Erdős Problem #1038

The problem

Determine the infimum and supremum of

$$\lvert \{ x\in \mathbb{R} : \lvert f(x)\rvert < 1\}\rvert$$

as $f\in \mathbb{R}[x]$ ranges over all non-constant monic polynomials, all of whose roots are real and in the interval $[-1,1]$.

Statement quoted from erdosproblems.com/1038, maintained by Thomas Bloom. Original source: [EHP58,p.131]. 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.

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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