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I found Novikov said that algebraic topology was dead in the early 1970's in this article.

Segal had been one of Atiyah's first students, working on equivariant K-theory, and then other equivariant generalized cohomology theories. He was a collaborator on the second of the Annals papers on the index theorem. Well known as an algebraic topologist, he arrived in Moscow in the early 1970s to give some lectures and met S. Novikov, who told him, “So you are a topologist? Here we think that algebraic topology is dead.”

I wonder what he meant by it. Any thoughts?

Note I heard that Thom also said so, but I could find only Japanese Wikipedia article saying he said so, which does not give a reference for that assertion.

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    $\begingroup$ I think the remark was from Novikov. To quote, I think, Mark Twain, rumours of its death were greatly exaggerated. $\endgroup$ – André Nicolas Sep 13 '12 at 0:13
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    $\begingroup$ It is very common to assert a field is dead. For example, calculus and real analysis is no longer considered to be active fields of research, and so are classical fields like Euclidean geometry, projective geometry, etc. But there are still numerous algebraic topology questions looming around(the homotopy group of spheres, for example), and to me it is hard to believe the subject will be dead. Various other branches of mathematics are more or less influenced by algebraic topology, for example differential topology, geometric topology, algebraic geometry, mathematical physics, etc. See "TQFT". $\endgroup$ – Bombyx mori Sep 13 '12 at 0:21
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    $\begingroup$ And from here: I belonged to a tiny group of students, led by Sergei Novikov, which studied algebraic topology. Just a decade before, Pontryagin's seminar in Moscow was a true center of the world topology; but then Cartan's seminar in Paris claimed the leadership, algebraic topology became more algebraic, and the rulers of Moscow mathematics pronounced topology dead. Our friends tried to convince us to drop all these exact sequences and commutative diagrams and do something reasonable, like functional analysis, or PDE, or probability. $\endgroup$ – Gone Sep 13 '12 at 0:27
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    $\begingroup$ So I have been to Moscow but never met Novikov(he is in St Petersburg's Steklov institute). My impression from the Moscow mathematicans (Arnold's students) is they are more interested in using algebraic topology as a useful working tool (say, calculating the homology of a knot complement) rather than treating it as isolated subject itself. Novikov probably means differential topology (Milnor, Thom, Novikov,etc) as a field is no longer active after 1970s, as people started to move on to other fields. But I doubt he means there will be no more development in this field. $\endgroup$ – Bombyx mori Sep 13 '12 at 0:27
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    $\begingroup$ @All Please remember that long meta discussions are strongly discouraged on the main site. If you wish to continue discussion of meta-level topics please do so in the associated meta thread. $\endgroup$ – Gone Sep 13 '12 at 21:09
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Novikov was mentioned in the comments as a possible source. Some of his views and memories are published in the article

http://arxiv.org/abs/math-ph/0004012

He calls 1970-80 a "period of decay" for topology, naming the following problems: migration of leaders to other fields; a relaxation of rigor and standards of documentation; the resulting "informational mess" about what had been proved and by whom.

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    $\begingroup$ I think this is the kind of pointer and answer I wished to see for the question I had in mind in the comments. Thanks a lot for this reference, I was unaware of this article. $\endgroup$ – t.b. Sep 13 '12 at 10:32

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