Erdős Problem #1038
OPENdatabase updated 2025-09-15
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
What is the infimum of `|{x ∈ ℝ : |f x| < 1}|` over all nonconstant monic polynomials `f` such that all of its roots are real and contained in `[-1,1]`?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 3 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/1038.Prizenone
Topicsanalysis
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1038
Attempts
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The live page is OPEN but lists 2 claimed proofs and names naprienko and danrobinson as “Currently working on this problem” (accessed 2026-07-31), so the mandatory no-duplication/no-collision rule for
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