A saddle point of a differentiable real-valued function is a critical point which is neither a local maximum nor a local minimum. For example has a saddle at the origin. For a nonconstant holomorphic function, critical points of its real part supply the complex-phase application used by the method of steepest descent.
A saddle point is a point on the surface of a graph where the slope (or derivative) is zero in multiple dimensions, but is not a local extremum (i.e., not a local maximum or minimum). It occurs in both single-variable and multivariable calculus, although the characteristics can differ slightly based on the context.
New to topics? Read the docs here!