# Shanghai AI Lab’s Shusheng‑S2 aids reported proof of three‑dimensional Ghys conjecture

Digest AI · Research · published 2026-10-17T09:20:37Z

Canonical: https://digestai.news/story/shanghai-ai-labs-shushengs2-aids-reported-proof-of-threedimensional-gh

## Summary

Mathematicians in China have reported a computer‑checked proof of the three‑dimensional case of the Ghys conjecture, a problem first posed in 1995. The effort combined expert judgement with Shanghai Artificial Intelligence Laboratory’s Shusheng‑S2 model. Over seven rounds of reasoning the model explored multiple routes, generated detailed arguments, and helped the team identify promising ideas while discarding dead ends.

The work was led by Great Bay University professor Xu Disheng. A separate team at Peking University translated the paper’s four main theorems into a form that Lean, a formal verification system, could check step by step. The Lean checks passed, and independent experts confirmed that the formal statements matched the published paper. The preprint and verification code have been posted on arXiv, allowing others to examine the proof.

The collaboration illustrates how human‑AI teams can tackle long‑standing mathematical puzzles, offering a template for future formal‑verification projects that blend domain expertise with advanced reasoning models.

## Key points

- Shusheng‑S2 model participated in seven reasoning rounds to aid the three‑dimensional Ghys conjecture proof
- Proof was formally verified with Lean and confirmed by independent experts; code released on arXiv
- Research led by Prof. Xu Disheng (Great Bay University) with Peking University translating theorems

## Why it matters

Demonstrates that AI models can meaningfully contribute to deep mathematical research, accelerating proof development and verification for problems that have resisted resolution for decades.

## Sources

1. [Shanghai AI Lab’s Shusheng-S2 helps develop a proof for a decades-old problem in chaos theory](https://goodnewsdigest.app/stories/human-ai-team-reports-proof-for-a-decades-old-chaos-puzzle-3df02243) (goodnewsdigest.app, 2026-10-17)

## Cite

Digest AI, "Shanghai AI Lab’s Shusheng‑S2 aids reported proof of three‑dimensional Ghys conjecture", 17 October 2026, https://digestai.news/story/shanghai-ai-labs-shushengs2-aids-reported-proof-of-threedimensional-gh

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