Chinese AI Proves Ghys's Conjecture: 30-Year Mathematical Problem Solved by Locally Developed Neural Network

A group of Chinese researchers led by Professor Xu Disheng from the Greater Bay Area University and the Shanghai Artificial Intelligence Laboratory has presented a proof of French mathematician Étienne Ghys's conjecture for the three-dimensional case. Formulated in 1995, the problem had remained unsolved for over three decades and was considered one of the key open problems in the theory of dynamical systems. The work utilized the Intern-S2 large language model created by the Shanghai AI Laboratory—marking the first recorded instance of Chinese scientists successfully solving a world-class mathematical problem using a locally developed neural network.

The Essence of the Conjecture and Its Significance for Mathematics

Étienne Ghys's conjecture, proposed in 1995, addresses a fundamental question in the theory of dynamical systems: whether the behavior of chaotic dynamical systems can uniquely determine their geometric classification. For over 30 years, this problem remained unsolved and served, in the words of experts, as a kind of "benchmark test" for evaluating artificial intelligence's mathematical reasoning capabilities. The successful proof of the three-dimensional case, as the researchers note, is not merely a solution to a specific problem, but a demonstration that AI is capable of working in the field of advanced fundamental research, rather than just applied or routine tasks.

How the Intern-S2 Model Worked: Full Cycle from Reasoning to Verification

During the project, the Intern-S2 model executed a full cycle of research tasks: from logical reasoning and human interaction to formal verification. The neural network performed large-scale recursive reasoning, conducted iterative searches, analyzed relevant scientific literature, broke down the statement into separate subtasks, and simultaneously explored various proof options. Meanwhile, scientists set the general direction of work, evaluated the significance of intermediate results, and determined promising solution paths. The model verified logical steps and rapidly tested numerous potential ideas, while researchers applied their professional expertise to refine the proof structure, make key decisions, and provide feedback to guide the model's further work. According to the authors, the breakthrough was the result of precisely this hybrid approach, combining the universal and specialized capabilities of AI with human expert competence.

Formalization of the Proof: The Role of Peking University

The formalization of the obtained proof was carried out by two independent research groups from Peking University using the SHEAF system they developed. This stage is critically important: in mathematics, a proof is considered definitively confirmed only after strict formalization that excludes any informal assumptions. The successful completion of formalization by two groups enhances the credibility of the result and distinguishes it from purely "textual" proofs, which may contain hidden logical gaps not detected during informal reading.

Scientific Research Platform and Applied Potential

The Shanghai AI Laboratory plans to package the described workflow as a reusable mathematical verification module for its scientific research platform. The platform integrates the Intern-S2 large language model, AI agents, databases, and actual experimental equipment. As part of one project, this platform has already helped reduce the development cycle in electrochemical synthesis from five to ten years down to one to two years. According to the scientists, this approach is applicable to physics, chemistry, biology, and related disciplines where AI accelerates trial-and-error solution searches and expands the boundaries of human thinking. The researchers are confident that the role of AI models will only grow: they are capable of taking on large-scale, routine, and branched tasks—conducting verification calculations, analyzing scientific literature, breaking down hypotheses into subtasks, and verifying individual research stages.

Context: OpenAI Statements and Debates in the Scientific Community

Recently, OpenAI announced similar achievements, stating that its AI solved the problem of the existence and smoothness of solutions to the Navier-Stokes equations, as well as over 100 other open mathematical problems. However, these statements sparked debates in the scientific community. Twenty-five Fields Medalists issued a warning about the risks to mathematical research associated with over-reliance on AI proofs. Later, scientists discovered discrepancies between OpenAI's textual proof and its formalized version, although, as noted, this does not in itself disprove the result. Against this background, the formalization of the Chinese proof by two independent Peking University groups via the specialized SHEAF system looks like a more rigorous and reproducible validation protocol.