In the early nineteenth century, a series of articles by Laplace and Poisson discussed the importance of ‘directness’ in mathematical methodology. In this thesis, we argue that their conception of a ‘direct’ proof is similar to the more widely contemplated notion of a ‘pure’ proof. More rigorous definitions of mathematical purity were proposed in recent publications by Arana and Detlefsen, as well as by Kahle and Pulcini: we compare Laplace and Poisson’s writings with these modern definitions of purity and show (...) how the modern definitions fail to grasp some more nuanced aspects. (shrink)