Nobel laureate Giorgio Parisi has used Anthropic’s Claude AI system to solve a mathematical puzzle in the theory of jamming that had resisted analytical proof for 12 years, marking one of the most concrete demonstrations yet of AI-assisted mathematical discovery.
Parisi, who won the 2021 Nobel Prize in Physics for his work on complex systems, and his Sapienza University of Rome colleague Francesco Zamponi published the proof July 1 in the Journal of Statistical Mechanics. The paper explicitly states that the result “could not have been obtained without the interaction with Claude.”
“This is not a case of an AI solving a problem on its own,” Zamponi said. “It is a case of a researcher and an AI working together, where the AI proposed an idea that the humans recognized as correct.”
A 12-year gap
The jamming transition, the sudden rigidification of a disordered system such as foam, sand, or grains as density increases, is one of the unsolved problems in statistical physics. In a landmark 2014 paper, Parisi and collaborators derived a full replica symmetry-breaking (fullRSB) solution for dense hard spheres in infinite dimensions. The solution introduced three critical exponents, a, b, and c, that characterize how physical quantities behave near the jamming point.
Two scaling relations had been established. Researchers had proven b = (1+c)/2 analytically, and a + b = 1 had been observed numerically to arbitrary precision through extensive simulations. But an analytical proof of a + b = 1 remained elusive. The missing link meant theorists could not confirm that two different approaches to jamming, the fullRSB framework and mechanical marginal-stability arguments, were mathematically equivalent.
“We could not see the path forward, and Claude did,” Zamponi said.
How the collaboration worked
Parisi began by prompting Claude to reproduce the numerical calculations from the 2014 CKPUZ paper, to establish whether the AI could handle the mathematical domain. Claude succeeded, earning a level of trust. Parisi then asked the AI to attempt a proof of a + b = 1.
Claude returned a LaTeX file containing a core idea that was essentially correct, though the initial output contained errors requiring human revision. Over approximately 40 iterative prompts, the researchers and the AI refined the proof, the humans identifying and correcting mistakes, the AI filling logical gaps.
The final proof links the scaling exponents to physical quantities: the gap exponent alpha = a/b, the force exponent theta = (c-a)/(b-c), and the mean-square-displacement exponent kappa = c+1. Proving a+b=1 yields the independent scaling relations alpha = 1/(2+theta) and kappa = 2-2/(3+theta), previously predicted by Matthieu Wyart at EPFL through mechanical-marginal-stability arguments.
The full conversation transcripts have been deposited in a Zenodo repository.
What the AI did, and did not, do
The paper’s authors are careful to distinguish what Claude contributed from what it did not. The relation a + b = 1 was not discovered, it had been known numerically for 12 years. The AI helped produce a proof, not a discovery. And the AI’s output required human expertise to correct; the paper states the proof was “obtained through interaction with Claude and verified by us.”
Zamponi acknowledged that a pure mathematician might eventually have found the proof without AI assistance. The novelty is that Claude gave non-specialist physicists access to mathematical techniques outside their usual expertise.
“Claude efficiently gave us instant access to a vast repository of mathematical training and formal skills that lay just outside our usual domain,” Zamponi told Live Science.
The proof also leaves several open questions. The authors explicitly note they did not prove the existence or uniqueness of the fullRSB profile, the rigorous derivation of the scaling regime, or the selection of the no-node branch from the flow.
A broader pattern
The paper joins a growing list of AI-assisted mathematical results. In recent months, an OpenAI model reportedly solved an 80-year-old mathematical problem internally, and researchers used AI to verify a prize-winning proof. But the Parisi-Zamponi collaboration stands out for its transparency, the interaction transcripts are public, and the paper’s narrative of human-AI collaboration is unusually detailed.
“It significantly shifted my perspective on what these models can achieve in theoretical physics,” Zamponi said.
Sources
Parisi G, Zamponi F. “Analytical proof of the scaling relation a+b=1 in the fullRSB solution of the jamming transition.” Journal of Statistical Mechanics 073301 (2026). DOI: 10.1088/1742-5468/ae7bd7. arXiv:2606.03300.
Skuse B. “Nobel Prize-winning physicist and team use Claude AI to solve decades-old math puzzle.” Live Science, July 16, 2026. https://www.livescience.com/physics-mathematics/mathematics/nobel-prize-winning-physicist-and-team-use-claude-ai-to-solve-decades-old-math-puzzle