Number crunching vs. number theory: computers and FLT,from Kummer to SWAC (1850–1960), and beyond |
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Authors: | Leo Corry |
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Institution: | (1) Cohn Institute for History and Philosophy of Science, Tel Aviv University, Ramat Aviv, 69978, Israel |
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Abstract: | The present article discusses the computational tools (both conceptual and material) used in various attempts to deal with
individual cases of FLT, as well as the changing historical contexts in which these tools were developed and used, and affected
research. It also explores the changing conceptions about the role of computations within the overall disciplinary picture
of number theory, how they influenced research on the theorem, and the kinds of general insights thus achieved. After an overview
of Kummer’s contributions and its immediate influence, I present work that favored intensive computations of particular cases
of FLT as a legitimate, fruitful, and worth-pursuing number-theoretical endeavor, and that were part of a coherent and active,
but essentially low-profile tradition within nineteenth century number theory. This work was related to table making activity
that was encouraged by institutions and individuals whose motivations came mainly from applied mathematics, astronomy, and
engineering, and seldom from number theory proper. A main section of the article is devoted to the fruitful collaboration
between Harry S. Vandiver and Emma and Dick Lehmer. I show how their early work led to the hesitant introduction of electronic
computers for research related with FLT. Their joint work became a milestone for computer-assisted activity in number theory
at large. |
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