Two physicists harnessed the power of artificial intelligence (AI) to tackle a complex mathematical issue in physics that has confounded researchers for over a decade.
The breakthrough, published on July 1st in the Journal of Statistical Mechanics: Theory and Experiment, occurred when the physicists revisited a problem they previously thought thoroughly examined: jamming. This phenomenon describes the abrupt shift from a fluid state to a rigid yet chaotic structure.
To grasp jamming, picture a pool table crowded with pool balls. As you add more balls, space diminishes, ultimately resulting in a scenario where each ball is trapped by its neighbors—this chaotic state is termed a jam.
Research authors, including Giorgio Parisi, a 2021 Nobel Prize in Physics winner, and Francesco Zamponi from Sapienza University, mathematically articulated jamming and provided numerical results. Their findings, detailed in a 2014 paper, uncovered a mysterious relationship where two parameters, $a$ and $b$, consistently sum to 1.
“The parameters $a$ and $b$ accurately define the forces of contact and the distribution of small gaps between the balls,” stated Zamponi. “Physical systems scale significantly when they encounter a major disturbance, and I was perplexed by my inability to mathematically prove $a+b=1$,” he remarked to Live Science.
Separately, Matthew Wyart, a physicist at the Swiss Federal Institute of Technology (EPFL), adopted a different methodology and also deduced the same relationship. This connection prompted Zamponi and his colleagues to explore the necessity of a “completely new physical concept” to explain the rationale behind $a+b=1$.
Despite a decade without progress in understanding these concepts or the reason for $a+b=1$, Parisi pondered if generative AI might shed new light. He collaborated with Claude from Anthropic, who successfully replicated the 2014 numerical findings. Parisi challenged the AI to elucidate why $a+b=1$.
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The researchers prompted Claude 40 times to produce a publishable solution to the jamming problem.
(Image credit: NurPhoto, Getty Images)
“Giorgio originally sent me Claude’s work while traveling. I reviewed it on the plane,” Zamponi recalls. “Upon reading Claude’s generated LaTeX file, it was evident that the fundamental idea was accurate. That moment transformed my outlook on the capabilities of these models in theoretical physics.”
While the initial output contained some errors requiring correction, the central concept remained sound. After just 40 prompts, the team achieved a validated, publishable analytical solution—remarkably found directly within the equation itself, without external assumptions or intricate function connections.
“A full-time mathematician could dedicate themselves to that research…” observed Zamponi. “This experience underscores how Claude provided us with immediate access to extensive mathematical training and formal expertise that resides just beyond our common understanding.”
To Zamponi, it is not a matter of debate whether Claude utilized vast mathematical resources through pattern recognition or exhibited a form of creativity. “We couldn’t envision a way forward, but Claude could.” Recognizing the need to reassess our definitions of reasoning and intuition, Zamponi remains committed to using this technology to enhance productivity and glean fresh insights on challenging topics.
Currently, Zamponi is employing this collaborative approach to address issues surrounding the “random sequential addition of hard hyperspheres.” “This represents another compelling case study. AI expedited code generation and optimization significantly, yet I contributed most of the conceptual ideas, affirming that human guidance is still crucial in this context.”
Source: www.livescience.com