Determinining the precise shape of the Earth has been a fundamental question for centuries. Of course, this can be approached by many different techniques. In this non technical talk, I would like to describe the work of famous mathematicians, including Newton, Lagrange, Laplace, Legendre and Poisson. However, my main emphasis will be on the fundamental contribution of Poincaré, leading to bifurcation theory. I will also describe the present situation, from the mathematical point of view.