Last Wednesday, this paper was posted to the arXiv, supposedly proving the Twin Prime Conjecture. Unfortunately, the arXiv isn’t peer-reviewed, so I don’t know whether to believe this or not. Further, the only person around the department (Serge Lang) who knows much about analytic number theory is out of state.

My question:
a) Is Arenstorf right?
b) if so, what was the missing ingredient? None of his references are really any later than 1970 (the review article notwithstanding). What did he do that hadn’t been tried in 34 years?

Maybe it’s because I’m not a mathematician but I don’t quite follow this. I get the idea that the fingers stand for prime numbers, thus “twin primes”. But I don’t follow how the tongue fits into the whole thing. Is it an inductive proof?

Then again, I see all the trouble that that could cause. Maybe if a moderator put the proper link (which I immediately posted as a follow-up) in the OP and just wiped what’s been written so far…

I have next to no knowledge about the subject at hand, but speaking as someone who sifts through gr-qc and hep-th daily: don’t believe everything you read in the arXiv. That said, Arenstorf seems to be a professor of mathematics at Vanderbilt, so he’s probably not a total crackpot.

Well, yes. A number of blogs seem to make a big deal of his emeritus status, which (to me) shows how little they understand of how mathematics is done. You can’t say you disbelieve someone just because he’s old. In fact, it seems that he’s been working on the problem at least since 1998. This bulletin shows him giving a talk in November 1998 about a not-quite-proof of the Conjecture. Also, he notes in the Acknowledgements two of his “longtime colleagues” who helped transcribe his paper into TeX, which means that two other mathematicians have read through the thing and typed it up without seeing anything glaringly wrong.

I don’t really have anything useful to add either. There are a couple of uninformativethreads on sci.math; so far there hasn’t been any authoritative reply, though.

On p.3 he says he’s been working on the problem “on and off” for about 20 years.