Fusion: AI finds counterexamples to Grad’s conjecture, a stellarator puzzle dating back to 1967

GPT-6 Astra Pro, followed by teams of Gemini 4 agents, produced plasma equilibria that the physicist Harold Grad had deemed impossible, for less than $3 per problem.

In 1967, mathematician Harold Grad had argued that a plasma in equilibrium, with variable pressure and well-attached magnetic surfaces, could only exist smoothly with additional symmetry, as in a tokamak. The stellarators, whose twisted geometry did not have this symmetry, therefore seemed excluded. On September 22, Matt Landreman (University of Maryland) published two families of smooth three-dimensional solutions that contradict this conjecture: they were discovered with GPT-6 Astra Pro, and Landreman checked each equation by hand.

Agents in a few hours

A second publication, on October 5, co-signed by researchers from Google DeepMind and Landreman, entrusted the research to teams of Gemini 4 agents: promising candidates appeared in a few hours. These are the first balances of this type obtained in explicit form, which can serve as a reference for testing the design codes of stellarators. On the TheoPhysEval test bench, the average cost remains below $3 per problem, and $116.28 for all 50 API tariff issues.

This work does not say anything about the timing of a future reactor, and it is always humans who choose the questions to ask. Landreman believes that other exact solutions remain to be discovered.