Muse Spark co-authors six papers on open math problems

Meta published six papers co-authored with external mathematicians using Muse Spark 1.1 and 1.2 in Thinking Mode, through the ordinary meta.ai chat interface with no custom research scaffold. Meta says five of the six present answers to previously open problems. The sixth, on arithmetic physics, establishes a connection rather than resolving a question.

The results are specific. On Gaussian ellipsoid fitting, the work gives the sharp threshold for fitting random Gaussian points in high dimensions to an ellipsoid: it exists with high probability below roughly n = d squared over 4, and almost certainly does not above it. On the biharmonic nonlinear Schrodinger equation, the paper proves finite-time blow-up of radial negative-energy solutions in two or more dimensions, which Meta says settles a question left open in 2015 and confirms a prediction from 2002 computer simulations. On group theory, it disproves Kida’s 2024 conjecture that every finite semiabelian group is monomial, via a counterexample in a group of 384 elements, and Muse Spark generated the GAP search program that found it. On optimization, it answers a question on the tightness of the cycle-based relaxation for completed length-three alpha-cycles, exact when each two-of-three pairwise block is a singleton. On non-associative algebra, it finds a three-dimensional counterexample to a solvability test and establishes an alternative subspace-level characterization.

The credit allocation is the story

What makes this post more useful than a typical research claim is how much overlap Meta discloses. The Gaussian threshold was reached independently by three other teams in August 2026, and the semiabelian counterexample was reported by an AI agent called Nilradical on September 16, 2026. Meta states its results were developed independently and credits the concurrent work by name and reference.

The methodology is stated too: a first group of mathematicians guided the research, a second group reviewed it, each paper marks which passages were drafted by researchers versus the model, and each credits prior work.

The limits are equally clear. These are preprints, not peer-reviewed results, and Meta publishes no quantitative accuracy claims at all — no benchmark score, no percentage of proof steps AI drafted, no reviewer agreement metric and no ablation against unaided mathematicians. Meta says the goal “wasn’t to mass-produce papers.” The Gaussian threshold is resolved except exactly at the threshold itself, which remains open. Attribution of the model’s contribution is self-reported by the human authors with no independent audit.

(Original source: Meta AI Research)