Sørensen, Henrik Kragh (Author)
British Society for the History of Mathematics Bulletin
Volume: 28, no. 1
Issue: 1
Pages: 37-51
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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