Meta says Muse Spark helped solve six open math problems and unveils Muse Gadgets hardware project

Six math problems solved with Muse Spark

Meta said on October 3, 2026 that its Muse Spark AI model helped mathematicians tackle six open research problems in areas including probability, differential equations, group theory, optimization, arithmetic physics and non-associative algebra. The company noted that five of the six were open questions with no answer key. "Open research is different. There is no answer key, no guarantee that an approach will work," Meta said in a blog post. "Making progress means trying and retrying ideas, making new mistakes and resolving them, and sometimes going back to the beginning." Mathematicians used Muse Spark versions 1.1 and 1.2 in Thinking Mode through the standard Meta AI chat interface, without research-specific modifications.

Mathematicians used the model to find proofs and counterexamples

In probability, Meta said the work identified a sharp threshold for fitting random Gaussian points in high dimensions to an ellipsoid: below the threshold such an ellipsoid exists with high probability, and above it almost certainly does not. In differential equations, researchers answered what Meta described as a long-standing question about wave collapse in a model inspired by laser physics, proving that symmetric waves with negative energy in two or more dimensions must collapse in finite time, settling a question left open in 2015 and confirming a 2002 prediction from simulations. In group theory, researchers disproved a proposed rule about mathematical structures that describe symmetry by finding a counterexample of order 384; Meta said Muse Spark generated the GAP search program that located it.

Optimization, arithmetic physics and algebra work

In optimization, researchers worked with Muse Spark to understand when a shortcut method of a math problem could capture the original and when it could not. In arithmetic physics, the team connected an idea from number theory with a calculation in string theory, proving the link works in more cases than previously known and building on ideas from the 1980s; Meta said Muse Spark drafted three core technical sections, which researchers then checked and refined. In non-associative algebra, the team used Muse Spark to find an exception to a proposed rule about mathematical structures inspired by biology. Meta said one group of mathematicians guided the research and developed the arguments with the model, while a second group reviewed the work.

Meta launches Muse Gadgets and Home Link

In a separate announcement on the same date, Meta's AI chief Alexander Wang introduced Muse Gadgets, an open-source project designed to let developers build hardware that works with the Muse AI agent. Meta also unveiled its own device, the Muse Home Link. The announcements pair research-claim news about Muse Spark with a push to seed a third-party hardware ecosystem around the Muse agent, while OpenAI separately faced scrutiny after claiming its own model solved the Navier-Stokes Millennium challenge.

What remains to be seen

It is not yet clear from the announcement which mathematicians or institutions led each of the six efforts, where the resulting papers will be published, or whether peer review has already been completed. The blog post framing also leaves unresolved how often Muse Spark will be credited as a co-author or tool contributor on the resulting publications, and how Meta plans to govern third-party hardware built through the open-source Muse Gadgets project.