The notion of stiffness, which originated in several applications of a different nature, has dominated the activities related to the numerical treatment of differential problems for the last fifty years. Contrary to what usually happens in Mathematics, its definition has been, for a long time, not formally precise (actually, there are too many of them). Again, the needs of applications, especially those arising in the construction of robust and general purpose codes, require nowadays a formally precise definition. In this talk, the evolution of such a notion will be reviewed and a precise definition which encompasses all the previous ones will be given.

[1] Luigi Brugnano, Francesca Mazzia, and Donato Trigiante, Fifty Years of Stiffness, Mathematics-Numerical Analysis, 2009.