What was already known
The conjecture was known through degree eight and for all sufficiently high degrees; intermediate degrees remained.
AI involvement
Lech Mazur reports that GPT-5.6 Pro contributed substantially to proof development and exact testing. Mazur designed and reconciled the work; Tao later explained and extended the result.
The model supplied substantial central proof mathematics within Mazur’s human-designed search and verification workflow.
Importance
Mazur’s theorem fills the remaining degree range of Sendov’s conjecture.
Limitations
The reported Lean proof reaches the same statement by a streamlined route, rather than checking the manuscript line by line. Terence Tao’s later strict-interior and equality results are separate extensions.
Technical verification
The paper reports a cited Lean 4/Mathlib build proving the exact Theorem 1.1 statement with only standard axioms; exact arithmetic separately certifies terminal inequalities. Tao digested the reasoning but is not recorded as a complete line-by-line check of the manuscript.
Formal checking
pinned Lean build and axiom report for theorem; exact rational programs for terminal inequalities
- Checker
- Lean 4 kernel and Mazur’s exact-arithmetic certificate verifiers
- Scope
- Sendov Theorem 1.1; separately manuscript terminal inequalities (7.19) and (7.21)
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Tao’s dated digestion gives a human account of the central identities and argument and explains the strict interior consequence.
Correction and publication history
Mazur’s proof covers Sendov’s conjecture in every degree; Tao’s later stronger consequences retain separate credit.
Read this published revision