Erdős problem #728 solved near-autonomously by GPT-5.2 Pro and Harmonic’s Aristotle, with a Lean proof
Result confirmed
Importance: major (4 of 5)The takeaway
On 4–6 Jan 2026 amateur Kevin Barreto relayed an informal argument from GPT-5.2 Pro to Harmonic’s Aristotle, which formalised it in Lean.
Status
- Claim
Result confirmed
- Our reporting
- High confidence
- Verification
- Lean-verified
- Importance
- Major (4 of 5)
- Last verified
- 29 September 2026
Your AI and this story
- GPT-6 AstraIn its training data
- Claude Opus 5.5In its training data
- Gemini 4 HydrogenIn its training data
- Grok 4.7In its training data
It happened before the cutoffs of all four assistants, so it can be in their training data.
Key facts
- Jan 4: first run solved an ambiguous reading of the problem; Jan 5: GPT-5.2 Pro upgraded the argument to the intended statement; Jan 6: Aristotle formalised it
- Tao: ‘a near-autonomous solution that has not been reproduced in existing literature’
- Human role: prompting and relaying only; Barreto clarified no mathematical hint was given
- Write-up: arXiv 2601.07421
What happened
An amateur used two commercial AI systems in tandem: one to find a proof and one to formally verify it. After fixing a misreading of the problem statement, the pipeline produced a Lean-checked solution.
Why it matters
It showed the combination of informal LLM reasoning with formal verification as a practical, trustworthy workflow for research maths that non-experts could run.
Sources
3 sources from 3 sites. Numbers match the chips in the text.
3 sources: 1 primary, 1 press, 1 reaction
Primary
- Resolution of Erdős Problem #728: a writeup of Aristotle’s Lean proof (arXiv 2601.07421)arxiv.org, paper
Press
- The Decoder: Tao says GPT-5.2 Pro cracked an Erdős problem but warns the win says more about speed than difficultythe-decoder.com, press
Reactions
- Terence Tao’s wiki: AI contributions to Erdős problemsgithub.com, discussion
Changes
- Filed