 The notion of purity of method has long been of interest to mathematicians and philosophers (for recent contributions see Detlefsen and Arana 2011 and Arana and Mancosu 2012). Informally, the notion can be explained s follows. Given a statement of a certain area of mathematics, one would like a proof of the statement, if provable, to make use of conceptual resources that are not ‘foreign’ to the content of the statement. For instance, given a statement of elementary number theory one would like its proof to make use of resources that belong to elementary number theory. Proofs of an elementary number theoretic statements that appeal to complex analysis or topological dynamics would seem to appeal to concepts that are ‘foreign’ to the subject matter. This is one way to draw the pure/impure distinction in mathematics. The relation between explanatoriness and purity has been emphasized in Skow 2015 and Lange 2014. Skow, using a proof of the Pythagorean theorem that relies on physical principles, argues that there are explanations of mathematical results that rely on physical principles and are thus not pure. As mentioned above, using the case of Desargues’ theorem, Lange claims that the proof of Desargues’ plane theorem that uses properties of projective space is explanatory but impure. 