Revisiting the reliability of published mathematical proofs: where do we go next?

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THEORIA. An International Journal for Theory, History and Foundations of Science, ISSN: 0495-4548, Vol: 29, Issue: 3, Page: 345-360

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Frans, Joachim; Kosolosky, Laszlo
UPV/EHU Press; Euskal Herriko Unibertsitatea / Universidad del PaĆ­s Vasco
Arts and Humanities
article description
Mathematics seems to have a special status when compared to other areas of human knowledge. This special status is linked with the role of proof. Mathematicians often believe that this type of argumentation leaves no room for errors and unclarity. Philosophers of mathematics have differentiated between absolutist and fallibilist views on mathematical knowledge, and argued that these views are related to whether one looks at mathematics-in-the-making or finished mathematics. In this paper we take a closer look at mathematical practice, more precisely at the publication process in mathematics. We argue that the apparent view that mathematical literature, given the special status of mathematics, is highly reliable is too naive. We will discuss several problems in the publication process that threaten this view, and give several suggestions on how this could be countered.