Number crunching vs. number theory: computers and FLT, from Kummer to SWAC (1850--1960), and beyond
type: Item
instance of: scholarly article
title: Number crunching vs. number theory: computers and FLT, from Kummer to SWAC (1850--1960), and beyond
zbMATH Open document ID: 1147.11003
author: Leo Corry
published in: Archive for History of Exact Sciences
publication date: 2008-09-08T00:00:00Z
review text: The article may serve as some kind of model for a historical study, investigating secondary unfruitful individual attempts that may even arrive at deadends. It covers a long period in the history of Fermat's last theorem [FLT] beginning essentially with the original papers due to Ernst Kummer and ending up with the introduction of electronics especially by Harry Vandiver and Dick Lehner, at AWAC (Standards Western Automatic Computers). The author also stresses the importance of later achievements built on ideas developed by Sophie Germain, and performed by Leonard Adleman, Roger Heath-Brown and Étienne Fouvry, i.e., there exists an infinity of prime numbers for which FLT holds. Obviously Andrew Wiles' complete proof takes totally different ways. The author comments saying that number theory defeated number crunching.
reviewed by: Jean-Paul Pier
Mathematics Subject Classification ID: 11-03
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 11D41
Mathematics Subject Classification ID: 11Y40
zbMATH DE Number: 5322539
zbMATH Keywords: Number Theory
zbMATH Keywords: Fermat's last theorem
Wikidata QID: Q56852392
MaRDI profile type: Publication
full work available at URL: s00407-007-0018-2
OpenAlex ID: W2000676640
cites work: The first case of Fermat's last theorem
cites work: The Class Number of the Cyclotomic Field
cites work: Q5732733
cites work: Q5666617
cites work: Q5771803
cites work: Q3240885
cites work: Derrick Henry Lehmer
cites work: Irregular Primes and Cyclotomic Invariants to Four Million
cites work: Irregular primes and cyclotomic invariants to 12 million
cites work: Q4433575
cites work: Note on Irregular Primes
cites work: Q4454196
cites work: Fermat comes to America: Harry Schultz Vandiver and FLT (1914--1963).
cites work: Fermat Meets SWAC: Vandiver, the Lehmers, Computers, and Number Theory
cites work: On the history of Fermat's last theorem: Fresh views on an old tale
cites work: Q4000221
cites work: Q4462107
cites work: Unpublished manuscripts of Sophie Germain and a revaluation of her work on Fermat's last theorem
cites work: The background of Kummer's proof of Fermat's last theorem for regular primes
cites work: Q4126428
cites work: Postscript to ''The background of Kummer's proof''
cites work: Théorème de Brun-Titchmarsh; application au théorème de Fermat
cites work: Q5493441
cites work: Zum Fermatschen Problem
cites work: The First Case of Fermat's Last Theorem is True for all Prime Exponents up to 714,591,416,091,389
cites work: Q4413075
cites work: Q5645655
cites work: Q4210020
cites work: Q5785009
cites work: Computation of invariants in the theory of cyclotomic fields
cites work: Q4177670
cites work: Mathematical Expeditions
cites work: Q3235883
cites work: On the first case of Fermat’s last theorem
cites work: A note on Fermat’s last theorem
cites work: A Photo-Electric Number Sieve
cites work: An extension of the table of Bernoulli numbers
cites work: The lattice points of an \(n\)-dimensional tetrahedron
cites work: The Sieve Problem for All-Purpose Computers
cites work: Q3243356
cites work: Alfred Edward Western
cites work: Q4482245
cites work: Über die Fermatsche Vermutung, VII
cites work: On Kummer's conjecture
cites work: Mersenne and Fermat Numbers
cites work: A new lower bound for the exponent in the first case of Fermat’s last theorem
cites work: An additional criterion for the first case of Fermat’s last theorem
cites work: Q4462102
cites work: Summary of Results and Proofs on Fermat's Last Theorem. (Sixth Paper)
cites work: Note on the Divisors of the Numerators of Bernoulli's Numbers
cites work: Fermat’s last theorem and the second factor in the cyclotomic class number
cites work: On Bernoulli's numbers and Fermat's last theorem
cites work: The minima of functionals with associated side conditions
cites work: Fermat's Last Theorem: Its History and the Nature of the Known Results Concerning It
cites work: EXAMINATION OF METHODS OF ATTACK ON THE SECOND CASE OF FERMAT'S LAST THEOREM
cites work: AN APPLICATION OF HIGH-SPEED COMPUTING TO FERMAT'S LAST THEOREM
cites work: PROOF OF FERMAT'S LAST THEOREM FOR ALL PRIME EXPONENTS LESS THAN 4002
cites work: The Irregular Primes to 125000

Number crunching vs. number theory: computers and FLT, from Kummer to SWAC (1850--1960), and beyond (cites work)
cites work: Q5690489

Number crunching vs. number theory: computers and FLT, from Kummer to SWAC (1850--1960), and beyond (DOI)
DOI: 10.1007/S00407-007-0018-2