VibeMathedMath problems solved by AI

Steurer's Conjecture on Vectors with Small Average Correlation

Steurer conjectured in 2010 that any family of nn unit vectors with polynomially small average correlation Ei,j∣⟨vi,vj⟩∣≤n−ε\mathbb{E}_{i,j}|\langle v_i,v_j\rangle| \le n^{-\varepsilon} contains linear-sized constant-separated sets. Refuted in a strong sense, using sparse high-dimensional expanders.

Result
Disproved
Status
Resolved
AI contribution
AI co-developed
Method
Construction
Field
Theoretical computer science
Posed by
David Steurer
Year posed
2010
Years open
16y
Solved
2026-05-29
Model
GPT-5.5 Pro via an agentic system on Codex
Vendor
OpenAI
Collaborators
Farzam Ebrahimnejad, Shayan Oveis Gharan
Verification
Unreviewed
Publication
Preprint
Significance
20 / 100
Disclosed cost
—
Wikipedia
No dedicated article

What the AI did

Notable for the setup rather than the model: the authors used GPT-5.5 Pro primarily through an agentic system for long-horizon mathematical research, built by the first author on top of Codex and GPT models, and supplied it with their evolving research notes.

Verification

arXiv preprint; not yet peer-reviewed.

Source

arXiv:2606.00292 - High-Dimensional Expanders, the Sparsest Cut Problem, and Steurer's Conjecture

Discussion