Meta Says Muse Spark Helped Settle Five Open Math Problems, but Priority Is Disputed

Meta says its Muse Spark model helped mathematicians write six research papers, five of which answer questions that had been open. A critic has since claimed that three of the six were already resolved elsewhere, a claim that has not been checked and that Meta has not answered publicly (Meta, RuntimeWire).

What Meta published

On October 2, Meta's research site posted "Solving Open Research Problems Together," describing six papers, each written by a human mathematician or small team working with Muse Spark over several months. The researchers chose the problems, a separate group of mathematicians reviewed the output, and each paper marks which passages were drafted mainly by humans and which by AI. The work used Muse Spark 1.1 and 1.2 in Thinking Mode through the ordinary meta.ai chat, without custom research tooling, so the result owes more to the model's reasoning than to special infrastructure.

Paper	Author(s)	Result
Fitting random Gaussian data to an ellipsoid	Aykut Arslan	Sharp threshold, near n = d²/4 (per RuntimeWire)
Nonlinear wave-type equation	Leonard Dinh	Finite-time blow-up, a question open since 2015 (per RuntimeWire)
Semiabelian groups	Joseph Phillip Brennan, Milana Golich	A 384-element group disproves the conjecture that they must be monomial
Cycle-based relaxations	-	Optimisation result
Solvable evolution algebras	-	Conjecture addressed
p-adic string theory correlation function	-	Extends a known number theory connection to more curves (not framed as an open problem)

In the group theory paper, Muse Spark wrote a search program in the GAP system that found the counterexample, which the researchers then checked before completing the proof. Meta lists named reviewers for five papers; the string theory paper lists none.

Meta's claim

Meta's framing is that five of the six papers answer previously open questions. It also acknowledges that other teams independently announced solutions to some of the same problems around the same time, using different approaches. AlphaSignal says three of the five results were proven by other teams in the same period. A problem solved by two groups at once is still a real result, but it is not the same as one solved long ago and merely unknown to the authors.

The dispute

On October 3, a user named Jason Dean Lee posted on X that three of the six problems had already been resolved, according to HuggingNews, which gave no list of which three, no links to earlier proofs and no response from Meta. HuggingNews describes Lee as a reviewer, but he does not appear in the reviewer lists on Meta's page, and his affiliation is unclear.

Two claims are therefore in circulation: that three problems were solved at about the same time by others, which Meta and two outlets support, and that three were solved before the papers appeared, which rests on a single post. Checking dates and citations will settle it; until then Meta's count of five open problems is the company's own claim and is disputed.

Why it matters

Language models have been tested on competition problems for some time, and Meta says its models reached gold-medal level in mathematics, physics and chemistry competitions. These papers are its attempt to show models can contribute to research where no solution path is known. Even if the strongest claims hold, they show humans and a model working together: the mathematicians picked the problems, directed the work and judged the results.

A proof counts once other mathematicians find no errors, and a paper counts as new once its priority is established. None of the six has been through journal peer review.

What to watch next

Watch for Meta to name which papers overlap with earlier or parallel work, for independent checks of the proofs, especially the 384-element group and the blow-up result, and for other labs to publish comparable collaborations with named reviewers.

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