A digestion of the proof of Sendov’s conjecture

Terence Tao reports that Sendov's conjecture, a long-standing problem in mathematics about the relationships between polynomials and their critical points, has been resolved. An AI tool produced the proof, and mathematician Lech Mazur had it formally verified in Lean. Tao spent several days with heavy AI assistance preparing the computer-generated proof for publication, discovering along the way that the solution is remarkably elementary—using only basic algebra and no deep mathematics. The same proof also establishes the related Phelps–Rodriguez conjecture, settling both problems completely.

Listen to this story

Hear this and more stories in a personalized audio briefing.

Open The Chonkerton