Researchers at La Sapienza University in Rome have successfully proven a decade-old mathematical conjecture regarding the physics of jamming, marking a notable milestone in human-AI scientific collaboration. The breakthrough, detailed in a recent publication in the Journal of Statistical Mechanics: Theory and Experiment, was achieved through a partnership between Nobel laureate Giorgio Parisi, theoretical physicist Francesco Zamponi, and the artificial intelligence model Claude. Jamming describes the abrupt transition of disordered systems, such as foams or granular materials, from a fluid-like state to a rigid one. Since 2014, Parisi and Zamponi had observed a striking numerical anomaly within their theoretical framework: two distinct mathematical parameters consistently summed to exactly one. While computational simulations verified the relationship with high precision, a formal proof remained elusive. The simplicity of the relation contrasted sharply with the researchers' expectations, leading them to suspect it masked a deeper, undiscovered mathematical symmetry. For years, the problem persisted as an unsolved puzzle in statistical physics, also informing models in neuroscience and machine learning. Recognizing the potential of large language models for formal reasoning, Parisi initiated the collaboration by tasking Claude with replicating the group's original numerical calculations from over a decade prior. Following successful reproduction, the researchers prompted the system to derive a mathematical proof for the relationship. Claude quickly generated an initial framework that, despite containing minor errors, captured the essential logic required for the solution. Parisi and Zamponi then engaged in iterative verification and correction, refining the AI's output into a complete, rigorous proof. The final result revealed that the underlying mechanism was far more straightforward than anticipated, dispelling the long-held assumption of hidden complexity. The proven conjecture formally establishes the equivalence between Parisi’s theoretical approach and an independent framework developed by physicist Matthieu Wyart and his team, confirming that both methodologies yield identical physical laws for jammed systems. Beyond resolving a specific mathematical problem, the study demonstrates the practical utility of generative AI in advanced theoretical research. By automating the reconstruction of complex derivations and proposing structural insights, the AI accelerated a process that human researchers had struggled to formalize for years. This collaboration underscores a shifting paradigm in scientific discovery, where artificial intelligence serves as a rigorous computational partner capable of validating and illuminating foundational physical theories.