AI宣布森多夫猜想告破！陶哲轩发现它隐藏的更强结果

TL;DR - An AI-assisted, Lean-verified proof reportedly resolves the 70-year-old Sendov conjecture. Terence Tao then simplified the formalization and found that it also proves the stronger Phelps–Rodriguez conjecture.

• Lech Mazur developed the proof with GPT-5.6 Pro assistance and approximately 90,000 lines of Lean 4 code.
• Tao reorganized and re-formalized it in roughly 15,000 Lean lines, exposing a surprisingly elementary argument based on algebraic identities and inequalities.
• The proof combines analytic arguments for broad degree ranges with Lean-checked Bernstein polynomial certificates for degrees 5–100.
• Its boundary-case analysis characterizes equality, yielding the stronger strict-distance result except for the known extremal polynomial family.