 Philosophical views concerning the ontology of mathematics run the gamut from platonism (mathematics is about a realm of abstract objects), to fictionalism (mathematics is a fiction whose subject matter does not exist), to formalism (mathematical statements are meaningless strings manipulated according to formal rules), with no consensus about which is correct. By contrast, it seems fair to say that there is a philosophically established received view of the basic methodology of mathematics. Roughly, it is that mathematicians aim to prove mathematical claims of various sorts, and that proof consists of the logical derivation of a given claim from axioms. This view has a long history; thus Descartes writes in his Rules for the Direction of the Mind (1627–28) that a mathematical proposition must be “deduced from true and known principles by the continuous and uninterrupted action of a mind that has a clear vision of each step in the process” (47). An important implication of this view is that there is no room, at least ideally, in mathematics for non-deductive methods. Frege, for example, states that “it is in the nature of mathematics always to prefer proof, where proof is possible, to any confirmation by induction” (1884, 2). Berry (2016) offers a more recent defense of proof as promoting key virtues of shared enquiry within the mathematical community.