A Path to the Epistemology of Mathematics: Homotopy Theory

Por • 27 ene, 2022 • Sección: Educacion

Jean-Pierre Marquis

the history of topology provides, … , a typical shortcut of the history of mathematics. Algebraic topology finds its origin, on the one hand, from the examination of problems arising in other parts of mathematics, notably functions of one complex variable and algebraic geometry, and on the other hand, from its own developments (like the Hauptvermutung); their solution requires new methods and techniques, and the reflection on these methods leads to new kinds of problems (theory of algorithms or decidability, for instance) or sparks the creation of new notions or theories (such as categories or homological algebra) which will allow instructive synthesis by shedding a new light on questions found in other chapters of mathematics, or that will even provide tools that will lead to significant progress in the study of other types of problems. (Hirsch, 1978, 260–261; our translation)

https://philarchive.org/archive/MARAPT-7

A Path to the Epistemology of Mathematics: Homotopy Theory

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por JP Marquis · Mencionado por 18 — the history of topology provides, … , a typical shortcut of the history of … of a homotopy of paths in 1912 and its applications by Brouwer himself;.

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