A 10-year-old mathematical puzzle explaining jamming - the sudden freezing of disordered particles into a solid - has been solved through a direct collaboration between physicists and Anthropic's Claude AI. The finding, published July 1 in the Journal of Statistical Mechanics: Theory and Experiment, shows generative AI contributing a key proof idea that human researchers then validated and refined.
A decade-old mystery
Jamming describes a phase transition where bubbles, sand, or grains moving in a fluid-like, disordered state suddenly lock into a rigid solid while remaining structurally disordered. The concept, originally developed for foams and granular materials, now also informs work in neuroscience and AI.
Nobel laureate Giorgio Parisi and Francesco Zamponi at Sapienza University of Rome built a theoretical model of jamming in 2014. In the process, they noticed that two parameters in the model - labeled "a" and "b" - always added up to 1. Numerical simulations confirmed this relationship with high precision, but no one could explain why. French physicist Matthieu Wyart's group at EPFL found the same relationship through a different theoretical route, reinforcing the suspicion that a deeper mathematical structure was at play.
How Claude helped crack the proof
Parisi decided to use the problem as a testbed for generative AI's ability to assist with real mathematical work - a question at the center of AI for Science & Research. The team first asked Claude to replicate their decade-old numerical calculations. Once it succeeded, they posed the core challenge: prove why a + b = 1.
According to the researchers, Claude returned the initial idea for a proof correctly within a short time. However, the AI made errors during the proof process that required multiple rounds of checking and correction. The human team used the AI's core intuition to fix mistakes and fill logical gaps, completing the final proof themselves.
"The answer was already there; we just hadn't seen it," Zamponi said.
The proof revealed that two seemingly different theoretical descriptions of jamming are linked by the same underlying physical law. The team also noted that the actual explanation turned out simpler than expected. "We had expected that proving the relationship would lead to a deeper understanding of a new mathematical structure or equations," they said.
The work illustrates how AI can act as a collaborative tool for hypothesis testing and mathematical proof, fitting into broader trends in research automation that complement rather than replace human insight.
Why this matters for science and research
For working scientists, this case underscrores a practical model: AI can propose ideas, but human judgment is still essential to validate, correct, and complete them. The paper offers a concrete reference for teams evaluating where to insert generative AI into their own research pipelines. It also shows that expertise remains critical - the researchers didn't simply accept Claude's output; they interrogated it, combined it with domain knowledge, and drove the work to a publishable conclusion.
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