The Proof Is in the Process: A Preamble for a Philosophy of Computer-Assisted Mathematics

TitleThe Proof Is in the Process: A Preamble for a Philosophy of Computer-Assisted Mathematics
Publication TypeBook Chapter (with title)
Year of Publication2014
AuthorsDe Mol, L
Secondary AuthorsGalavotti, MCarla, Dieks, D, Gonzalez, WJ, Hartmann, S, Uebel, T, Weber, M
Book TitleNew Directions in the Philosophy of Science
SeriesThe Philosophy of Science in a European Perspective

According to some well-known mathematicians well-versed in computer-assisted mathematics (CaM), “Computers are changing the way we are doing mathematics”. To what extent this is really true is still an open question. Indeed, even though some philosophers of math have taken up the challenge to think about CaM, it is unclear in what sense exactly a machine (can) affect(s) the so-called “queen of the sciences”. In fact, some have concluded that issues raised by the use of the computer in mathematics are not specific to the use of the computer per se. However, such findings seem precarious since a systematic study of computer-assisted mathematics is still lacking. In this paper I argue that in order to understand the impact of CaM, it is necessary to take more seriously the computer itself and how it is actually used in the process of doing mathematics. Within such an approach, one searches for characteristics that are specific to the use of the computer in mathematics. I will focus on a feature that is beyond any doubt inherently connected to the use of computing machinery, viz. mathematician-computer interactions. I will show how such interactions are fundamentally different from the usual interactions between mathematicians and non-human aids (a piece of paper, a blackboard etc) and how such interactions determine at least two more characteristics of CaM, viz. the significance of time and processes and the steady process of internalization of mathematical tools and knowledge into the machine. I will restrict myself to the use of the computer within so-called experimental mathematics since this is the main object of CaM within the philosophical literature.

Citation Keyde2014proof
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