Two Italian physicists who had been stuck for years on a mathematical physics problem used Claude to unlock their thinking. The initial demonstration by the AI was riddled with mistakes — but its underlying approach led the researchers to a solution that was “conceptually simple” that they simply hadn’t seen. The results are published in the Journal of Statistical Mechanics.
What you will learn
- What the jamming problem in granular materials physics is — and why its mathematical proof had resisted since 2014
- How Claude proposed a fundamentally correct lead despite numerous errors in its demonstration
- What this episode reveals about the true value of AI in mathematics — and its current limits
A Decade Without a Proof
In 2014, Giorgio Parisi — Nobel Prize in Physics 2021 — and Francesco Zamponi of Sapienza University in Rome mathematically described the jamming phenomenon, the process by which a granular material such as a ball-pool becomes suddenly rigid as its density increases — somewhat like a particle traffic jam.
In their calculations, one observation stood out: the sum of two key parameters of the model was always equal to one. “The result appeared clearly from the outset in the numerical computations, but no one could explain its validity,” notes the press release accompanying the study. For ten years, researchers sought a rigorous mathematical proof of this relation, convinced that a deeper structure lay behind its apparent simplicity.
Claude as a “Fresh Look”
Facing this impasse, Parisi and Zamponi decided to submit the problem to Claude. They first asked the AI to reproduce their numerical calculations, then challenged it to prove that the sum of the two parameters is always equal to one.
The first demonstration provided by Claude “contained errors and required several cycles of verification and revision.” But the underlying approach looked promising. The researchers pursued this path and arrived at a surprisingly simple proof.
“Claude quickly proposed an initial idea that was fundamentally correct,” says Zamponi. “The answer was right before our eyes, and we simply hadn’t seen it.”
Why Had the Experts Not Seen This Solution?
In their paper, Parisi and Zamponi admit that it is “hard to say” why they had overlooked it. The answer seems to hinge on a cognitive bias: they “were looking for something deeper” and had neglected a more “conceptually simple” case, toward which Claude’s hint directed them.
That is precisely where the value of AI, as identified by Will Sawin, a Princeton mathematician, comes into play in an interview with Gizmodo: AI is effective at exploring scientific literature and identifying patterns that human eyes might miss — not by generating wholly new ideas, but by proposing angles that experts might overlook due to their own assumptions.
The AI did not solve the problem on its own. It provided direction; the experts performed verification, correction, and formalization. A collaboration model that could become standard in scientific research.
