Mathematical Unconcealment and the Surveying of Proofs

Abstract: Ever since the advent of computerized methods for solving mathematical problems, the concept of surveyability has played a central role in the debate surrounding what constitutes a mathematical proof. Ordinarily, it is by surveying the argument presented that the mathematician ascertains the truth of the conclusion, but with the advent of computer assisted technologies, there are mathematical conclusions known to be true without anyone ever having been able to survey the argument in its entirety. What this seems to suggest is that what is called "mathematical knowledge" encompasses two different types of knowledge: one gained through the act of surveying a proof, and the other through computerized empirical experiments. The goal of this thesis is to investigate the connection between surveyability and the acquisition of mathematical knowledge, thereby elucidating the difference between the two epistemological categories. The claim is that this can be accomplished by applying Heidegger's account of unconcealment to the notion of mathematical truth, supported by a Wittgensteinian analysis of the act of surveying as a type of reproduction of the proof. While much has been written on how his early mathematical training influenced Heidegger's philosophy, attempts at applying elements from his thinking to problems belonging to the philosophy of mathematics are rare. This investigation has the ambition of making a convincing case for the potential in this kind of approach.