AI Models Advance High-Level Math Problem Solving
Key Points
- OpenAI's ChatGPT demonstrated the ability to solve complex math problems after extended reasoning.
- AI contributions were credited for moving fifteen Erdős problems from "open" to "solved".
- Eleven of those solutions specifically acknowledged AI involvement.
- Terence Tao reported eight problems with autonomous AI progress and six with AI‑assisted research.
- AI tools are seen as well‑suited for tackling the long tail of obscure mathematical questions.
- Formal proof assistants like Lean, paired with AI, are streamlining verification processes.
- Academic adoption of AI tools is growing, indicating increased trust in their capabilities.
Recent experiments show that large language models, particularly OpenAI's ChatGPT, are increasingly capable of tackling complex mathematical problems. Researchers have used the model to solve several open problems from the Erdős collection, with AI contributions credited for moving numerous problems from "open" to "solved." The progress highlights the growing role of AI tools in mathematical research, formal proof verification, and the broader scientific community.
AI Breakthroughs in Advanced Mathematics
Software engineer and former quant researcher Neel Somani tested the mathematical abilities of OpenAI’s latest model by presenting a challenging problem. After allowing the model to reason for an extended period, it produced a full solution that checked out when formalized with the Harmonic tool.
The model demonstrated a sophisticated chain of thought, referencing mathematical axioms and locating relevant prior work, yet ultimately delivering a distinct and more complete solution. This success is part of a broader trend where AI tools are being used to address high‑level math problems.
Erdős Problems and AI Contributions
The Erdős problem set, a collection of over a thousand conjectures, has become a testing ground for AI‑driven mathematics. Recent efforts have seen AI models credited for solving several of these problems. Specifically, fifteen problems have moved from “open” to “solved,” with eleven of those solutions acknowledging AI involvement. Prominent mathematician Terence Tao notes eight problems where AI made meaningful autonomous progress and six additional cases where AI helped locate and build on existing research.
Implications for the Research Community
The advancements suggest that AI systems may be especially suited to addressing the “long tail” of obscure mathematical questions, many of which have straightforward solutions. Formalization tools such as the Lean proof assistant, combined with AI assistants like Harmonic’s Aristotle, are simplifying the verification and extension of mathematical reasoning.
Harmonic founder Tudor Achim emphasizes that the growing adoption of AI tools by mathematics and computer science professors signals a shift in credibility and acceptance within the academic community.