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 -