A saddle point in mathematics refers to a point on a surface (such as a function or equation) where the surface curves up in one direction and down in another, resembling the shape of a saddle. In optimization and game theory, a saddle point is a point in a function where the gradient is zero but is not a local maximum or minimum. Saddle points play a crucial role in various optimization problems, equilibrium analysis, and decision-making processes. Researchers in this area focus on studying the properties and behavior of saddle points in different contexts, developing algorithms to locate and analyze saddle points, and understanding their implications in various fields such as economics, engineering, and computer science.