Chinese AI Solves 30-Year-Old 3D Ghys Conjecture

Overview

Chinese researchers have announced the full proof of the 3D Ghys conjecture, resolving a major mathematical puzzle that has challenged scientists for over three decades. The achievement marks a significant milestone in the intersection of artificial intelligence and pure mathematics, demonstrating that domestic large-scale AI models can handle problems of exceptional theoretical complexity.

Led by Professor Xu Disheng of Greater Bay University and a visiting scholar at the Shanghai Artificial Intelligence Laboratory, the team collaborated with the lab's Intern-S2 science large model. This partnership produced a complete, rigorous proof of the conjecture, marking the first time Chinese scientists have relied on a homegrown AI system to crack a problem of this magnitude.

The result has been released on an international preprint platform, with all verification code open-sourced for global peer review. Independent mathematicians from Peking University have already validated the work, confirming that the proof is logically sound and free of gaps.

"This is a landmark moment where artificial intelligence transitions from being a computational tool to becoming a genuine partner in fundamental scientific discovery."

The Challenge of the Ghys Conjecture

First proposed in 1995 by French mathematician Étienne Ghys, the conjecture sits at the heart of complex dynamics and the study of chaotic systems. It specifically addresses the behavior of Anosov systems—dynamical systems characterized by strong structural stability and chaotic stretching, such as the classic Arnold cat map.

For more than 30 years, the conjecture remained an unsolved world-class problem, baffling the international mathematics community due to its extreme reasoning difficulty. While a real-number counterpart to the problem still remains open globally, the 3D version was considered a critical benchmark for testing advanced mathematical reasoning capabilities.

The core challenge involves untangling long-chain derivations across high-dimensional spaces. Traditional human-led approaches often stall when the number of variables and interaction paths grows beyond manageable limits. This is precisely where the structural limitations of manual calculation become apparent, necessitating new methodologies for progress.

AI-Driven Collaboration Model

The breakthrough was achieved through a novel collaborative framework between human experts and the Intern-S2 science large model. Rather than treating AI as a simple calculator, the research team utilized it as an active reasoning partner capable of navigating massive search spaces in mathematical logic.

The division of labor was strategically designed to leverage the strengths of both parties:

• AI Capabilities: The Intern-S2 model handled large-scale, long-chain, and highly complex mathematical derivations. It explored thousands of potential proof paths, identifying patterns and logical bridges that might remain invisible to human observers.
• Human Direction: Professor Xu and his team steered the overall strategic direction, screening out unpromising lines of reasoning and validating the theoretical integrity of the AI's suggestions.
• Iterative Refinement: The process involved multiple rounds of iterative interaction. The AI generated hypotheses, the researchers critiqued and refined them, and the cycle repeated until a coherent, rigorous proof emerged.

This hybrid approach proved essential. The conjecture required not just raw computational power, but deep conceptual understanding to ensure that every step in the derivation adhered to strict mathematical axioms. The AI accelerated the exploration of possibilities, while the human researchers provided the necessary oversight to maintain logical rigor.

Independent Verification and Open Science

A critical component of this achievement is the emphasis on verifiability. In an era where AI-generated proofs can sometimes suffer from "hallucinations" or subtle logical errors, the team prioritized independent validation.

A separate verification team from Peking University, led by Liu Ruochuan (an academician of the Chinese Academy of Sciences) and Professor Dong Bin, undertook the task of formally verifying the proof. Using a self-developed framework and massive parallel computing powered by AI agents, they generated hundreds of thousands of lines of verification code.

The verification process confirmed that:

1. All core theorems within the proof are logically complete.
2. There are no gaps or unstated assumptions in the derivation chain.
3. The entire argument is fully valid under standard mathematical axioms.

This independent audit serves as a robust check against potential AI errors, setting a new standard for how AI-assisted mathematical discoveries should be published and reviewed.

"The open-sourcing of the verification code ensures transparency and allows the global community to scrutinize every line of logic, reinforcing trust in AI-assisted scientific breakthroughs."

Implications for Future Research

The successful resolution of the 3D Ghys conjecture has far-reaching implications for the field of computational mathematics. It demonstrates that large AI models can assist in solving problems previously thought to be beyond the reach of automated reasoning systems.

Key takeaways from this study include:

• Scalability of AI Reasoning: The Intern-S2 model proved capable of handling multi-step, high-complexity logical chains, suggesting that current AI architectures can be refined for deeper theoretical work.
• Human-AI Synergy: The project highlights the importance of keeping humans in the loop. AI excels at exploration, but human expertise is indispensable for guidance, validation, and conceptual framing.
• Open Science Standards: By releasing both the proof and the verification code, the researchers contribute to a culture of openness that accelerates future discoveries.

The real-number counterpart of the Ghys conjecture remains an open problem, and the methods developed here may provide the roadmap for its eventual solution. As AI models continue to evolve, their role in fundamental science is likely to expand from data analysis to active hypothesis generation and proof construction.

This achievement underscores China's growing influence in both AI development and high-level mathematical research, signaling a shift toward domestically developed tools addressing global scientific challenges.