In mathematics, Sendov's conjecture, sometimes also called Ilieff's conjecture, concerns the relationship between the locations of roots and critical points of a polynomial function of a complex variable.
The Gauss–Lucas theorem says that all of the critical points lie within the convex hull of the roots.
The conjecture has been proven for n < 9 by Brown-Xiang and for n sufficiently large by Tao.
In 1967 the conjecture was misattributed[3] to Ljubomir Iliev by Walter Hayman.
Terence Tao proved the conjecture for sufficiently large n in 2020.