Number crunching vs. number theory: computers and FLT, from Kummer to SWAC (1850-1960), and beyond

Details Number crunching vs. number theory: computers and FLT, from Kummer to SWAC (1850-1960), and beyond Number crunching vs. number theory: computers and FLT, from Kummer to SWAC (1850-1960), and beyond

Jul 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008ahes...62..393c&link_type=abstract

Archive for History of Exact Sciences (ISSN 0003-9519), Vol. 62, No. 4, p. 393 - 455 (2008)

Mathematics

History Of Science, Mathematics

Scientific paper

The article discusses the computational tools (both conceptual and material) used in various attempts to deal with individual cases of FLT [Fermat's Last Theorem], 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, the author presents 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. The author shows 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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