Amateur Armed with ChatGPT 'Vibe-Maths' A 60-Year-Old Problem

Why It Matters

The breakthrough demonstrates that AI can generate genuinely new mathematical reasoning, potentially accelerating research in number theory. It also signals a shift toward collaborative human‑AI problem solving in fields once thought immune to automation.

Key Takeaways

• Liam Price solved 60‑year‑old Erdős primitive set problem using ChatGPT.
• GPT‑5.4 Pro generated a novel proof method unseen by mathematicians.
• Experts say AI’s insight could reshape approaches to large‑number theory.
• Proof required human refinement; raw AI output was difficult to parse.
• Success highlights growing role of LLMs in advancing pure mathematics.

Pulse Analysis

The intersection of artificial intelligence and pure mathematics has moved from speculative experiments to headline‑making results in recent years. Large language models such as OpenAI’s GPT series have been tasked with the so‑called Erdős problems—conjectures left by the prolific Hungarian mathematician Paul Erdős that range from trivial to notoriously deep. While earlier AI attempts often produced proofs that required substantial human correction or merely re‑hashed known arguments, the community has been watching for a genuine, original contribution. The latest episode provides the first clear indication that a language model can propose a previously unseen line of reasoning.

In early April, 23‑year‑old Liam Price entered a prompt describing the primitive‑set conjecture into GPT‑5.4 Pro. The model returned a sketch of a proof that leveraged a formula from a peripheral area of analytic number theory, a connection no specialist had previously considered. After Price shared the output with undergraduate collaborator Kevin Barreto, mathematicians Terence Tao and Jared Lichtman examined the derivation, distilled the core insight, and verified that it indeed settled the lower bound of the Erdős sum at 1. The raw AI text was rough, but the underlying idea was unmistakably novel.

The episode raises both excitement and caution for the research ecosystem. On one hand, AI‑generated insights could shorten the time to resolve long‑standing conjectures, democratize access to high‑level problem solving, and inspire new interdisciplinary methods. On the other hand, the need for expert vetting highlights the current limits of LLMs in producing polished, fully rigorous arguments. As subscription models like ChatGPT Pro become more powerful, universities and research institutes may need to develop frameworks for credit, reproducibility, and ethical use of AI‑assisted proofs.