Nobel laureate Giorgio Parisi and Francesco Zamponi of La Sapienza asked Anthropic's Claude for help on a long standing puzzle about why disordered particle systems, from sand piles to coffee grounds in a jar, suddenly lock up, and then had to write the proof themselves.
The interesting thing about the new paper in the Journal of Statistical Mechanics: Theory and Experiment is not that an AI helped. It is the precise distance between “essentially correct” and “correct,” and what that distance says about where Claude actually fits in the research stack.
For more than a decade, physicists studying granular materials (think sand, ball-pit beads, or the slow crush of coffee grounds in a jar) have run into a stubborn pattern. As you pack such a system more tightly, it does not gradually stiffen. At some threshold density it locks up. The transition has a name: the jamming transition. Numerics going back to the mid-2010s kept producing the same result. Two critical exponents, called gamma and 1/sigma, summed to exactly 1. Every simulation said so. Nobody could prove it.
In 2014, Patrick Charbonneau, Jorge Kurchan, Giorgio Parisi, Pierfrancesco Urbani, and Francesco Zamponi laid out the foundational formulation the community has been chasing since. The paper, published in the same journal where the new proof now appears, gave the field its working language and a clean target: prove that gamma plus 1/sigma equals 1.
Ten years later, two of those original authors closed the loop.
Giorgio Parisi, the Nobel-winning statistical physicist, and Francesco Zamponi of La Sapienza University of Rome describe the breakthrough in a paper titled “A proof of an identity for the critical exponents of jamming,” available on arXiv (with an HTML version here) and now formally published in the Journal of Statistical Mechanics: Theory and Experiment. The result is exactly what the field had been waiting for: a rigorous derivation of the identity numerics had been waving at for a decade.
The new variable in the story is Anthropic’s Claude. According to the institutional press release reported by EurekAlert and mirrored by phys.org and Mirage News, the researchers turned to the model after conventional approaches had stalled. Claude’s first draft of the proof contained multiple errors. It took several rounds of human verification and revision to get to a publishable version.
But the underlying direction, the physicists say, was right.
“Quite quickly, Claude came up with an initial idea that was essentially correct,” Zamponi told the press. “The answer was right there, and we simply hadn’t seen it.”
That phrasing, “essentially correct,” is doing a lot of work. It is also where the story actually lives.
Read one way, the line is a flattering verdict on the model: Claude saw a path that two of the field’s most credentialed researchers had walked past for a decade. Read another way, it is a careful acknowledgment that the AI’s draft was not a proof at all. It was a sketch of one. The decisive moves (closing the remaining logical gaps, checking each step against the underlying statistical-mechanics framework, and writing the version that survives peer review) were made by Parisi and Zamponi. The published paper credits the AI as a thought partner, not as an author of mathematics.
Gizmodo’s coverage frames it the same way: a human-AI collaboration in which the human work was, by the physicists’ own description, the larger part. That detail is worth holding onto because it cuts against the louder narratives around AI in science. The story is not “AI beat physicists at physics.” It is the more specific and more useful claim: an AI assistant surfaced a direction that two expert physicists, working alone, had not seen. Then the experts did what experts do.
It also fits a pattern. A separate Gizmodo feature covers a recent case in which an OpenAI model produced results that appeared to disprove a famous math conjecture, until a human mathematician, working without the model, arrived at the opposite answer. AI mathematical work, the two cases together suggest, is a high-leverage but high-error-rate activity. The first move is often fast. The second move is still human.
What to watch now is whether the new identity holds up under independent scrutiny, and whether other long-standing identities in the jamming literature (there are several) yield to similar human-AI passes. The 2014 paper that set the agenda sketched a wider program. One of its conjectures is now a theorem. The next ones are the obvious place to look.