Corners theorem
From Polymath Wiki
Corners theorem: If n is sufficiently large depending on [math]\displaystyle{ \delta }[/math], then any subset A of [math]\displaystyle{ {}[n]^2 }[/math] must contain a "corner" (x,y), (x+r,y), (x,y+r) with [math]\displaystyle{ r \gt 0 }[/math].
This result was first proven by Ajtai and Szemerédi. A simpler proof, based on the triangle removal lemma, was obtained by Solymosi. The corners theorem implies Roth's theorem and is in turn implied by DHJ(3).
