21
$\begingroup$

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.

  • 7
    I think the remark was from Novikov. To quote, I think, Mark Twain, rumours of its death were greatly exaggerated.2012-09-13
  • 3
    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".2012-09-13
  • 10
    And [from here:](http://goo.gl/ge9Nf) 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.2012-09-13
  • 1
    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.2012-09-13
  • 0
    @t.b: Fuchs was reflecting the difference of mathematical taste: Russian mathematicans favors intuitive proof that has a geometric meaning or is easy to understand. Much of the modern algebraic topology involves a decent part of homological algebra, and can be quite 'Bourbaki' in their paper's writing style. For example, the K-theory proof of Atiyah-Singer usually involves some spectral sequence. The later of the article reflects the change in attitude. When I went to Moscow 2 years ago the trend is already reversed: people talk about k-algebra and kozul complexs all the time.2012-09-13
  • 6
    **@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.](http://meta.math.stackexchange.com/questions/5132/voting-to-reopen-question-on-a-remark-of-novikov)2012-09-13
  • 0
    Casting the last vote to re-open, as now the question has been edited to reflect most of the constructive criticisms given in this comment thread. As a side effect, I will proceed to clean up the comments a bit so it is not so distracting. Further discussions should be had on the meta thread Bill pointed out.2012-09-14
  • 1
    I have voted to close as not constructive. I realize the question has been improved, and was re-opened, but I still do not think it is suitable for this site.2012-09-16

1 Answers 1