Earlier this year, Meta's models reached gold-medal-level performance across five high-school Olympiad competitions in mathematics, physics, and chemistry. However hard a competition problem gets, an answer key exists. Open research problems do not: there is no guaranteed path, and a wrong turn can mean starting over. Following that leap, Meta's research team has delivered a new kind of specimen: six papers co-authored by mathematicians and Muse Spark, five of which present answers to previously open questions. (Official blog: https://research.meta.ai/blog/solving-open-research-problems-together)
Six Papers, Five Fields
The probability paper establishes the strict threshold for Gaussian ellipsoid fitting: below the threshold an ellipsoid exists with high probability, above it one almost certainly does not, while behavior exactly at the threshold remains unresolved. The PDE paper proves that radial negative-energy solutions of the mass-critical biharmonic nonlinear Schrödinger equation must collapse in finite time, settling a question left open in 2015 and confirming predictions from 2002 simulations. The group theory paper disproves a conjecture proposed by Kida in 2024: Muse Spark generated the GAP search program that found a counterexample in a group with 384 elements, with humans verifying the result and completing the argument. The optimization paper characterizes when the cycle-based relaxation for completed length-three alpha-cycles is exact. The arithmetic physics paper equates the string two-point function with a height function on a curve, pursuing a direction envisioned by Manin in the 1980s. The non-associative algebra paper overturns a classification conjecture with a three-dimensional counterexample and offers an alternative criterion built on whole subspaces.
A Plain Chat Window, No Custom Scaffold
All collaborations ran through the regular meta.ai chat interface, using Muse Spark 1.1 and 1.2 in Thinking Mode, with no dedicated research system. Four rules governed the process: mathematicians guided the research; a second group of mathematicians reviewed the work; each paper clearly marks which passages were primarily drafted by AI; and all prior research is credited. In the arithmetic physics paper, Muse Spark drafted three core technical sections, which the researchers then checked, corrected, and rewrote.
Three Problems, Solved by Others Almost Simultaneously
For the probability threshold question, three external teams independently posted answers in August 2026 using different approaches, and the paper acknowledges each one. For the group theory counterexample, an AI agent named Nilradical reported a different counterexample on September 16. That is the competitive nature of open problems: you are rarely alone on the road, and independent work confirming each other makes the conclusions sturdier.
So What
Outside reporting puts the event in context: when OpenAI claimed ten open problems solved by an internal Astra model in August, the proofs came with Lean certificates and the model stayed private; DeepMind's co-mathematician agent, which resolved a 1965 group theory question in May, is a purpose-built hierarchical system. Meta's pitch is the opposite — a consumer chat product, in the hands of mathematicians who know what to ask, can already do research-grade work. A little over two weeks earlier, Fields medalists were signing an open letter warning that AI problem-solving contests harm mathematics. The two stories read together feel more honest: what a tool produces depends on who is asking. For ordinary developers the lesson may be plainer — the same chat window some people use for small talk, others use to prove theorems.