Peking University Team Tackles 35-Year-Old Queueing Theory Conjecture via Human-AI Collaboration

A Peking University research team successfully proved the uniqueness conjecture for BAR (Balanced Arrival Rate equations), a core tool in queueing theory that had remained unsolved for 35 years. BAR is considered the "master equation" for determining whether a queueing network reaches equilibrium. This breakthrough demonstrates the immense potential of human-AI collaboration in solving hardcore mathematical problems.

Key Details and AI's Limitations

During the exploration, AI demonstrated strong literature retrieval capabilities by discovering a key paper on pathwise-differentiability, allowing the team to condense a 150-page proof into 10 pages. However, AI also exposed systematic limitations: it tended to provide trivial examples. The crucial Harrison-Reiman class was identified by human researchers using professional intuition, as AI failed to independently discover this key structural property. Furthermore, even when provided with the correct subclass and the key paper, both ChatGPT 5.5 Pro and Claude Opus 4.8 completely failed to complete the proof independently in fresh conversations.

Controversies and Doubts

The team found that the original conjecture was actually mathematically incorrect; it had counterexamples in natural extensions and only held true within the Harrison-Reiman subclass. When attempting to prove it with GPT, the model repeatedly got stuck at a critical juncture. This specific stumbling block prompted the researchers to search for counterexamples, ultimately driving the research toward a genuine breakthrough.

Reactions

The author @2prime_PKU concluded that while AI will not replace mathematicians in the short term, human-AI collaboration has become a superpower for solving decades-old mathematical problems. The author also expressed gratitude to PhD student Youheng Zhu for feedback during the exploration.

2026-07-07 ~ 2026-07-07 · 7 related posts