Posted in Abel, Matematikhistorie

New publication: What’s Abelian about abelian groups?

My paper entitled “What’s Abelian about abelian groups?” has just been published in the Bulletin of the British Society for History of Mathematics.

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.

Posted in Abel, Matematik i Danmark, Matematikhistorie, Projektforslag

Henrik Gerner von Schmidten: En dansk matematiker, som tjente som Abel’s forbillede

Napoléon Bonaparte by Andrea Appiani (1754&nda...
Napoléon Bonaparte by Andrea Appiani (1754–1817) (Photo credit: Wikipedia)

Han havde en slående lighed med Napoleon, og han korresponderede med digteren Jens Baggesen. Han var en af Hans Christian Ørsteds protegeer, og hans matematiske arbejder blev publiceret i Videnskabernes Selskabs Skrifter, Gergonnes Annales des mathématiques og Crelles Journal für die reine und angewandte Mathematik. Hans erfaringer var med til at bane vejen for Niels Henrik Abel’s internationale kontakter og gennembrud. Og i det hele taget fremviser hans biografi besynderlige sammenfald med den berømte norske matematiker. Men alligevel er Henrik Gerner von Schmidten (1799–1831) i dag ikke kendt uden for en mindre kreds af dansk matematikhistorie.

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