Article ID: CBB000850599

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

unapi

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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Description On Fermat's problem.


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Authors & Contributors
Goldstein, Catherine
Singh, Simon
Fletcher, Colin R.
Bendegem, Jean Paul van
Ribet, Kenneth A.
Campbell-Kelly, Martin
Journals
Historia Mathematica
IEEE Annals of the History of Computing
Archive for History of Exact Sciences
Recherche
Scientific American
Historia Scientiarum: International Journal of the History of Science Society of Japan
Publishers
Princeton University Press
Presses Universitaires de Vincennes
Walker
John Wiley & Sons
Pantheon Books
American Mathematical Society
Concepts
Number theory; number concept
Mathematics
Fermat's problem
Computers and computing
Computer science
Correspondence and corresponding
People
Fermat, Pierre de
Lehmer, Derrick Henry
Germain, Sophie
Wiles, Andrew J.
Glaisher, James Whitbread Lee
Lodge, Alfred
Time Periods
20th century
19th century
17th century
18th century
20th century, late
Places
United States
Russia
St. Petersburg (Russia)
Italy
Turin (Italy)
Institutions
British Association for the Advancement of Science
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