Erdős Problem #224

Codex and GPT-5.2 Thinking found a new proof of a problem that was already solved (14 Jan 2026).

Problem
Erdős problem #224 (geometry); current status: proved (Lean)
Credit
Codex and GPT-5.2 Thinking · AI building on known literature
Checked
Lean formalizationListed in Tao's wiki
Timeline
First AI contribution 2026-01-14 · wiki data as of 2026-06-30
Sources
Problem page (erdosproblems.com)Tao's AI-contributions wiki
PRIOR
ARTPer Tao's AI-contributions wiki

The problem

If A⊆RdA\subseteq \mathbb{R}^d is any set of 2d+12^d+1 points then some three points in AA determine an obtuse angle.

Statement quoted from erdosproblems.com/224, maintained by Thomas Bloom. Original source: [Er57][Er61,p.244]. Current status there: proved (Lean).

AI contributions

As recorded in Terence Tao's wiki AI contributions to Erdős problems (data as of 30 Jun 2026). 🟢 full, 🟡 partial, ⚪ unverified, 🔴 incorrect.

Date Kind AI systems Outcome Literature
14 Jan, 2026 AI building on known literature Codex, GPT-5.2 Thinking 🟢 New proof found (Lean) 🟢 Danzer and Grünbaum (1962)

Caveats

The wiki's classifications are provisional and are not a benchmark. Many Erdős problems have never had a thorough literature review, so a result that looks new may later turn out to be known; some problems were also stated ambiguously or incorrectly. See the problem page for the full discussion.

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