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Jun, 2019
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History of Topology

From my personal experiences, studying the origin of topology and ideas in the earlier stage of the developement of topology helps us to understand modern concepts and techniques in topology.

Manin says in [ Man ] that category theory , homotopy theory, and their higher versions are now playing fundamental roles in modern mathematics. In order to understand such roles of algebraic topology and homotopy theory in the current developement of mathematics, it is important to grasp the developement of topology.

Diedonné’s book [ Die89 ] is a good place to start.

Nowadays, the intractions of mathematics and physics is inevitable. There have been discussions on the “style” of mathematics.

It would be interesting to read the following articles in the Bulletin of the A.M.S. appeared in the early 90s.

  • the article by Jaffe and Quinn [ JQ93 ]
  • responses by many mathematicians and physicists including Atiyah [ Aea94 ]
  • the response by Jaffe and Quinn [ JQ94 ]
  • Thurston’s article [ Thu94 ]

References