Abstract: From the perspective of a pure mathematician, the application of mathematics to concrete problems (like evolution of the species) is not of primary importance. However, that does not imply that applied mathematics deals with problems that are trivial mathematically speaking, or that there is nothing to learn from applications. In this talk, I will showcase different ways in which mathematics are being used in the study of Evolution, ranging from systems of ODEs and PDEs to "simple" stochastic models, with some sprinkles of numerical analysis. My goal is to spark the interest of the pure math audience not only in applying math to biology, but also in further analyzing the mathematics that arise from biological problems for mathematics' sake.