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This question has been closed as "not constructive"; it asks about a quotation by an unnamed, but famous, topologist from the 1970s to the affect that "algebraic topology is dead". As Bill Dubuque noted in a comment, it is not hard to google the quote and find it attributed (by Hitchin) to Novikov.

I had not heard this quote before, and investigating it by googling, I learned a lot of interesting history of mathematics. Thus, personally I found it a very constructive question. Furthermore, I think that it will admit reasonable answers. I have thus voted to reopen the question, and I invite others to do so.

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I'm going to throw in my 2c here. I voted to close the question as "not constructive" when it was a quote by an unknown mathematician of unknown significance. I think that was a fair assessment of the question as it currently stood, which is the official standard given in the close reasons. Now that it has been revealed who the mathematician is, I think the question is at least potentially interesting. However, I (and I suspect others) do not want to reopen the question because it might give Makoto the idea that asking questions in this manner is acceptable, as these reopenings seem to have – Alex Becker Sep 13 '12 at 4:35
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-in the past. Now, if Makoto were to edit the question to include the source of the quote, I would reconsider. After all, the question sans comments is no better than it was to begin with. – Alex Becker Sep 13 '12 at 4:36
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I think that question is not a good question in its current form. It is extremely discouraged to have a "discussion" on this site, and this question is more or less "Hey, do you know this quote? Who said it? What do you think they meant?" is an excellent topic for discussion during lunch, dinner, coffee breaks or even beer. Not for this site, though. – Asaf Karagila Sep 13 '12 at 7:13
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I think a question of that kind can be worthwile, but it needs more context and specific questions. Otherwise, one can ask something similar about probably every field of mathematics- even without knowing anything about mathematics. Bourbaki and combinatorics, Halmos and applied math, Lefschetz and "pretty proofs", Poincare and general topology, Erret Bishop and most of infinitary mathematics, Halmos and NSA, Nelson and Peano arithmetic,... – Michael Greinecker Sep 13 '12 at 9:27
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It's not clear from the links and quotations that Novikov is the source, but I posted an answer about some of his writings on the state of topology in the 1970's. – zyx Sep 13 '12 at 10:02
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@Michael I agree that questions of this kind can be worthwhile - they can lead to very interesting answers touching on history, pedagogy, etc. We are one of the few general-level math forums with enough breadth and depth to provide good answers to such questions. I hope that the OP will flesh out his question before it gets closed again. – Gone Sep 13 '12 at 15:29
@All: the question has been re-opened, and the question text edited to fit the various suggestions made in the comments both on the OP and here on Meta. I've cleaned up the comments on the OP so it is less cluttered. The original transcript is posted as an answer below. – Willie Wong♦ Sep 14 '12 at 8:50

2 Answers

up vote 10 down vote

The FAQ rather clearly states

You should only ask practical, answerable questions based on actual problems that you face. Chatty, open-ended questions diminish the usefulness of our site and push other questions off the front page.

The question in its original form amounted to "Why could somebody at some point in time think that algebraic topology is dead?" Even that is not so clear, since "dead" can have several meanings. The question was basically an invitation to write "I think algebraic topology sucks because..." That one can learn something useful when googling it is IMHO not a reason for making it constructive. Good questions and good lists of keywords are not the same thing.

Now it turns out that the source of the quote is "easily googled." It is due to Novikov, an influential algebraic topologist and that could provide a basis for an excellent questions. One might be interested in the historical circumstances around algebraic topology in the Soviet Union. One might be familiar with the biography of Novikov and have trouble relating it to his life. One might be familiar with writings of Novikov and therefore appreciate his perspective and want to understand it better.

These are all quite different questions, and it is not clear which one is the intended one. Moreover, I don't see any sign that the OP was really interested in any of these questions. It was after all only that other people commented that they think such a question, which is completely different from the original one, might be worthwhile. The OP has not shown in any way that he is really interested in any of these questions.

Coming back to the quotation from the FAQ, I think the "problems you face" part does matter. I could post a lot of mathematically interesting questions by looking at the blogs of notable mathematicians and whenever I see them posting "It would be interesting to know if..." post it as a question on MSE. I don't need to actually understand "my" own question in order to do this. The edited question doesn't demonstrate any interest but not getting closed, and that is IMHO just not enough.

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Dear Michael, I appreciate the point made at the beginning of your answer, although I probably have a more permissive view on what is reasonable as a question than many others on the site. But I don't see that the question could be construed in any reasonable way as an invitation to rail against algebraic topology. Anyone at all familiar with the burst of activity in the 50s and 60s and the changes in topology and reemergence of geometric considerations in the 70s could intuit what such a quote might have meant, although without knowing who said it, it could be hard to write a ... – Matt E Sep 14 '12 at 2:56
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... non-speculative answer. And so it is entirely conceivable to me that there are people who have a much more detailed knowledge of the history and the various protagonists, who could shed light on the quote, and write a much less speculative answer. At the same time, it may well be that the OP doesn't know this history at all, and so doesn't have any knowledge of what might lie behind the comment; in that case, asking for an explanation seems entirely reasonable. Regards, – Matt E Sep 14 '12 at 3:03
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@MattE Dear Matt, my issue is that this is mainly a shot in the dark that happened to point to interesting material. Also, I don't know whether OP is interested in Novikov or Thom. Asking about random math quotes might lead to interesting answers in some cases, but it is not behavior that I would want to encourage. And why couldn't the original version invite railing against AT? It might have been possible that someone said "Algebraic Topolofy is dead. It has now become a mindless form of diagram chasing devoid of any geometric intuition or insight"... – Michael Greinecker Sep 14 '12 at 9:59
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...The point is that there was no a priori way to judge whether the answer would be insightful or not. I'm sure you have heard some toxic ramblings on some topic from some great mathematician. Best, – Michael Greinecker Sep 14 '12 at 10:02
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Dear Michael, Thanks for your thoughtful response. Best wishes, – Matt E Sep 14 '12 at 11:07
up vote 6 down vote

For full disclosure at the prompting of Asaf, here is the full transcript of comments from the post (the red shaded ones are deleted by moderator). It is too verbose to try to copy/paste/reformat everything, so I just took a screen grab. It will be more legible if you click through to the full sized images. The time should be measured w.r.t. to the creation time of this post. (The creation time of all the comments on the first page are listed as "1 day ago", so I omitted them from the screen shot.)

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