From duality in mathematical programming to Fenchel duality and convex analysis: Duality as a force of inspiration in the creation of new mathematics

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Abstract

“Duality” is an intriguing notion in the history of mathematics that refers to a variety of phenomena in many different areas and sub-disciplines of mathematics throughout time. Michael Atiyah (2007, p. 69) characterized it as being “not a theorem, but a “principle”. [. . .] Fundamentally, duality gives two different points of views of looking at the same object.” Similar statements can be found in lectures and literature in and about mathematics: “In mathematics duality refers to the phenomenon whereby two objects that look very different are actually the same in a technical sense” (Arora, 2014) “ [. . .] two sides of the same coin” (Maruyama, 2016, p. 5). “ “Duality” in math really just means having 2 ways to think about a problem” (MathStack, 2013) to name just a few examples. Such utterances have philosophical implications: duality is a principle, it is points of views, it is about objects that are the same (technically), it is different ways to approach a problem and so on and so forth.
Original languageEnglish
Title of host publicationDuality in 19th and 20th Century Editors Mathematical Thinking
Editors Ralf Krömer, Emmylou Haffner , Klaus Volkert
Number of pages27
PublisherSpringer
Publication date2024
Pages733–758
Chapter16
ISBN (Print) 978-3-031-59796-1
ISBN (Electronic) 978-3-031-59797-8
DOIs
Publication statusPublished - 2024
SeriesScience Networks. Historical Studies
Volume63
ISSN1421-6329

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