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
The fledgling AI firm behind Axiom has just posted a set of results that would have been headline fodder a decade ago. In a single week the team announced proofs for the Chen‑Gendron conjecture and three other problems that have lingered on the research frontier without resolution. While most machine‑learning tools in mathematics still churn out conjectures or suggest heuristics, Axiom’s platform claims to go a step further: it not only generates candidate arguments but also runs them through a dedicated verification engine.
The company says the system’s “specialized m” module checks each logical step against formal standards, something that ordinary language models cannot do. Critics have long questioned whether AI could move beyond pattern matching to genuine mathematical insight. Yet the startup’s latest batch of proofs, released as open‑source code, appears to answer that doubt with concrete, peer‑reviewable artifacts.
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 m.
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.
Can a machine truly replace the intuition of a mathematician? The startup's claim of resolving the Chen‑Gendron conjecture and three other open problems rests on an AI system that not only generates but also checks proofs. According to Ono, the AI‑generated proof demonstrates that AI can now meaningfully assist professional mathematicians, and he calls the approach a new paradigm for proving theorems.
Yet the article provides no detail on peer review, leaving it unclear whether the broader community accepts the results. The system, described as more than a regular AI model because it incorporates a specialized verification module, appears to bridge generation and validation. Still, the lack of independent verification raises questions about reproducibility.
If the proofs withstand scrutiny, the episode could mark a notable step for computational assistance in pure mathematics; if not, the excitement may prove premature. At present, the evidence is limited to the startup’s announcement and a single endorsement, and further confirmation will be required before the claims can be fully evaluated.
Further Reading
- AI and Proving Theorems - Mean Green Math
- Mathematics with large language models as provers and verifiers - arXiv
- AI Solves the World's Hardest Math Exam (Putnam 2025) - YouTube
- Putnam-AXIOM: A Functional & Static Benchmark for ... - ICML 2026
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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.