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I'm interested in knowing what typically happens when a research field is largely regarded as being "dead".

Do professors in the field treat this dead period as a permanent effect and look to build new skills to do research in another field?

For instance, I recently had a conversation with a well-known topologist; he mentioned how topology had become dead ever since the Poincaré conjecture was solved by Perelman. And now, he looks outside of mathematics, to physics, because he feels many questions in physics can be formulated as questions of topology. Is this the typical thing to do when one's own research area becomes dead?

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    I do not believe that topology is 'largely regarded as being "dead".' This does not invalidate your question, but I still meant to make it explicit.
    – quid
    Sep 27, 2017 at 23:12
  • Lot's of possibiltities: Keep on riding the dead horse, look for applications, look for sth. related, look for sth. unrelated. Totally POV.
    – Karl
    Sep 28, 2017 at 0:14
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    Answerers: Please do not get distracted by the example. Focus on the question. Thank you.
    – eykanal
    Sep 28, 2017 at 17:16
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    What happens is that a lot of people reinvent the wheel about 20 years later. (Your well-known topologist clearly really doesn't really think topology is dead. If he did, he wouldn't be looking for more topology questions!)
    – JeffE
    Sep 28, 2017 at 22:34

1 Answer 1

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Topology is surely not dead. Maybe geometric topology, or its specific parts that were targeted at the Poincaré conjecture?

Even then, there are several inequivalent definitions of deadness. One meaningful watershed is when advisers stop suggesting the field to their grad students because they don't believe the students can build their career on it anymore; a lot of fields are dead by these standards. Another, more restrictive, criterion is when editors can no longer find referees for papers on the field.

None of these things dooms the field to eternal dormance (in fact, many dead fields have recovered, some many times), and in fact people do sometimes work on dead fields: some because they don't care about building their career (e.g., since they already have a steady job, or since they are too idealistic to care), some because they feel like they can revitalize the subject, some because they hope to find things of use for other fields, and some simply because they don't know that it's dead.

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    I would add that death or dormancy of a field is sometimes signaled by the lack of funding for it. One recent example is superconductivity which went dormant after 2001 and then got resurrected in 2008 and after a while went dormant again.
    – user21264
    Sep 28, 2017 at 9:42
  • @Magicsowon: Is that field so small that a globally valid statement like "there is no funding for it" is possible, and so isolated that its research would not somehow keep happening based upon funding from related/interacting fields? Sep 29, 2017 at 5:06

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