Mancosu - Philosophy of Mathematical Practice (Oxford, 2008).pdf

11Computers in MathematicalInquiryJEREMY AVIGAD11.1 IntroductionComputers are playing an increasingly central role in mathematical practice.What are we to make of the new methods of inquiry?In Section 11.2, I survey some of the ways in which computers are usedin mathematics. These raise questions that seem to have a generally epistemologicalcharacter, although they do not fall squarely under a traditionalphilosophical purview. The goal of this article is to try to articulate someof these questions more clearly, and assess the philosophical methods thatmay be brought to bear. In Section 11.3, I note that most of the issues canbe classified under two headings: some deal with the ability of computersto deliver appropriate ‘evidence’ for mathematical assertions, a notion that isexplored in Section 11.4, while others deal with the ability of computers todeliver appropriate mathematical ‘understanding’, a notion that is consideredin Section 11.5. Final thoughts are provided in Section 11.6.11.2 Uses of computers in mathematicsComputers have had a dramatic influence on almost every arena of scientificand technological development, and large tracts of mathematics have beendeveloped to support such applications. But this essay is not about theI am grateful to Ben Jantzen and Teddy Seidenfeld for discussions of the notion of plausibility inmathematics; to Ed Dean, Steve Kieffer, and Paolo Mancosu, for comments and corrections; and toAlasdair Urquhart for pointing me to Kyburg’s comments on Pólya’s essay.