From duality in mathematical programming to Fenchel duality and convex analysis: Duality as a force of inspiration in the creation of new mathematics
Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review
“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 language | English |
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Title of host publication | Duality in 19th and 20th Century Editors Mathematical Thinking |
Editors | Ralf Krömer, Emmylou Haffner , Klaus Volkert |
Number of pages | 27 |
Publisher | Springer |
Publication date | 2024 |
Pages | 733–758 |
Chapter | 16 |
ISBN (Print) | 978-3-031-59796-1 |
ISBN (Electronic) | 978-3-031-59797-8 |
Publication status | Published - 2024 |
Series | Science Networks. Historical Studies |
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Volume | 63 |
ISSN | 1421-6329 |
Links
- https://link.springer.com/chapter/10.1007/978-3-031-59797-8_16
Final published version
ID: 280283564