Article ID: CBB000850599

Number Crunching vs. Number Theory: Computers and FLT, from Kummer to SWAC (1850--1960), and Beyond (2008)


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.


Description On Fermat's problem.

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Authors & Contributors
Singh, Simon
Goldstein, Catherine
Scalambro, Elena
Terracini, Lea
Vandendriessche, Eric
Schwermer, Joachim
Historia Mathematica
IEEE Annals of the History of Computing
Scientific American
History and Philosophy of Logic
Historia Scientiarum: International Journal of the History of Science Society of Japan
Princeton University Press
Presses Universitaires de Vincennes
Pantheon Books
John Wiley & Sons
European Mathematical Society
Number theory; number concept
Fermat's problem
Computers and computing
Prime numbers
Fermat, Pierre de
Germain, Sophie
Langlands, Robert
Fubini, Guido
Zolotarev, Yegor
Wiles, Andrew J.
Time Periods
20th century
19th century
20th century, late
18th century
17th century
St. Petersburg (Russia)
Turin (Italy)
British Association for the Advancement of Science

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