The article reviews how AI systems—from OpenAI’s internal models to DeepMind’s agents—have begun solving longstanding Erdős problems, detailing specific breakthroughs, the iterative LLM methodology, and the emerging paradigm of AI‑augmented pure mathematics research.
An Anthropic AI model, Claude Fable 5, produced a concise counterexample that disproves the 87‑year‑old Jacobian conjecture, sparking worldwide reaction and highlighting both the mathematical breakthrough and the poignant story of Zhang Yitang’s seven‑year effort.
DeepMind’s AlphaProof Nexus, powered by Gemini 3.1 Pro and a Lean‑based proof‑checking loop, open‑sourced its code on GitHub and solved nine long‑standing Erdős problems—including a 56‑year‑old set—for only a few hundred dollars per theorem, while also proving 44 OEIS conjectures and advancing convex‑optimization theory.
A Princeton team’s Goedel‑Architect framework, built on the open‑source DeepSeek‑V4‑Flash model, uses a blueprint‑driven, parallel proof strategy to solve hundreds of formal mathematics benchmarks at a fraction of the cost of prior systems, highlighting a shift from proof scarcity to verification challenges in AI‑generated mathematics.
A 23‑year‑old without formal math training teamed with a Cambridge student and ChatGPT, solving the 60‑year‑old Erdős primitive‑set conjecture in 80 minutes, while traditional mathematicians had been stuck for decades, highlighting a radically different AI‑driven proof strategy.
DeepSeek‑Prover‑V2, an open‑source LLM specialized for Lean 4, bridges intuitive high‑level reasoning and strict formal verification through sub‑goal decomposition, dual operation modes, and a novel cold‑start data pipeline, achieving state‑of‑the‑art results on MiniF2F, PutnamBench and CombiBench while highlighting trade‑offs in inference cost and model scalability.
