Nobel Laureate Giorgio Parisi Used Claude to Prove a Decade-Old Physics Theorem

Giorgio Parisi, the 2021 Nobel Prize winner in Physics, and Francesco Zamponi of Rome's Sapienza University have published the proof of a mathematical relationship they had worked on for a decade. A key role in completing the proof was played by Anthropic's Claude model, with which the researchers held a dialogue spanning around 40 prompts.

The problem solved by Parisi and Zamponi concerns jamming, the moment when systems of disordered particles, such as granular materials, foams, or dense colloidal suspensions, abruptly stop flowing and start behaving like solids, even though they form no ordered crystalline structure. The phenomenon is described by two independently developed theories, one stemming from Parisi's own earlier work, the other from Matthieu Wyart's team. Both predict the same critical exponents, which suggested a simple relationship between them in the form a+b=1.

A Decade Without Proof

Zamponi admitted that the a+b=1 relationship had been confirmed numerically with high precision as early as 2014, but no one had managed to prove it formally. The gap particularly bothered Parisi, since it suggested some simple, overlooked step was missing from the reasoning. The researchers repeatedly returned to the problem over the years without success.

Eventually they decided to ask a language model for help. They chose Claude, judging that, compared with competing models, it showed somewhat more advanced mathematical reasoning abilities. The exchange was not a single query but an iterative process, in which the model proposed proof steps, the researchers checked them, pointed out errors, and the model went back to make corrections.

How the Collaboration Worked

According to Zamponi's account, Claude fairly quickly proposed an initial idea that turned out to be fundamentally sound, though the first version of the formal proof contained errors. It was the physicists, not the model, who could tell where elegant-sounding reasoning ended and rigorous mathematical proof began. Parisi and Zamponi themselves refined the final, published version of the proof, building on the lead the model had pointed to.

Claude fairly quickly hit on an initial idea that was fundamentally correct - Francesco Zamponi, Sapienza University of Rome

The answer was right there, we just hadn't noticed it - Francesco Zamponi, Sapienza University of Rome

What It Means for Science and AI

The Parisi and Zamponi case is being cited as one of the first documented examples, published in a peer-reviewed journal, of a large language model meaningfully contributing to solving an open problem in theoretical physics, rather than merely speeding up calculations or literature searches. In the paper's abstract, the authors explicitly state that the proof was developed through interaction with the Claude model and was subsequently verified by them, a rarity in mathematical physics publications.

Experts commenting on the case stress, however, that the human role remains crucial. The model generated a lead, but it was the researchers' years of experience that allowed them to distinguish the correct line of reasoning from dead ends and then turn it into a rigorous, publishable proof. Without that expertise, the model's suggestion would have remained just another piece of text generated by a language system, with no scientific value.

What It Means for Polish Scientists

For Poland's scientific community, Parisi's story offers a concrete, proven pattern for using tools like Claude or competing models in research work: not as an oracle, but as a partner for iteratively searching the solution space, whose suggestions still need to be independently verified. More and more mathematics and physics teams worldwide are testing similar approaches on problems that have resisted classical methods for years.

The very fact that this kind of collaboration was recorded in a respected journal such as the Journal of Statistical Mechanics could speed up the acceptance of language models as a legitimate scientific working tool, much as happened earlier with symbolic computation software. At the same time, it raises questions about how to describe AI's contribution in scientific publications and about the standards reviewers should use to verify such proofs.

Sources: A proof of an identity for the critical exponents of jamming (arxiv.org), Physicists and AI model Claude collaborate to prove a 10-year-old jamming conjecture (phys.org), Claude Aids Solution to Decades-Old Jamming Problem (letsdatascience.com), Claude AI helped a Nobel laureate close a decade-old problem (trybuna.info)