Nobel physics laureate Giorgio Parisi and physicist Francesco Zamponi proved, with help from the AI model Claude in 2026, the jamming critical-exponent identity a+b=1 that had held numerically for more than ten years without a proof, publishing the result in the Journal of Statistical Mechanics: Theory and Experiment (JSTAT). When the two physicists built their jamming theory in 2014, they noticed that the two exponents a and b always summed to exactly one, yet they were never able to prove why, and Claude filled that gap.

What Was Proved: Why a and b Always Sum to One

Jamming is the phenomenon in which a system of particles that once flowed like a fluid abruptly becomes rigid while staying disordered, which Parisi and Zamponi liken to a kind of traffic jam among particles. In 2014, they and their collaborators built a theory of jamming and found in numerical calculations that two critical exponents, a and b, always added up to exactly one. The values matched with striking precision, but there was no mathematical proof of why. The identity remained an open problem backed only by strong numerical evidence for over a decade.

What this work supplied is precisely that proof. It did not discover a new phenomenon; it formally confirmed that a long-suspected equation is true.

What Parisi Asked Claude to Do: Reproduce First, Prove Second

Parisi opened the collaboration with a verification step, first asking Claude to reproduce the group's own numerical calculations from more than a decade earlier. Once Claude succeeded, the researchers posed the next question: if a and b sum to one, can you also prove why. Zamponi reported that "quite quickly, Claude came up with an initial idea that was essentially correct."

The team chose Claude because its mathematical reasoning ability seemed comparatively more advanced. Reflecting on the result, Zamponi said, "The answer was right there, and we simply hadn't seen it." The model pointed to a connection that humans had missed despite years of effort.

Why This Is Completion, Not Discovery, and Why That Matters

The Parisi-Zamponi proof is a completion-type contribution rather than a discovery-type one, which sets it apart from many recent AI mathematics headlines. The earlier headline results were mostly discovery-type, where a model generated on its own a construction or counterexample that humans did not know. This one is closer to a completion-type, filling in a relation that humans already strongly believed by supplying a proof. The answer was effectively known; what was missing was the argument leading to it.

That distinction is subtle but consequential. In discovery mode, the model's creativity takes center stage; in completion mode, how far the humans have already narrowed the problem largely decides success. A Nobel laureate aimed at a precise target, first cleared a trust-building replication step, and only then asked for a proof. That sequence is half the result. As tools grow more capable, the skill of designing the question grows more decisive.

Reading the Numbers and the Narrative: Errors and Rounds of Verification

The initial proof from Claude was imperfect, containing errors that required several rounds of verification and revision by the authors before it reached final form. The summary version reads easily as "AI solved a 10-year problem," but the actual process was messier and, for that reason, more honest. The model quickly offered a seed pointed in the right direction, but shaping it into a publication-grade proof was the repeated labor of human physicists.

Blurring this point distorts the story. The value here is not "the model proved it alone" but "the model sharply reduced the human search cost." Idea generation was accelerated while the burden of verification stayed with people, a structure consistent with other recent AI-mathematics collaborations.

Two Theories Met in One Place: Agreement with Wyart's Approach

The proved identity a+b=1 leads to the same physical laws produced by a separate theoretical approach that French physicist Matthieu Wyart (EPFL, Lausanne) developed independently at roughly the same time. That two theories starting from different premises ultimately point to the same physics is now formally confirmed by this proof.

This also serves as an independent cross-check that strengthens confidence in the result, since the model did not merely conjure a plausible-looking equation by chance but landed on something that matches a theory built along a completely different path.

Implications for Research Practice

First, using a general-purpose LLM as a tool for calculation replication and idea generation while keeping final verification in the researcher's hands becomes a realistic template, and Parisi's step of first replicating old calculations to establish trust is worth adopting as a benchmark. Second, questions of credit allocation grow sharper: how to describe contributions between a model that produced a seed idea and humans who completed the proof becomes a matter of academic convention. Third, accurately documenting such cases, clearly separating what the model did from what humans did, is itself a citable asset that remains scarce.

The Open Question: Even the Model Version Was Not Disclosed

The most notable gap is reproducibility. Neither the public press materials nor the main coverage specify exactly which Claude model and version were used. Whether a third party could reproduce the result with the same prompts and the same procedure is unconfirmed. What the errors in the model's initial proof were, and where things diverged, is also hard to know from outside the paper.

This achievement is a clear example that AI can be a substantive collaborator in mathematics and physics research. For that collaboration to rest on reproducibility, a basic tenet of scientific method, the practice of recording which model did what, and how, must take hold alongside it.

References: Parisi & Zamponi et al., "A proof of an identity for the critical exponents of jamming", Journal of Statistical Mechanics: Theory and Experiment (2026) · phys.org report · EurekAlert press release