Their solution, described July 1 in the Journal of Statistical Mechanics: Theory and Experiment, came about when the physicists chose to revisit a problem they thought they had attempted to solve exhaustively within a topic they knew intimately. This concept, known as jamming, refers to the sudden transition from a fluid system to a rigid-but-disordered one.
The study authors — Giorgio Parisi, winner of the 2021 Nobel Prize in physics, and Francesco Zamponi, both physicists at the Sapienza University of Rome — and collaborators had mathematically described jamming and offered numerical solutions in a 2014 paper. In the process, they noticed that two parameters — $a$ and $b$ — would mysteriously always add up to 1.
Moreover, separate work by Matthieu Wyart, a physicist at the Swiss Federal Technology Institute (EPFL), took a completely different approach but yielded the same relation. For Zamponi and colleagues, this suggested "entirely new physical concepts" were needed to link their and Wyart's work and simultaneously explain why $a+b=1$.
The researchers prompted Claude 40 times in order to get a publishable solution to the jamming problem. (Image credit: NurPhoto via Getty Images)
"Giorgio initially sent me Claude's output while I was traveling, so I ended up reviewing it on an airplane," Zamponi recalled. "As I read through the LaTeX file Claude generated, it became immediately clear that the core idea was correct … That moment significantly shifted my perspective on what these models can achieve in theoretical physics."
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Whether Claude simply trawled the vast mathematical literature and used pattern matching to find a way to solve their problem or if it applied something akin to creativity is, for Zamponi, moot because they "could not see the path forward, and Claude did," he said. And although he admitted that interacting with AI forces him to reconsider his definitions of reasoning, intuition, and creativity, Zamponi will continue to collaborate with the technology to speed up mundane tasks and provide fresh perspectives on challenging problems.
Now, Zamponi is applying this collaborative approach to a problem involving the “random sequential addition of hard hyperspheres," he said. “It is another excellent case study because, while the AI drastically accelerates writing and optimizing code, I have had to provide the vast majority of the conceptual ideas, which suggests that human guidance remains indispensable, at least in this case."
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