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COMPUTERS IN MATHEMATICAL INQUIRY JEREMY AVIGAD
 

Summary: COMPUTERS IN MATHEMATICAL INQUIRY
JEREMY AVIGAD
1. Introduction
Computers are playing an increasingly central role in mathematical practice.
What are we to make of the new methods of inquiry?
In Section 2, I survey some of the ways that computers are used in mathemat-
ics. These raise questions that seem to have a generally epistemological character,
although they do not fall squarely under a traditional philosophical purview. The
goal of this article is to try to articulate some of these questions more clearly, and
assess the philosophical methods that may be brought to bear. In Section 3, I
note that most of the issues can be classified under two headings: some deal with
the ability of computers to deliver appropriate "evidence" for mathematical asser-
tions, a notion that is explored in Section 4, while others deal with the ability of
computers to deliver appropriate mathematical "understanding," a notion that is
considered in Section 5. Final thoughts are provided in Section 6.
2. Uses of computers in mathematics
Computers have had a dramatic influence on almost every arena of scientific and
technological development, and large tracts of mathematics have been developed to
support such applications. But this essay is not about the numerical, symbolic, and
statistical methods that make it possible to use the computer effectively in scientific

  

Source: Avigad, Jeremy - Departments of Mathematical Sciences & Philosophy, Carnegie Mellon University

 

Collections: Multidisciplinary Databases and Resources; Mathematics