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By this I mean that there is much to be learned and gained by studying this area, but for whatever reason, it's been a long time since something significant was discovered in this area.

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closed as not constructive by Harry Gindi, Loop Space, José Figueroa-O'Farrill, S. Carnahan, Hailong Dao May 11 '10 at 15:31

As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, visit the help center for guidance.If this question can be reworded to fit the rules in the help center, please edit the question.

This certainly has the potential to be "subjective and argumentative", but it might also get some interesting answers: let's see. As a point of clarification, when you say "there is much to be learned and gained", do you mean in the future -- i.e., information that we do not already know? If so, how could we know that for sure? – Pete L. Clark May 11 '10 at 9:30
I don't think that this question has to be closed. Perhaps there are interesting answers of the form "Ten years ago, ... had given up to classify ... Only few mathematicians, namely ... still study ... There are more accessible, related problems from ... which are more popular now, namely ..." – Martin Brandenburg May 11 '10 at 13:12
It might be interesting to collect historical examples -- fields that <i>did</i> lie dormant for long stretches before someone revitalized it. I agree that the question as posed is almost completely opinion-based. – Cam McLeman May 11 '10 at 14:15
Superior version of the same question:… – Ilya Grigoriev May 13 '10 at 23:43
Superior version my arse. – teil May 14 '10 at 12:27

Topos theory?

(at least before Jacob Lurie's recent work)

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