An Amateur Just Cracked a 60-Year-Old Erdős Problem With ChatGPT

Math Twitter had a strange weekend. Someone without a PhD, working alongside ChatGPT, produced a solution to one of Paul Erdős’s open problems — a question that had sat unsolved since the 1960s. Cue the predictable split: half the community is thrilled, the other half is sharpening knives. The interesting question isn’t whether the proof holds. It’s what this episode says about who gets to do mathematics now.

A quick refresher on Erdős problems

For readers outside the math world: Paul Erdős was a mid-20th-century Hungarian mathematician who published over 1,500 papers and left behind a sprawling collection of open problems. Many of them read like riddles — short, almost innocent statements that turn out to be brutally hard. Generations of Fields Medalists have chipped away at them.

The one that just fell is in that mold. A two-line statement, posed in the 1960s, resistant to every serious attempt since. And the person who appears to have cracked it isn’t sitting in a Princeton office. They’re a hobbyist who spent months bouncing ideas off a chatbot.

Welcome to “vibe math”

The term making the rounds is vibe math — the mathematical cousin of vibe coding, which Andrej Karpathy popularized last year on X. The idea is the same: you don’t write rigorous proofs line by line. You sketch intuitions in natural language, let the model riff back, push on what looks promising, and iterate until something clicks.

Here’s roughly how the workflow ran, by the author’s own description:

• Talk through the structure of the problem with ChatGPT in plain English, forming hypotheses
• Ping-pong on proposed approaches, manually verifying each step and pushing back on dead ends
• When a key idea emerged, translate it into formal mathematical language and submit it for human review

Note what’s missing from that list: the AI did not produce the proof. The final logical scaffolding came from the human, with help from professional mathematicians at the review stage. What the model did was compress months of literature-grazing and intuition-building into something that fits in a chat window.

The split reaction

Two camps emerged on Hacker News and the math corners of X.

The optimists frame this as democratization. PhDs are no longer the only entry ticket. Erdős himself was a famously collaborative mathematician — he traveled the world couch-surfing with co-authors — and some are arguing that AI is just the latest collaborator in that spirit.

The skeptics are more worried about hallucinations. In math, a plausible-looking but wrong proof isn’t a typo — it’s a load-bearing wall that quietly isn’t there. LLMs produce these constantly. There’s a real concern that “AI solved an Erdős problem” headlines will outpace careful peer review, and that we’ll see a flood of confidently-wrong claims dressed up in LaTeX. Terence Tao has been making this point in his own AI-assisted work: the model is a brainstorming partner, not an oracle.

Replacement, or leverage

This is the question everyone actually wants answered, and the honest read is: leverage, not replacement — at least for now.

Two things stand out from this case. First, LLMs are extraordinary at scanning a vast literature and surfacing distant analogies fast. That’s a task humans are bad at and bored by. Second, the rigorous part — closing the gaps, ruling out edge cases, certifying the logic — is still a human job, often supported by formal proof assistants like Lean. So the accurate phrasing isn’t “AI solved it.” It’s “a human solved it, with AI as a force multiplier.”

The more interesting shift is the rise of the outsider. The traditional path into serious math research runs through grad school, postdocs, and dense co-author networks. That gate is now slightly ajar. A curious amateur with good taste in questions and access to a frontier model can poke at problems that used to require institutional backing. Expect this to ripple beyond math — into theoretical physics, biology, and economics, where the bottleneck has often been “knowing what to read” rather than raw cognitive horsepower.

What this actually signals

This isn’t “AI conquered mathematics.” It’s something quieter and more durable: the collaboration model for research is changing. Verification still belongs to humans. Hallucinations are still a trap that swallows careless users whole. But the bar to sit down with a 60-year-old problem just dropped, and it dropped a lot.

The right takeaway isn’t that PhDs are obsolete. It’s that good questions are now worth more than ever, and the people who know how to ask them — credentialed or not — have a new kind of leverage. Somewhere out there, another long-stuck problem is sitting next to someone who finally has the tools to stare it down.