Meta's Muse Spark co-writes six maths papers, five solve open problems

What happened: On 2 October 2026, Meta released six mathematics papers produced by mathematicians working with Muse Spark 1.1 and 1.2 in Thinking Mode. They used the regular meta.ai chat, with no custom research scaffold, according to Meta AI's research blog.

The numbers: Five of the six papers answer previously open research questions. All were peer reviewed. Each paper marks which passages the AI drafted and which the researchers wrote.

The details: The six papers cover:

Probability: a sharp threshold for fitting random Gaussian points to an ellipsoid in high dimensions ("The Strict Threshold for Gaussian Ellipsoid Fitting").

Differential equations: finite-time blow-up (wave collapse) for radial negative-energy solutions of the mass-critical biharmonic nonlinear Schrödinger equation.

Group theory: a 384-element counterexample that disproves a 2024 conjecture (Kida) in "Semiabelian Groups Need Not Be Monomial".

Optimisation: tightness of the cycle-based relaxation for completed length-three alpha-cycles.

Arithmetic physics: a string two-point function equals a height function on a curve, linking number theory and p-adic string theory.

Non-associative algebra: a three-dimensional counterexample to a conjecture by García-Martínez and Pérez-Rodríguez on solvable evolution algebras.

How it worked: The model developed proof strategies, worked through calculations, wrote search programs and drafted technical sections. Humans set the direction and verified the results.

In their words: Meta's research blog said: "Making progress means trying and retrying ideas, making new mistakes and resolving them, and sometimes going back to the beginning."

The context: Muse Spark had earlier reached gold-medal level on five high-school olympiad competitions. Muse recently hit #1 on the App Store. OpenAI and Google DeepMind have also published AI-assisted maths results this year.

What's next: The notes give no further Meta plans for the work.