Sørensen, Henrik Kragh (Author)
The association of names to mathematical concepts and results (the creation of eponyms) is often a curious process. For the case of abelian groups, we will be taken on a quick, guided tour of the life of Niels Henrik Abel, elliptic functions, a curve called the lemniscate, the construction of the regular 17-gon, and a particular class of solvable equations before we can begin to appreciate how Abel's name was attributed to a concept (groups) not yet invented in his lifetime. Therefore, I will have to address how `group theory' was done before it was even invented. As the story unfolds, indications of a broader development in mathematics in the early nineteenth century will emerge. In that century, large parts of analysis underwent transformations from a predominantly formula-centred approach to a more conceptual one, and our story features important examples of how the processes of generalization functioned.
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Book
Ehrhardt, Caroline;
(2011)
Évariste Galois: La fabrication d'une icône mathématique
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Article
Ehrhardt, Caroline;
(2011)
Évariste Galois and the Social Time of Mathematics
(/isis/citation/CBB001221117/)
Article
Adelmann, Clemens;
Gerbracht, Eberhard H.-A.;
(2009)
Letters From William Burnside to Robert Fricke: Automorphic Functions, and the Emergence of the Burnside Problem
(/isis/citation/CBB000932072/)
Article
Sørensen, Henrik Kragh;
(2005)
Exceptions and Counterexamples: Understanding Abel's Comment on Cauchy's Theorem
(/isis/citation/CBB000771350/)
Book
Laudal, Olav Arnfinn;
Piene, Ragni;
(2004)
The Legacy of Niels Henrik Abel
(/isis/citation/CBB000471411/)
Article
Craik, Alex D. D.;
(2013)
Polylogarithms, Functional Equations and More: The Elusive Essays of William Spence (1777--1815)
(/isis/citation/CBB001213656/)
Article
Nabonnand, Philippe;
(2008)
La théorie des Würfe de von Staudt -- Une irruption de l'algèbre dans la géométrie pure
(/isis/citation/CBB000850593/)
Article
Meo, M.;
(2004)
The Mathematical Life of Cauchy's Group Theorem
(/isis/citation/CBB000410846/)
Book
Gray, Jeremy;
Parshall, Karen Hunger;
(2007)
Episodes in the History of Modern Algebra (1800--1950)
(/isis/citation/CBB000774194/)
Article
Ehrhardt, Caroline;
(2010)
A Social History of the “Galois Affair” at the Paris Academy of Sciences (1831)
(/isis/citation/CBB000932775/)
Article
Anderson, Ian;
Crilly, Tony;
(2013)
Robert Richard Anstice (1813--1853): A Hertfordshire Bicentenary
(/isis/citation/CBB001212300/)
Article
Gandon, Sébastien;
(2004)
Russell et l'Universal Algebra de Whitehead: la géométrie projective entre ordre et incidence (1898--1903)
(/isis/citation/CBB000501687/)
Article
Christopher D. Hollings;
(2017)
‘Nobody Could Possibly Misunderstand What a Group Is’: A Study in Early Twentieth-Century Group Axiomatics
(/isis/citation/CBB787330938/)
Article
Guo, Jinhai;
(2014)
William Fogg Osgood and the Dissemination of Theories of Functions in China
(/isis/citation/CBB001214103/)
Book
Hollings, Christopher David;
(2014)
Mathematics across the Iron Curtain: A History of the Algebraic Theory of Semigroups
(/isis/citation/CBB001510062/)
Article
Hollings, Christopher;
(2009)
The Early Development of the Algebraic Theory of Semigroups
(/isis/citation/CBB000932084/)
Article
Hollings, Christopher;
(2014)
Investigating a Claim for Russian Priority in the Abstract Definition of a Ring
(/isis/citation/CBB001420039/)
Article
Rosen, Michael I.;
(1995)
Niels Hendrik Abel and equations of the fifth degree
(/isis/citation/CBB000061095/)
Book
Derbyshire, John;
(2006)
Unknown Quantity: A Real and Imaginary History of Algebra
(/isis/citation/CBB000641585/)
Article
Gao, Jin-hai;
(2002)
K. T. Wang and the Differentiation of Quaternion Functions
(/isis/citation/CBB000340066/)
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