The article chronicles how leading AI labs like OpenAI and DeepMind have leveraged large language models to crack decades‑old Erdős conjectures, turning a mathematician’s legacy of cash‑rewarded puzzles into a high‑stakes benchmark that reshapes research, community dynamics, and the future of mathematics.
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.
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.
DeepMind’s AlphaProof Nexus framework enabled an AI agent to automatically prove and verify nine long‑standing Erdős conjectures at a cost of only a few hundred dollars per problem, using a simple “think‑try” loop and a more advanced multi‑agent evolution architecture, and demonstrating a shift toward leveraging raw large‑model reasoning for formal mathematics.
