Amateur with GPT-5.4 Pro ‘vibe-maths’ a 60-year-old Erdős conjecture on primitive sets
Tao co-authors the paper
Event confirmedAwaiting review
Importance: major (4 of 5)The takeaway
23-year-old amateur Liam Price gave GPT-5.4 Pro a single prompt.
Status
- Claim
Event confirmedAwaiting review
- Our reporting
- High confidence
- Verification
- Expert-checked
- Importance
- Major (4 of 5)
- Last verified
- 19 October 2026
Your AI and this story
- GPT-6 Astra3 days after its cutoff
- Claude Opus 5.5In its training data
- Gemini 4 Hydrogen33 days after its cutoff
- Grok 4.7In its training data
It is after the cutoff of GPT-6 Astra and Gemini 4 Hydrogen, and can be in the training data of Claude Opus 5.5 and Grok 4.7.
Key facts
- Problem open since 1966 (~60 years)
- Proof sketch by GPT-5.4 Pro in ~80 minutes from one prompt by Liam Price; escalated by Kevin Barreto
- Paper authors include Tao, Alexeev, Barreto, Lichtman, Price and others
- Lichtman (who proved the Erdős primitive set conjecture in 2022) said the argument looked like it came ‘from The Book’
- erdosproblems.com lists #1196 as PROVED; formalisation reported underway
- AI disclosure (abstract, arXiv 2605.00301): ‘We introduce a new method for bounding Erdős sums of primitive sets, suggested from output of GPT-5.4 Pro, based on Markov chains with von Mangoldt weights.’
What happened
An amateur prompted a public model, which found a proof strategy via random divisibility chains. The problem’s leading experts confirmed and extended it within days.
Why it matters
It was the first AI solution to a well-known, decades-old Erdős conjecture that specialists had actively worked on, not just an obscure entry. It came weeks before the unit-distance disproof.
What is disputed or not yet verified
| Verification | Unrefereed arXiv preprint (2605.00301) by eight authors including the specialists Jared Duker Lichtman and Terence Tao (both co-authors, so not independent checks); no formal proof |
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Sources
3 sources from 3 sites. Numbers match the chips in the text.
3 sources: 1 primary, 1 press, 1 reaction
Primary
- Primitive sets and von Mangoldt chains (arXiv 2605.00301)arxiv.org, paper
Press
- Scientific American: Amateur armed with ChatGPT vibe-maths a 60-year-old problemscientificamerican.com, press
Reactions
- Terence Tao: Primitive sets and von Mangoldt chains — Erdős problem #1196 and beyondterrytao.wordpress.com, discussion
Changes
- Status confirmed → pending: Tao and Lichtman, previously named as checkers, are co-authors of the unrefereed preprint; added the abstract’s AI disclosure verbatim
- Filed