Muse Spark and mathematicians publish six research papers solving open problems

Meta has released six collaborative mathematics papers where human researchers used Muse Spark 1.1 and 1.2 in Thinking Mode to answer open research problems. Five of the papers resolve previously unsolved questions across probability, differential equations, group theory, optimization, and non-associative algebra. The work follows a partnership model: mathematicians guided the exploration, a separate group reviewed the findings, and each paper clearly marks which passages were drafted by researchers and which by the AI.

How the collaboration worked

The researchers accessed Muse Spark through the standard meta.ai chat interface, with no custom research scaffold. A team of mathematicians directed the research and worked with the model to explore ideas and develop arguments. A second group then reviewed their work. The papers credit earlier research they build on and label AI-drafted versus human-drafted sections.

"Open research takes time. Our goal here wasn't to mass-produce papers, but to empower researchers and help them develop mathematical insights that others can understand and build on," the team said in its announcement.

The six papers at a glance

Probability: Aykut Arslan and Muse Spark identified a sharp threshold for fitting random Gaussian points in high dimensions to an ellipsoid. Below the threshold, an ellipsoid exists with high probability; above it, one almost certainly does not. Three independent concurrent works from other teams, posted in August 2026, used different approaches to reach related conclusions and are acknowledged in the paper.

Differential equations: Leonard Dinh and Muse Spark proved that for the mass-critical biharmonic nonlinear Schrödinger equation, radial negative-energy solutions must collapse in finite time in two or more dimensions. This settles a question left open since 2015 and confirms predictions from 2002 computer simulations.

Group theory: Joseph Phillip Brennan, Milana Golich, and Muse Spark disproved a 2024 conjecture by M. Kida that every finite semiabelian group must also be monomial. Muse Spark generated a search program in GAP that found a counterexample with 384 elements. The AI agent Nilradical independently reported a different counterexample on September 16, 2026.

Optimization: Arslan and Muse Spark answered a 2026 question from Del Pia and Khajavirad about when a relaxation of a binary polynomial optimization problem exactly captures the original. The approximation is exact when each region shared by two circles in a Venn diagram structure contains exactly one decision; if any region holds more, a gap remains.

Arithmetic physics: Anindya Dey, Gabriel Herczeg, An Huang, Nicolas Jaramillo Torres, Jacob H. Swenberg, and Muse Spark connected number theory and p-adic string theory, following a direction Yuri Manin envisioned in the 1980s. The paper shows that two calculations from different mathematical languages describe the same quantity. Muse Spark drafted three core technical sections, which the researchers then checked and refined.

Non-associative algebra: Andres Barei and Muse Spark disproved a conjecture by García-Martínez and Pérez-Rodríguez for classifying evolution algebras. Beyond finding a three-dimensional counterexample, the paper establishes an alternative rule based on whole subspaces rather than individual elements. Independent work by Hu and Wen reported counterexamples to the same conjecture.

Why this matters for writers and science communicators

These papers offer a concrete case study in transparent AI attribution. Each one labels which passages came from Muse Spark and which from human researchers. For writers covering AI in science, this provides a model for how to describe human-AI collaboration without inflating or obscuring the technology's role. The partnership principles - expert guidance, separate review, clear labeling, and credit to prior work - establish a template you can reference when evaluating similar claims about AI-assisted research.