The key quantity in chemistry is the chemical reaction rate. To find the rate, one needs to know the transition state that separates the reactants from the products.
Transition states are saddle points on the system's potential energy surface.
Ab initio calculations of potentials are expensive and so one often faces the difficult task of finding saddle points on a surface whose entire landscape is too time consuming to explore. From then on the obvious path, known to the applied mathematicians as the Newton-Raphson algorithm, takes one to the saddle.