A Nobel laureate asked Claude to re-check his math. It helped close a decade-old physics puzzle.

Giorgio Parisi did not ask Claude to invent a theory. He asked it to re-check one. The result, the first analytic proof of an identity called a+b=1, lands in the peer-reviewed Journal of Statistical Mechanics: Theory and Experiment (J. Stat. Mech.) issue 073301 this July, and the full transcript of the working sessions is public on Zenodo.

The problem is a 12-year-old stalemate over the math of "jamming." Picture a pool table so crowded with billiard balls that none can move. The fluid has become a rigid, disordered solid. That is jamming, the same physics that governs grains packing in a silo, the way traffic stops without an obvious cause, and why glass never quite flows. Jamming has been a touchstone problem in statistical physics, in part because it sits at the boundary between liquid-like and solid-like behavior.

In 2014, a group now known by the initials CKPUZ (Charbonneau, Kurchan, Parisi, Urbani, Zamponi) ran large numerical simulations and found a curious relation among the critical exponents a, b, and c that govern the matching region near the jamming transition: a+b=1. The companion identity b=(1+c)/2 was proved analytically within a few years. The identity a+b=1 refused to follow. The result sat unproven for more than a decade.

Francesco Zamponi, a co-author of that 2014 paper, posted the resolution on arXiv in June as paper 2606.03300. The proof is narrow but exact: a+b=1 holds inside the full replica-symmetry-breaking (fullRSB) ansatz, the standard mathematical machinery for disordered systems in infinite dimensions. The exponents connect to the same scaling relations that mechanical-stability arguments by Wyart and collaborators predict, but those arguments had no closed-form proof. The new paper supplies it.

The tool that produced the proof was Anthropic's Claude, used in two successive model versions, Sonnet 4.6 and Opus 4.7, working through the argument over many sessions. The full transcript of those conversations is archived on Zenodo as record 20633432, a rare public audit trail for an AI-assisted mathematical argument. The work was authored by Zamponi and Parisi, and the paper's abstract states that the proof was "verified by us," the authors, not the model.

Gizmodo reported that other physicists called Claude's solution "essentially correct," a supportive but not load-bearing read. Parisi, in comments reported by Live Science, said the collaboration "significantly shifted my perspective on what these models can achieve in theoretical physics." The framing is partnership, not replacement: a tired old proof, a patient interlocutor, a human author willing to be wrong.

The wire version of the story reads as "AI solves Nobel winner's puzzle." The actual mechanism is narrower and more useful: Claude served as a re-examination partner for an argument the field had stopped trying to prove, prompting the authors to chase branches they would have skipped alone. The result is not a new theory of jamming. It is the closure of a known gap, by a known method, in a known regime, with a known tool now named in the paper.

The next "AI solved X" headline deserves a more honest test: did the model generate the question, or did it re-examine someone else's? In the Zamponi–Parisi case, the credit for the question belongs entirely to a 12-year-old simulation, and the proof sits in a journal that takes years of peer review. Mature, human-stuck problems with established formalisms, where the math is hard but the structure is known, are the natural niche for an LLM that has no creative insight but no fatigue.

A press release on EurekAlert from Sapienza frames the work as a milestone in human-AI collaboration. The published paper is more measured. The proof is for one specific identity inside one specific ansatz. The mechanism that made it possible, patient re-examination by an AI assistant under human authorship, is now on the record, and is the part of the story most likely to matter when the next decade-old problem comes around.