In mathematics, the monkey saddle is the surface defined by the equation

z = x³ − 3xy².

Its name derives from the observation that a saddle for a monkey requires three depressions: two for the legs, and one for the tail. The origin of the monkey saddle is an example of a degenerate critical point.

The term horse saddle is used, by contrast with monkey saddle, to designate a saddle point that is a minimax, that is to say a local minimum or maximum depending on the intersecting plane used. The monkey saddle will have a local maximum along certain planes, but it won't be a local minimum along others —just a point of inflection.

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Multivariate calculus