Physicists and AI model Claude 'collaborate' to prove a 10-year-old jamming conjecture Sadie Harley Scientific Editor Robert Egan Senior Editor A mathematical problem that had remained unsolved for more than 10 years in the physics of complex systems has finally been resolved through an unusual collaboration: one involving two theoretical physicists and an artificial intelligence system. In a study published in the Journal of Statistical Mechanics: Theory and Experiment, Giorgio Parisi, Nobel Prize winner in physics, and Francesco Zamponi, physicist at LaSapienza University of Rome, show how the AI model Claude contributed to finding the proof of a mathematical relation that had resisted researchers' efforts for years. Beyond its scientific significance, the result offers a concrete glimpse into how artificial intelligence is transforming the work of researchers.

In physics, jamming describes the formation of a kind of "traffic jam" of particles: A system that is initially fluid suddenly becomes rigid while remaining disordered. Originally introduced to describe materials such as foams and granular matter, the concept has proved surprisingly general and is now also used in fields such as neuroscience and artificial intelligence. In 2014, Parisi, emeritus professor at LaSapienza University of Rome and recipient of the 2021 Nobel Prize in physics, Zamponi, professor of physics at LaSapienza University of Rome, and collaborators developed a theoretical description of jamming and noticed a surprising relationship: Two mathematical parameters of the model, denoted by a and b, always added up to 1, as numerical calculations showed with extraordinary accuracy.

A surprising relationship This relationship, Zamponi explains, yields the same physical laws obtained through a different theoretical approach to jamming developed almost simultaneously by French physicist Matthieu Wyart (EPFL, Lausanne). In other words, it suggests that two very different ways of describing the phenomenon actually lead to the same conclusions. The result emerged clearly from numerical calculations from the beginning, but no one could explain why it was true.

For years, researchers searched for a mathematical proof of the relation, convinced that some deeper structure of the theory lay behind its apparent simplicity. A persistent obsession After several unsuccessful years, the problem gradually faded into the background. Not for Parisi, however.

"It really bothered him that we had never managed to prove it," Zamponi recalls. When the first generative AI models began to appear, Parisi identified this old problem as an ideal test case. Claude was chosen because it "seemed to have somewhat more advanced mathematical reasoning abilities," Zamponi says.

The problem, after all, was well-defined: a clear conjecture, relatively simple mathematics, and an answer that was known numerically but had never been formally proved. The initial prompt was not to find the proof. Parisi asked the model to reproduce the numerical calculations developed by the group more than a decade earlier, in order to understand how far it could go in tackling a real mathematical problem.