Erdős Problem #211
PROVEDdatabase updated 2025-08-31
The statement as posed is true, and a proof exists.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Distinct lines containing two distinct points of the configuration.
The uniform Erdős–Beck lower bound.
The quadratic lower bound for configurations with at most half the points on a line.
Let \(1\leq k<n\). Given \(n\) points in \(\mathbb{R}^2\), at most \(n-k\) on any line, there are \(\gg kn\) many lines which contain at least two points. Solved by Beck [Be83] and Szemerédi and Trotter [SzTr83].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 3 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/211.Prize$100
Topicsgeometry
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/211
Attempts
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