Gemini 4 Argon Helps Researchers Extend Solutions to a 59-Year-Old Fusion Math Problem

A team of three Google DeepMind researchers and University of Maryland plasma physicist Matt Landreman used Google’s Gemini 4 Argon to extend a set of exact solutions for the magnetic fields inside stellarator fusion reactors, solutions that had only recently overturned a conjecture Harold Grad posed in 1967.

The work, posted to arXiv on Oct. 5 by Opal Issan, Jonathan Citrin, Landreman and Brendan Tracey, builds on a paper Landreman posted on Sept. 22. That paper gave two families of explicit, smooth 3D equilibrium solutions with nested magnetic surfaces, counterexamples to Grad’s conjecture that such solutions don’t exist without special symmetries. Landreman found them with OpenAI’s GPT-6 Astra Pro, and his acknowledgments say all equations were confirmed manually.

Breaking the symmetry

Both of Landreman’s families shared a property called stellarator symmetry, which left an open problem: exact, closed-form examples for configurations without it. The DeepMind paper adds a symmetry-breaking parameter to each family, producing new solutions that reduce to the originals when that parameter is set to zero.

According to the paper’s section on AI use, the work “was carried out using Gemini 4 running as a small team of agents in Google Antigravity,” the company’s agentic development environment. Given Landreman’s paper and a list of the open questions it raised, the agents proposed the generalized solutions. “Promising candidates appeared within hours,” the authors wrote. Gemini 4 Argon also drafted parts of the manuscript and wrote symbolic and numerical verification code, while the authors chose the problem, steered the agents, ran several rounds of adversarial review and independently re-derived every derivation.

The practical payoff is for software. Equilibrium solvers such as VMEC, SPEC and DESC use stellarator symmetry to halve the number of Fourier coefficients they solve for, so testing them on asymmetric cases needs benchmarks that break that symmetry, the paper says. TechRadar, despite an “It’s over, AI won” headline, noted the result is a larger set of exact solutions for researchers, not evidence that AI has solved fusion or its engineering obstacles.

Landreman’s paper wasn’t the only counterexample. Mathematicians Javier Gómez-Serrano, Lukas Liehr and Mitchell Taylor posted their own on Sept. 21, and the University of Maryland’s ECE department said the two papers, posted within a day of each other, produced three families of counterexamples. Those solutions can break stellarator symmetry, but they have no explicit closed-form expression, which limits their use as code benchmarks, according to the DeepMind paper.

Google featured the result in its Oct. 13 post making Gemini 4 Argon generally available, alongside examples in quantum computing and rare-disease research. Landreman, for his part, wrote in September that for the stellarator concept “it is reassuring to know with certainty that strongly asymmetric equilibria with perfect flux surfaces do in principle exist.”