Editorial illustration for AI startup solves Chen‑Gendron conjecture, cracks four unsolved problems
AI Startup Solves 4 Unsolved Math Research Problems
AI startup solves Chen‑Gendron conjecture, cracks four unsolved problems
Mathematicians just lost a job to a server rack. A stealth AI lab, Axiom, built a system called AxiomProver that solved five unsolved math problems. The biggest was the Chen-Gendron conjecture, a knotty problem in modern geometry that had resisted human intuition for years.
This isn't pattern recognition or a library search. The AI works in Lean, a formal language for stating and verifying proofs. It doesn't find answers.
It builds them, from first principles, in a logical structure it constructs itself. The result is a verifiable proof that exists because the machine willed it into being.
Ono says the AI-generated proof for the Chen-Gendron conjecture shows how AI can now meaningfully assist professional mathematicians. "This is a new paradigm for proving theorems," he says. Axiom's system is more than just a regular AI model, in that it is able to verify proofs using a specialized mathematical language called Lean.
Rather than just search through the literature, this allows AxiomProver to develop genuinely novel ways of solving problems. Another one of the new proofs generated by AxiomProver demonstrates how the AI is capable of solving math problems entirely on its own.
Ken Ono calls it a new paradigm. He's being polite. It's an invasion.
The system also cracked four other problems we hadn't solved, generating the solutions autonomously. The work is silent, cold, and correct. Mathematics has forever been a conversation among minds, a slow climb up a mountain of logic.
Now there's a drill. The terrain ahead looks different. We are no longer the only ones doing the looking.
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Common Questions Answered
How did GPT-5 help mathematician Ernest Ryu solve a 40-year-old optimization problem?
Ernest Ryu used GPT-5 to explore mathematical ideas faster and tackle an open problem in optimization theory involving the Nesterov Accelerated Gradient (NAG). The large language model helped Ryu quickly surface ideas and techniques from across a wide range of mathematical papers, potentially providing insights that could contribute to solving the longstanding question.
What makes GPT-5 different from earlier language models in mathematical reasoning?
Unlike earlier models like ChatGPT-3.5, GPT-5 demonstrated significantly advanced capabilities in mathematics, particularly in understanding and exploring complex mathematical problems. Ryu noticed that GPT-5 had matured to a point where it could potentially contribute meaningfully to solving open mathematical questions, which previous versions could not.
What specific mathematical challenge was Ernest Ryu investigating with GPT-5?
Ryu was exploring an open problem related to the Nesterov Accelerated Gradient (NAG), specifically questioning whether the extra momentum added to an algorithm affects its stability. His mathematical intuition suggested the problem might have a simple solution that had not yet been discovered by human researchers.
Further Reading
- AI and Proving Theorems — Mean Green Math
- AI Solves the World's Hardest Math Exam (Putnam 2025) — YouTube
- Mathematics with large language models as provers and verifiers — arXiv
- Putnam-AXIOM: A Functional & Static Benchmark for ... — ICML 2026
