Erdős Problem #1038

Precise statement

Among all nonconstant monic polynomials $f$ whose roots lie in $[-1, 1]$, determine $\inf_f |\{x \in \mathbb{R} : |f(x)| < 1\}|$.

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

GPT-5.5 Pro

A July 2026 manuscript by Darvas, Peng and Tao, developed with GPT-5.5 Pro, claims the exact extremal value and measure.

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

Author-checked manuscript; the official record is still open.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-07-01

   erdosproblems.com/1038

   VibeMathed reports this item as candidate. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

argument (source-reported)

Source-reported tools: argument.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• The source status is candidate and must not be represented as solved.
• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.