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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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2 
 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 2010 at 9:30
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 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 2010 at 13:12
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 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 2010 at 14:15
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 Superior version of the same question: mathoverflow.net/questions/24256/… – Ilya Grigoriev May 13 2010 at 23:43
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 Superior version my arse. – teil May 14 2010 at 12:27
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closed as subjective and argumentative by Harry Gindi, Andrew Stacey, José Figueroa-O'Farrill, S. Carnahan♦, Hailong Dao May 11 2010 at 15:31

1 Answer

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Topos theory?

(at least before Jacob Lurie's recent work)

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