AI in Scientific Research and Mathematics: From IMO Perfect Score to Conjecture Disproof, AI Accelerates Penetration into Scientific Frontiers

Recent breakthroughs in AI research and mathematics have drawn widespread attention.

Mathematical Conjecture Disproved: Claude Fable 5 Finds Counterexample to Jacobian Conjecture

In July, Anthropic mathematician Levent Alpoge announced on Twitter that the large model Claude Fable 5 had found a counterexample to the Jacobian conjecture. Proposed in 1939 and listed in Stephen Smale's "Mathematical Problems for the 21st Century," the conjecture had long remained unsolved. Alpoge's polynomial mapping satisfies the conjecture's premise (Jacobian determinant constant -2) but maps three distinct points to the same image, directly disproving it. The tweet received over 5 million views, and multiple mathematicians have verified the result using Wolfram Alpha. However, the result has not yet undergone formal peer review.

AI Solves Erdős Problem: One Page Surpasses 44-Page Top Journal Paper

Mathematician Thomas Bloom confirmed that GPT-5.6 Sol, prompted by mathematician Korsky, solved the third question of Erdős Problem #119 (with a $100 prize) using just one page of harmonic analysis techniques, outperforming a 44-page paper by Beck published in 1991 in the Annals of Mathematics. Bloom commented that AI discovered a detour humans could have avoided. Additionally, GPT-5.6 Sol produced a complete proof of the Cycle Double Cover Conjecture in under an hour.

2026 IMO: Chinese Team Wins All Golds, GPT-5.6 Pro Scores Perfect on First Try

The 67th IMO was held in Shanghai. The Chinese team defended its first-place title with 232 points, all six members winning gold, including perfect scores by Deng Leyan, Liu Che, and Zhang Bailun. GPT-5.6 Pro, without human assistance, solved all six problems on its first attempt. OpenAI provided ChatGPT Pro subscriptions to all gold medalists.

AI4S Competitions and Platforms: Driving Autonomous AI Research

The 4th World Scientific Intelligence Competition was held in Shanghai, debuting the AI4S Agent CNS Challenge, which tests the full-process autonomous capabilities of research agents. Concurrently, the Shanghai AI Laboratory released the "Shusheng·Duanyan" scientific discovery platform, building a closed loop of dry and wet experiments; the Shanghai Artificial Intelligence Institute released the multimodal scientific foundation model "Shenzhen" (11B parameters), covering six data types including DNA, RNA, and proteins; and Zhongke Wenge released the S1-Omni unified reasoning model, surpassing GPT-5.5 and Claude Science in blind tests.

ARC-AGI-3 Nearly Cracked: Harness Makes AI Think Like a Physicist

The [schema] agent framework developed by the Berkeley team, combined with Claude Opus 4.8 and Fable 5, achieved 98.98% RHAE on the ARC-AGI-3 public set. The framework implements an interpretable, verifiable, and searchable reasoning loop by writing world models as executable programs. ARC Prize President Greg Kamradt acknowledged the approach but raised questions about some testing methods.