Zhang is an outlier. From what I followed when his proof came out, there were actually very similar ideas being developed by Terry Tao at UCLA and by a PhD student at Oxford. The sort of places you'd expect. And IIRC, Zhang actually come from the top math department in China. He just had trouble getting a good job in the U.S.
It is also fair to wonder just where this twin prime conjecture is leading us in terms of usefulness. I know it's hard, but we should be able to draw direct comparisons to how something like RSA panned out. Though RSA is pretty easy to understand. Maybe a better example is elliptic curve cryptography, though I know nothing about that. Can we at least provide a road map for how understanding the twin prime conjecture will lead to useful, practical techniques?
(And yeah, I accidentally added a "not" there. Will edit.)
> Zhang is an outlier. … And IIRC, Zhang actually come from the top math department in China.
Well, sure, and that's my point; there will be outliers. They'll probably have some indicators, like coming from good schools, or prior good work, even if they are currently in lower-ranked places. Every time an outlier comes along, one can certainly retroactively find something that reveals all along that he or she was going to excel; the challenge is finding the people with this potential in advance. (You don't want to fund only the people who have done good work; eventually you'll just get an unduly privileged class of people who did a lot of good math now and no longer can.) So we should have some way of finding these outliers by evaluating their academic history and apparent future potential … and that's a grant committee. (Hey, I hate to find myself defending them! I'm an academic and grant writing is low down on my list of favourite things to do; but it's better than being told that, since I'm not at Princeton, I won't even get a chance to seek funding.)
> From what I followed when his proof came out, there were actually very similar ideas being developed by Terry Tao at UCLA and by a PhD student at Oxford.
I don't know about the Ph.D. student at Oxford, but (although I can't find it now) I am pretty sure I remember reading a post on Terry Tao's blog in which he was much more charitable than this; essentially, his view (I believe, though I can't find it) was that commonalities could be found between his work and Zhang's, as there always can between even the most revolutionary work and its predecessors, but that Zhang's work represented a genuinely new idea and huge step forward.
> It is also fair to wonder just where this twin prime conjecture is leading us in terms of usefulness. I know it's hard, but we should be able to draw direct comparisons to how something like RSA panned out.
RSA took essentially from the dawn of recorded mathematics (Euclid) to about 70 years ago; it's now the prototypical example (second, perhaps, to Riemannian geometry) of apparently "purely pure" mathematics that turned out to have applications. I think that's an excellent argument for taking the long view.
It is also fair to wonder just where this twin prime conjecture is leading us in terms of usefulness. I know it's hard, but we should be able to draw direct comparisons to how something like RSA panned out. Though RSA is pretty easy to understand. Maybe a better example is elliptic curve cryptography, though I know nothing about that. Can we at least provide a road map for how understanding the twin prime conjecture will lead to useful, practical techniques?
(And yeah, I accidentally added a "not" there. Will edit.)