Definition of saddle point in US English:

saddle point


  • 1A point at which a curved surface is locally level but at which its curvature in two directions differs in sign, i.e. for a surface defined by a function f of x and y, a point at which ∂f/∂x = ∂f/∂y = 0 and (∂2 f/∂x 2)(∂2 f/∂y 2) < 0.

  • 2(In a zero-sum game) the joint outcome of the two parties following their unmixed optimal strategies, where these exist.


Early 20th century; earliest use found in American Journal of Mathematics.