 384-element counterexample to a conjecture that certain finite groups must also have a property called monomial.
A fourth result gives a condition for when a particular relaxation of a binary polynomial optimization problem exactly matches the original problem. The fifth paper, on evolution algebras, disproves a conjecture about how to classify them. The sixth, on arithmetic physics, connects a calculation in p-adic string theory to a mathematical height function on a broader class of curves. Meta classifies five of the six papers as answers to previously open research questions.
Researchers directed and checked the work
The model’s role varied from paper to paper. Meta says Muse Spark helped develop and revise proof strategies for the ellipsoid result; for the group-theory paper, it generated a search program that found the counterexample. In the p-adic string paper, the model helped identify a connection, generated candidate proofs and drafted three technical sections, which researchers then checked and revised.
Those descriptions put human researchers in the work at several stages. Aykut Arslan guided the ellipsoid investigation, while four other mathematicians checked and refined its arguments. For the nonlinear Schrödinger result, Dinh selected the question and key proof ideas; a separate pair of mathematicians reviewed and helped refine the work.
Some answers appeared independently elsewhere
Meta says other teams independently announced solutions to some of the same problems using different approaches. Its paper on Gaussian ellipsoid fitting acknowledges three independent works posted in August 2026, including one that proved the same threshold. The group-theory paper also notes that the AI agent Nilradical reported a different counterexample to the conjecture on September 16.
Those overlaps matter when interpreting the announcement: Meta presents the papers as contributions made with Muse Spark, not as the sole solutions to every question. The company’s own account records both independent work and unresolved boundaries, including the Gaussian threshold case. Its evidence here is six research papers, with human mathematicians credited for choosing, guiding and checking the work alongside Muse Spark.