TY - CHAP
T1 - From duality in mathematical programming to Fenchel duality and convex analysis
T2 - Duality as a force of inspiration in the creation of new mathematics
AU - Kjeldsen, Tinne Hoff
PY - 2024
Y1 - 2024
N2 - “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.
AB - “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.
U2 - 10.1007/978-3-031-59797-8_16
DO - 10.1007/978-3-031-59797-8_16
M3 - Book chapter
SN - 978-3-031-59796-1
T3 - Science Networks. Historical Studies
SP - 733
EP - 758
BT - Duality in 19th and 20th Century Editors Mathematical Thinking
A2 - Krömer, Ralf
A2 - Haffner , Emmylou
A2 - Volkert, Klaus
PB - Springer
ER -