Smale's mean value conjecture (Smale 1981) asserts that, for every complex polynomial 
of degree at least 2 and every point 
with 
, some critical point 
of 
satisfies
 |
Smale (1981) proved the weaker inequality with right side 
. A stronger proposed constant for degree 
is 
. Unlike the real mean
value theorem, the statement compares a secant quotient with a derivative
at the prescribed point and selects the other endpoint among the critical
points.
Adamczewski (2026) released a proposed counterexample to the constant 1, constructed autonomously by GPT-6 Astra. The claimed polynomial
satisfies 
and 
,
but 
at every critical point. A Lean proof
was checked against an independently supplied formal statement with only standard
logical axioms. Independent mathematical review of the construction had not been
reported as of Sep. 7, 2026 (VibeMathed 2026).
