Nobel Prize-winning Physicist and Team Use AI to Crack Decades-Old Math Puzzle

A team of researchers, led by Nobel laureate Giorgio Parisi and collaborator Francesco Zamponi, has made a significant breakthrough in solving a long-standing mathematical problem. The solution was found using the generative artificial intelligence (AI) tool Claude, developed by Anthropic. This achievement marks a major milestone in understanding the physics of ‘jamming,’ a phenomenon that had been puzzling researchers for over a decade.

The concept of jamming refers to the sudden transition from a fluid system to a rigid-but-disordered one. To illustrate this idea, imagine a pool table covered with billiard balls. As more and more balls are added, the table eventually becomes congested, and each ball is securely held in place by its neighbors. This disordered, completely frozen situation is known as a jammed state.

The study authors had previously mathematically described jamming and offered numerical solutions in a 2014 paper. However, they noticed that two parameters, $a$ and $b$, would mysteriously always add up to 1. The researchers were puzzled by this relationship and struggled to find an explanation for it.

In separate work, physicist Matthieu Wyart took a different approach but arrived at the same relation. This suggested that entirely new physical concepts were needed to link their work with Wyart’s and explain why $a+b=1$. Despite efforts over the past decade, no progress had been made in finding these new concepts or understanding the reason behind this relationship.

Parisi, who won the 2021 Nobel Prize in physics, decided to revisit the problem. He turned to Anthropic’s Claude AI tool, which he believed could offer a fresh perspective on the issue. After successfully reproducing the 2014 numerical result using Claude, Parisi prompted the AI to prove why $a+b=1$. The initial output contained some errors that required revision, but the fundamental idea was correct.

The researchers were surprised when they found that the solution was hidden directly within the equations themselves. They didn’t need any external physical assumptions or deep connections between functions. This achievement highlights the potential of AI in providing instant access to a vast repository of mathematical training and formal skills that may lie outside one’s usual domain.

Zamponi, who collaborated with Parisi on this project, noted that it is possible for a pure mathematician working full-time on such equations might have spotted the solution. However, he emphasized how Claude gave them instant access to these skills, which they couldn’t see themselves. Zamponi also acknowledged that interacting with AI forces him to reconsider his definitions of reasoning, intuition, and creativity.

The team’s experience with Claude has sparked a new approach to problem-solving in physics. They are now applying this collaborative method to another challenging problem involving the ‘random sequential addition of hard hyperspheres.’ While the AI significantly accelerates writing and optimizing code, Zamponi emphasized that human guidance remains indispensable at least in this case.

The solution to the jamming problem has been published in the Journal of Statistical Mechanics: Theory and Experiment. The study’s authors hope that their work will contribute to a deeper understanding of complex systems and inspire further research in the field.