Physicists Use Generative AI to Solve Decade-Old Jamming Problem

Physicists Giorgio Parisi and Francesco Zamponi used Anthropic’s Claude AI to solve a mathematical problem regarding jamming that had remained unresolved for over a decade. According to a July 1 report in the Journal of Statistical Mechanics: Theory and Experiment, the AI helped the researchers prove a specific mathematical relation, a+b=1, which describes how contact forces and gaps scale as a physical system reaches a critical jamming point.

Jamming occurs when a fluid system transitions into a rigid but disordered state. Francesco Zamponi, a physicist at Sapienza University of Rome, compared the concept to a pool table filled with billiard balls. When too many balls are added, the table becomes so congested that the balls are held securely in place by their neighbors, creating a frozen, disordered state.

The Decade-Long Struggle to Prove a+b=1

The problem began with a 2014 paper authored by Parisi, Zamponi, and their collaborators, which provided numerical solutions for jamming. During that research, the team observed that two specific parameters, labeled a and b, consistently added up to 1. However, they could not mathematically prove why this relation existed.

Parallel research by Matthieu Wyart of the Swiss Federal Technology Institute (EPFL) used a different methodology but arrived at the same a+b=1 result. Zamponi told Live Science that this consistency suggested the need for new physical concepts to link the two different approaches and explain the underlying cause of the relation.

Despite the shared result across different research paths, no progress was made on a formal proof for ten years. Parisi eventually decided to use generative AI to seek a new perspective on the equations.

How Claude AI Generated the Solution

Parisi utilized Claude by first prompting the AI to reproduce the numerical results from the 2014 study. Once the AI successfully replicated the data, Parisi asked the model to prove the a+b=1 relation.

The process required 40 prompts to reach a publishable solution. Zamponi recalled reviewing the resulting LaTeX file while traveling on an airplane and noting that the core idea was immediately correct.

While the initial AI output contained some errors that the physicists had to revise, the fundamental analytical solution was sound. The researchers discovered that the answer was hidden within the equations themselves and did not require external physical assumptions or deep connections between functions.

It is entirely possible that a pure mathematician who works full time on such[kind] of equations might have spotted the solution. But this is a particularly interesting point for us, as it highlights how Claude gave us instant access to a vast repository of mathematical training and formal skills that lay just outside our usual domain.
Francesco Zamponi, via Live Science

Implications for Theoretical Physics and AI

The collaboration has led Zamponi to reconsider his definitions of intuition and creativity. He told Live Science that whether the AI used pattern matching from existing literature or a form of creativity is irrelevant because the AI identified a path forward that the human researchers could not see.

Zamponi is now using a similar collaborative approach to study the random sequential addition of hard hyperspheres. He noted that while AI accelerates the writing and optimization of code, human guidance remains essential for providing the primary conceptual ideas.