

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
]
[Aea94]
Michael Atiyah and et al. Responses to: A.
Jaffe and F. Quinn, “Theoretical mathematics:
toward a cultural synthesis of mathematics and
theoretical physics”
[Bull. Amer. Math. Soc. (N.S.)
29
(1993), no. 1, 1–13; MR1202292 (94h:00007)].
Bull. Amer. Math. Soc. (N.S.)
, 30(2):178–207, 1994.
[Die89]
Jean Dieudonné.
A history of algebraic and differential topology.
1900–1960
. Birkhäuser Boston Inc., Boston, MA, 1989.
[JQ93]
Arthur Jaffe and Frank Quinn. “Theoretical
mathematics”: toward a cultural synthesis of
mathematics and theoretical physics.
Bull.
Amer. Math. Soc. (N.S.)
, 29(1):1–13, 1993.
[JQ94]
Arthur Jaffe and Frank Quinn. Response to:
“Responses to: A. Jaffe and F. Quinn,
‘Theoretical mathematics: toward a cultural
synthesis of mathematics and theoretical
physics’ ”
[Bull. Amer. Math. Soc. (N.S.)
30
(1994), no. 2, 178–207; MR1254073 (95b:00003)]
by M. Atiyah et al.
Bull.
Amer. Math. Soc. (N.S.)
, 30(2):208–211, 1994.
[Man]
Yu. I. Manin. Truth as value and duty:
lessons of mathematics,
arXiv:0805.4057
.
[Thu94]
William P. Thurston. On proof and progress in
mathematics.
Bull.
Amer. Math. Soc. (N.S.)
, 30(2):161–177, 1994.


