Erdős Problem #89
Erdős distance problem
OPENdatabase updated 2025-08-31
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).
Erdős [Er46] asked whether every set of \(n\) distinct points in \(\mathbb{R}^2\) determines \(\gg \frac{n}{\sqrt{\log n}}\) many distinct distances.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/89.Attempts
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