A long-standing mathematical problem in physics has been solved through a unique partnership. Two theoretical physicists worked with an artificial intelligence system.
Giorgio Parisi, a Nobel Prize winner, and Francesco Zamponi, a physicist at LaSapienza University of Rome, published their findings in the Journal of Statistical Mechanics: Theory and Experiment. They showed how the AI model Claude helped prove a mathematical relationship that had stumped researchers for years.
This achievement highlights how AI is changing research.
Understanding Jamming
In physics, "jamming" describes when particles form a "traffic jam." A liquid system suddenly becomes stiff but stays disorganized. This idea first described materials like foams and granular matter. Now, it's used in fields like neuroscience and AI.
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Start Your News DetoxIn 2014, Parisi, Zamponi, and their team created a theory for jamming. They found a surprising link: two mathematical parameters, 'a' and 'b', always added up to one. Numerical tests showed this with great accuracy.
The Elusive Proof
Zamponi explained that this relationship leads to the same physical laws found by French physicist Matthieu Wyart. Wyart developed a different theory for jamming around the same time. This means two very different ways of describing jamming actually reach the same conclusions.
The numerical results were clear from the start. But no one could explain why it was true. For years, researchers tried to find a mathematical proof. They believed a deeper structure of the theory was hidden behind its simple appearance.
Claude's Contribution
After many failed attempts, the problem faded for most. But it still bothered Parisi. "It really bothered him that we had never managed to prove it," Zamponi recalled.
When generative AI models appeared, Parisi saw this old problem as a perfect test. They chose Claude because it "seemed to have somewhat more advanced mathematical reasoning abilities," Zamponi said.
The problem was well-defined: a clear guess, fairly simple math, and an answer known numerically but never formally proven.
Parisi first asked Claude to redo the numerical calculations from a decade earlier. This was to see how well it could handle a real math problem.
Once Claude could reproduce the result, the next question was natural: If a+b equals one, can you prove why?
"Quite quickly, Claude came up with an initial idea that was essentially correct," Zamponi noted.
The proof still had errors and needed several rounds of checks and changes by the physicists. But the core idea was right.
The surprise wasn't just the AI's result. For years, researchers looked for a deep explanation, hoping for a new math structure or unknown symmetry. "We were hoping this would reveal some new understanding of the equations," Zamponi explained.
Instead, the solution was much simpler. "The answer was right there, and we simply hadn't seen it."
The proof confirms that two different theoretical approaches to jamming, developed independently, do lead to the same physical laws.
Deep Dive & References
A proof of an identity for the critical exponents of jamming - Journal of Statistical Mechanics: Theory and Experiment, 2026
