AI Refutes Century-Old Math Conjectures but Lacks Ability to Invent New Theories; World Models May Be Key

On July 29, three American mathematicians uploaded a paper titled 'Maxwell's Conjecture Is Wrong' to arXiv, constructing a counterexample that overturns this classical physics conjecture. The acknowledgments show that the core idea came from GPT-5.6 Sol. They constructed a 'five-charge triangular bipyramid' and found at least 24 non-degenerate equilibrium points, far exceeding the upper bound of 16 set by the conjecture.

Earlier, on July 20, an Anthropic number theorist announced the refutation of the Jacobian conjecture with Claude Fable 5, and Terence Tao subsequently used ChatGPT to follow up and publicly verify the process. On July 24, at the International Congress of Mathematicians, he warned that the mathematical community is entering an era of 'proof surplus' rather than 'proof scarcity.'

Amid the wave of AI-assisted scientific discovery, a position paper titled 'Large Language Models Cannot Jump' by Tom Zahavy, a Google DeepMind researcher and core developer of AlphaProof, written in January 2026, has been widely circulated. He uses Peirce's trichotomy to divide reasoning into deduction, induction, and abduction, pointing out that abduction is the only form of reasoning that can generate new premises and is currently a shortcoming of large models.

He cites Einstein's 1907 thought experiment of imagining free fall to propose the equivalence principle as an example, explaining that such 'embodied simulation' relies on bodily sensations, whereas large language models are like 'high-dimensional Chinese rooms,' capable of processing physical language but lacking a sensory channel for physical objects. Therefore, he argues that AI needs to build physically consistent world models to achieve the 'jump.'

Taking the falsification of Maxwell's conjecture as an example, AI proposed a geometric configuration based on existing frameworks, but it did not invent a new theory or question the system of assumptions. Therefore, according to Zahavy's classification, it still falls within the category of efficient exploration under deduction. However, AI's suggestion was a direction that the mathematical community had not attempted in 150 years, so it cannot be simply reduced to symbolic search.

Zahavy himself acknowledges that induction, deduction, and abduction are intertwined in practice. He responded that his article does not claim 'LLMs are a dead end,' but rather explores what AI still lacks to achieve Einstein-level discoveries.

The 'Einstein Test' proposed by Google DeepMind chairman Hassabis shows that today's systems cannot independently derive general relativity under limited knowledge. Zahavy's paper proposes 'embodied simulation' approaches such as world models as a solution.

Regarding the sim-real gap, there are three paths: robotics provides real physical experience, world models provide high-fidelity digital simulations, and AlphaEvolve uses evolutionary code generation to bypass 'physical intuition.' These three paths are converging: the robotics route uses world models as training environments, and evolutionary search also uses world models to replace offline experiments.