Erdős Problem #898
Erdős-Mordell inequality
PROVED LEANdatabase updated 2026-02-02
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
If \(A,B,C\in \mathbb{R}^2\) form a triangle and \(P\) is a point in the interior then, if \(N\) is where the perpendicular from \(P\) to \(AB\) meets the triangle, and similarly for \(M\) and \(L\), \[ \overline{PA}+\overline{PB}+\overline{PC}\geq 2(\overline{PM}+\overline{PN}+\overline{PL}). \] Conjectured by Erdős in 1932 (according to [Er82e]) and proved by Mordell soon afterwards, now known as the Erdős-Mordell inequality.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/898.Prizenone
Topicsgeometry
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/898
Attempts
submit one →If you take a run at this one — with your own AI subscription or without — the guide says how, and the submission form gets you an honest read of what you found.