IT Home, October 15: The Shanghai Artificial Intelligence Laboratory announced today that the three-dimensional Ghys conjecture, a world-class mathematical problem that has puzzled the field for over 30 years, has been solved.
The team led by Professor Xu Disheng, a visiting scholar at the Shanghai Artificial Intelligence Laboratory and a professor at the Greater Bay Area University, leveraged the Shuwen-S2 multimodal large model and followed a "integration of general and specialized knowledge" approach to achieve the proof of the three-dimensional Ghys conjecture through human-machine collaboration.
Professor Dong Bin and Academician Liu Ruochuan’s team from Peking University used their developed SHEAF framework to perform formal verification of this proof, confirming its correctness. This marks the first time Chinese scientists have solved a world-class mathematical problem using a Chinese large model.
The Ghys conjecture, proposed by French mathematician Étienne Ghys in 1995, posits that every holomorphic Anosov system on a compact complex manifold is biholomorphically conjugate to a holomorphic affine automorphism on some complex infra-nilmanifold. This problem, due to its theoretical difficulty and landmark significance in the field, is widely regarded by experts in dynamical systems as one of the most important long-standing open problems and serves as a litmus test for mathematical reasoning ability.
The related paper has been published on the preprint platform arXiv, and its formalized code is also publicly available on GitHub. Links provided by IT Home are as follows:
https://github.com/frenzymath/HolomorphicAnosov
The Shanghai Artificial Intelligence Laboratory stated that the significance of this research also lies in validating a new scientific paradigm. Traditional mathematical research relies on the prolonged, individual efforts of genius minds, whereas this breakthrough systematically integrates expert intuition into machine-solving loops, creating a closed loop of “systematic exploration—expert judgment—outcome accumulation—feedback refinement.” This paradigm can be replicated and scaled to other fundamental research areas characterized by vast search spaces and scarce expert knowledge, enabling more original “zero to one” breakthroughs.
Next, building on the complete capability loop established in this study, the team will further encapsulate the mathematical verification module into the Shengwen·Duanyan Scientific Discovery Platform for direct reuse in future scientific research. Meanwhile, leveraging the breakthrough on the three-dimensional Ghys conjecture as a starting point, the Shanghai Artificial Intelligence Laboratory will extend its accumulated reasoning capabilities to other disciplines with mathematically analogous structures. Upon achieving new breakthroughs, these enhanced reasoning capabilities will be encapsulated back into the Duanyan platform for reuse, integrated with additional disciplines to seek the next round of breakthroughs, forming a self-evolving flywheel of “breakthrough — encapsulation — reuse — further breakthrough.”