Genuine AI-assisted solutions to Erdős problems begin
#124 (Aristotle), #1026 (48-hour human–AI collaboration)
Result confirmed
Importance: major (4 of 5)The takeaway
In Nov–Dec 2025 AI tools produced the first genuinely new (if modest) solutions to Erdős problems.
Status
- Claim
Result confirmed
- Our reporting
- Medium 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
- #124 (from a 1995 paper): Aristotle proved it autonomously in Lean from the formal statement; Bloom noted it was the easier of two variants, and Tao’s wiki lists it as partial
- #1026: Aristotle proved the key case c(k²)=1/k in Lean (7 Dec); full answer c(k²+2a+1) = k/(k²+a) assembled by 8–9 Dec
- Tao on #1026: ‘It was only through the combined efforts of all the contributors and their tools that all these key inputs were able to be assembled within 48 hours.’
- #367: partial result by Alexeev, van Doorn and Tao with Aristotle and Gemini Deep Think (Nov 2025)
- #707 ($1000 problem): Alexeev & Mixon disproved it with ChatGPT-assisted Lean checks, then found Marshall Hall Jr. had a counterexample in 1947
- Tao: such results ‘do not meet the hyped up goal of AI autonomously solving major mathematical open problems’
What happened
After the October 2025 fiasco, a distributed community of mathematicians and amateurs began systematically attacking the ~1,100 Erdős problems with AI tools, with results logged on Tao’s wiki. The first genuinely new results arrived within weeks.
Why it matters
Erdős problems became the first large, public, verifiable scoreboard for AI in research mathematics, and set the stage for 2026’s much larger results.
Sources
5 sources from 5 sites. Numbers match the chips in the text.
5 sources: 1 primary, 4 reactions
Primary
- Alexeev & Mixon on Erdős #707 (arXiv 2510.19804)arxiv.org, paper
Reactions
- Terence Tao’s wiki: AI contributions to Erdős problemsgithub.com, discussion
- Terence Tao: The story of Erdős problem #1026terrytao.wordpress.com, discussion
- erdosproblems.com forum: problem #124erdosproblems.com, discussion
- Xena Project: formalization of Erdős problemsxenaproject.wordpress.com, discussion
Changes
- Filed