Amateur Armed with ChatGPT Solves a 60-Year-Old Erdős Problem

The News: An amateur mathematician without formal training used ChatGPT to solve an Erdős problem that had remained open for 60 years. The breakthrough, reported by Scientific American, demonstrates how large language models are enabling entirely new pathways to mathematical discovery by non-specialists.

Why it matters: This is not just another "AI helped solve a problem" story. The solver — a non-mathematician — used ChatGPT not as a calculator but as a collaborative reasoning partner, iteratively refining conjectures and checking logic. This "vibe maths" approach (as the solver called it) suggests a fundamental shift in who can contribute to formal mathematics. If AI can lower the barrier to entry this dramatically, the implications for research, education, and innovation are profound.

The Details

The Erdős problem in question — part of a famously difficult set of unsolved problems in number theory and combinatorics — had resisted professional mathematicians for six decades. The amateur solver, working entirely outside traditional academia, described a process of iterative dialogue with ChatGPT: proposing partial solutions, asking the model to stress-test assumptions, and using its feedback to refine the approach.

What makes this case remarkable is the methodology. The solver had no formal background in the specific subfield. ChatGPT acted as a conversational proof assistant — not generating the solution whole-cloth, but helping the human navigate the logical landscape, flagging edge cases, and suggesting related theorems to explore.

How "Vibe Maths" Works

The term "vibe maths" was coined by the solver to describe the process:

1. Intuition phase: Propose a rough idea in natural language
2. Stress-test phase: Ask ChatGPT to find counterexamples or holes
3. Refinement phase: Iterate based on feedback
4. Formalization phase: Use the model to translate the final argument into rigorous notation

This stands in contrast to traditional mathematical research, which requires years of domain-specific training before one can even formulate meaningful conjectures.

Relevance to AI Tool Users

For anyone using ChatGPT or similar conversational AI tools, this case study offers a blueprint for AI-assisted reasoning beyond simple Q&A. The key insight is not that AI solved the problem — it's that the human-AI pair outperformed either alone.

Perplexity and other tools in the Conversational AI category are increasingly being used for research-grade work, not just content generation.

Broader Implications

• Democratization of research: If domain expertise is no longer a prerequisite for contribution, who gets to do science?
• AI as reasoning partner: The most effective use of LLMs may not be autonomous problem-solving but collaborative reasoning
• Verification challenges: Who validates a proof when neither the solver nor the AI is a domain expert?

Key Takeaways

• An amateur mathematician solved a 60-year-old Erdős problem using ChatGPT as a collaborative reasoning partner
• The "vibe maths" approach — iterative natural-language refinement — may represent a new paradigm for AI-assisted research
• This demonstrates the growing power of conversational AI tools beyond content generation into genuine problem-solving
• The finding was reported by Scientific American and has sparked debate on Hacker News about the role of AI in formal mathematics

Sources

1. Scientific American — "Amateur Armed with ChatGPT Vibe Maths a 60-Year-Old Problem"
2. Hacker News Discussion
3. Best-AI.org — ChatGPT Tool Page