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.

中文翻译：

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“非凡的技巧”：拉普拉斯、泊松和数学纯粹性

十九世纪初，拉普拉斯和泊松的一系列文章讨论了数学方法论中“直接性”的重要性。在本文中，我们认为他们的“直接”证明概念类似于更广泛考虑的“纯粹”证明概念。Arana 和 Detlefsen 以及 Kahle 和 Pulcini 在最近的出版物中提出了更严格的数学纯度定义：我们将拉普拉斯和泊松的著作与这些现代的纯度定义进行比较，并表明现代定义如何未能抓住一些更微妙的方面。