Erdős Problem #352

Partial progress by Aleksandar Bulj and Vjekoslav Kovač with GPT-5.4 Pro and GPT-5.5 Pro (29 May 2026): partial result of variant problem.

Problem
Erdős problem #352 (geometry); current status: open
Credit
Aleksandar Bulj and Vjekoslav Kovač with GPT-5.4 Pro and GPT-5.5 Pro · AI working with humans
Checked
Listed in Tao's wiki
Timeline
First AI contribution 2026-05-29 · wiki data as of 2026-06-30
Sources
Problem page (erdosproblems.com)Tao's AI-contributions wiki
PARTIALPer Tao's AI-contributions wiki

The problem

Is there some c>0c>0 such that every measurable A⊆R2A\subseteq \mathbb{R}^2 of measure ≥c\geq c contains the vertices of a triangle of area 1?

Statement quoted from erdosproblems.com/352, maintained by Thomas Bloom. Original source: [Er78d,p.122][Er81b,p.30][Er83d,p.323][Va99,2.47]. Current status there: open.

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 Humans Outcome
29 May, 2026 AI working with humans GPT-5.4 Pro, GPT-5.5 Pro Aleksandar Bulj, Vjekoslav Kovač 🟡 Partial result of variant problem

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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