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When I was an undergraduate 35 years ago, I made the mistake of asking some of my mathematics professors what well-known open problems they liked to think about. I got the message that this was something one did not discuss in polite society. Perhaps the culture has changed?

This question asks mathematicians to "out" technical trends which (only) experts understand as lines of attack against well-known outstanding problems.

I suggest that answers take the form of a citation or two from the literature plus a statement or mere naming of the target open problem. A few words additional about the philosophy underlying a given approach might also help, but I suggest allowing users to submit further questions if they want copious details.

Please be careful not to "out" individual mathematicians, unless you are one. Lots of mathematicians are really uncomfortable with their private tentative thoughts being made public. The goal here is to "out" technical trends that are in the public record, but not widely known. Alternately, if you are an expert in a famous open problem and want to out your own methods, feel free to do so.

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closed as off topic by Angelo, Willie Wong, Loop Space, Gil Kalai, S. Carnahan Dec 20 '10 at 19:22

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Mathematicians tend to be very cautious about endorsing lines of attack against well-known outstanding problems, because most of the time, these problems are so good at defending themselves that the attack is unsuccessful. – Peter Shor Dec 20 '10 at 18:19
David, in my opinion your question is too close to the area of gossiping. It seems that the question asks people to repeat what mathematicians told them privately as is the Mazur's example. In this form I think it cannot be accepted – Gil Kalai Dec 20 '10 at 19:04
Closed. I don't think MathOverflow should be a rumor mill. – S. Carnahan Dec 20 '10 at 19:23
In light of a vote to reopen, meta thread opened here: Could whoever voted to re-open please comment on the meta thread, in the interests of debate etc – Yemon Choi Dec 20 '10 at 19:42
There is a meta thread, why don't you lobby for your question there? See also… – Alex B. Dec 21 '10 at 3:00

The study of L-functions is related to a few of the Millennium problems.

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I guess this is not really quiet or secret. – maxdev Dec 20 '10 at 19:18

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