Meta Partners with Mathematicians to Solve Open Research Problems Using Muse Spark

Meta has partnered with mathematicians to use Muse Spark 1.1 and 1.2 in Thinking Mode via the meta.ai interface to solve open research problems. Unlike competition problems with known solutions, these collaborations required iterative exploration without an answer key, resulting in six papers where five provide answers to previously open questions.

Collaboration Principles

The research followed strict transparency guidelines:

• Mathematicians guided the research and developed arguments with Muse Spark.
• A separate group of mathematicians reviewed the work.
• Papers clearly distinguish between passages drafted by researchers and those drafted by AI.
• Credit is given to earlier research and concurrent independent works.

Key Mathematical Results

The papers cover diverse areas of mathematics, with Muse Spark assisting in proof development, counterexample generation, and theoretical connections:

• Probability: Aykut Arslan identified a sharp threshold for fitting random Gaussian points to an ellipsoid in high dimensions. The result defines when such a fit exists with high probability versus when it almost certainly does not, though behavior at the exact threshold remains unresolved.
• Differential Equations: Leonard Dinh proved that radial negative-energy solutions for the Mass-Critical Biharmonic Nonlinear Schrödinger Equation must collapse within a finite time in two or more dimensions, settling a question open since 2015.
• Group Theory: Joseph Phillip Brennan and Milana Golich disproved a 2024 conjecture by M. Kida that all finite semiabelian groups are monomial. They found a counterexample in a group with 384 elements, using a search program generated by Muse Spark in GAP.
• Optimization: Aykut Arslan determined when a cycle-based relaxation for binary polynomial optimization is exact. The approximation is exact only when specific regions in the problem structure contain exactly one decision; otherwise, a gap remains.
• Arithmetic Physics: A team including Anindya Dey and others connected number theory and p-adic string theory, showing that a string two-point function equals a height function on a curve, fulfilling a direction envisioned by Yuri Manin in the 1980s.
• Non-Associative Algebra: Andres Barei disproved a conjecture by García-Martínez and Pérez-Rodríguez regarding solvable evolution algebras by finding a three-dimensional counterexample and establishing an alternative rule based on subspaces.

Independent Contributions

Meta acknowledged that other teams independently solved some of these problems using different approaches. For instance, three independent works on the Gaussian ellipsoid threshold were posted in August 2026, and the AI agent Nilradical reported a different counterexample to the semiabelian group conjecture in September 2026. Meta’s results were developed independently and are credited alongside these concurrent findings.