Amateur Armed with ChatGPT Solves an Erdős Problem

An amateur mathematician used ChatGPT to solve an open problem posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. No institutional affiliation, no research grant, no doctorate — just a curious person with an AI assistant and enough persistence to push through. That alone should make the math world uncomfortable in the best possible way.

The Erdős Problems and Why They Matter

Paul Erdős spent his life obsessively posing problems in number theory, combinatorics, and graph theory — often offering small cash prizes to whoever could solve them. These weren't homework exercises; many stumped professional mathematicians for decades. After his death in 1996, hundreds of these problems remained open, quietly sitting on the edge of what human mathematical thinking had been able to reach.

What Actually Happened

A user with no known academic affiliation published a solution to one of Erdős's open problems, with large language models (LLMs) playing a central role in the process. Crucially, this wasn't a case of typing a question and pasting the output — the solver used ChatGPT iteratively: forming hypotheses, checking logical steps, stress-testing arguments, and refining the approach over multiple sessions. The result was shared on Hacker News, where credentialed mathematicians began reviewing it and, at least initially, found no fundamental flaws. It's not the first time an outsider has contributed to serious math, but it may be the first time an AI was this deeply embedded in the reasoning process.

What This Really Means

This isn't a story about AI being "smart" — it's a story about the democratization of rigorous thinking. ChatGPT didn't solve anything on its own; it functioned as a high-speed intellectual sparring partner, helping a human organize ideas, catch inconsistencies, and explore dead ends faster than solo thinking allows. The losers here are those who gatekeep serious mathematics behind institutional walls. The winners are everyone who's ever had a sharp mind but no access to elite academic circles.

What Comes Next

This case forces some uncomfortable but necessary questions onto the scientific community:

• How do journals and peer reviewers handle submissions from unaffiliated contributors who used AI?
• Should AI-assisted proofs be labeled differently from traditional ones?
• Are Erdős's cash prizes payable to a human who used a machine to get there?

Expect more cases like this. LLMs are steadily improving at formal reasoning, and there are thousands of open problems sitting in mathematical literature waiting for fresh approaches. The question isn't whether AI will contribute more to mathematics — it's how much credit the establishment is willing to grant when it does.

The real test now is whether the math community builds new walls to protect its territory, or opens the door to a much larger room of solvers.

Source: Hacker News