ive read in the new scientist (march 22nd edition) that de Branges might have solved the Riemann Hypothesis by combining set theory with the zeta function, with links to Bieberbach's conjecture(don't know what that is exactly), any opinions:

It's nothing new, de Branges has been claiming he has solved the Riemann Hypothesis (even the Generalized RH) for quite a while now.
I have no idea at all if his proof is correct but I doubt it (as we surely would have heard more about it), apparently it's quite hard to check because he relies on plenty of methods he created himself... Still, it might come out right as he has proved quite a few relatively important conjectures in the past (Bierbach's...).

But apparently "any number theorist will have no trouble checking the proof", get going Cosmin !

Ah, cool! It's rare to see a maths article in the NS, thanks for the heads-up Andy.

Does anyone know how to get the institutional IP login (I presume we have one at Warwick) to work? So I can read it online.

There's a very interesting page of "false" RH proofs

http://www.secamlocal.ex.ac.uk/people/staff/mrwatkin/zeta/RHproofs.htm

My dad gets NS delivered, I'll see if he can post up that one. Honestly, though, it's Louis De Branges => false :P It'd be interesting to see something about it, if only the NS article, I'll see if I can get hold of it then you can have a read next term :) Thanks for the link andrew :D

Jamie

I think it's unlikely. The fact is, De Branges actually does this every 4 years or so. He's continuously refining a fairly incomprehensible approach (by the way, there's no real "set theory" in it but a fair bit of functional analysis) which people have actually shown is not very likely to actually work (I recall reading a paper about this a few years ago - the authors showed that his proof would work only if some fairly restrictive related conjecture did, which they found improbable). If anyone is interested, here's De Branges' paper (gotta love how all his references are written by himself) and an "apology" for it (that said, far from "any" number theorist will be able to check it :P - the apology is a sort of popular(ish) maths explanation of some of the related maths with bits about himself lumped in). The trouble with De Branges, as opposed to most people claiming to have proven RH, is that he's actually proven the Bieberbach conjecture in roughly the same way: using an approach deemed questionable and unconvincing by most. It took a few long sessions of explaining his work (clarity isn't really his forte) to a few Russian mathematicians to actually check it and realise it was actually a valid proof. That said, I still don't think it's going to happen in this case.

I've always found it fascinating how mathematical proofs, which surely should be a cut-and-dry procedure, can be "controversial". It really puts paid to the idea of mathematicians as unquestioning logical machines - we still grapple with the same problems of verisimilitude as social sciencists and experimental scientists

I wouldn't really say we have the same problems. A proof is never controversial, an attempted one can be. In the end it's still theoretically possible to reduce any such attempt to known statements (or even the axioms) and check its validity without any possible doubt, which is something experimentalists can't claim. Our problem simply stems from the fact that some mathematics is excessively difficult while theirs is an inherent part of their discipline (and, more generally, of our perception of the real world).

Just thought you might like to see this as well, just saw it on my RSS feed:

http://science.slashdot.org/article.pl?sid=08/03/20/1728236&from=rss

Jamie

Someone needs to do a DG on L-functions for epic justice

I'm glad you asked (and using a modified all your base phrase, no less!). :p
L-functions kick ass.

P.S. The transcendental L-Function thing is pretty cool but I very much doubt it'll help to make significant progress on the RH itself. It's funny how they say stuff like that every time anything remotely related to it is found.

It's funny how they say stuff like that every time anything remotely related to it is found.

That's the way you get your papers published. Every new piece of mathematics has an abstract like

"We discuss a categorification of the chern simmons action via temperley lieb algebras that... ...applications to representations of Lie algebras... ...Leading to a 4-D TQFT, A proof of RH, a cure for cancer, solutions to the mass gap and world peace... ...making Harry Potter, Terminators 1&3 and magic carpets a reality... ...Buy yours today!"

It's all about getting the keywords up kids.

P.S. L-function Dg sounds ace.

I was talking about slashdot and the article it links to though. I don't think the paper actually says that since the L-function itself is a big enough deal. Similarly, every time there's something on RH in the news they say solving it might break RSA or something of the sort. I guess it's just journalists' natural leaning towards sensationalism.

That said, I've seen a pretty large number of abstracts of that kind as well. Seems to me that the good ones usually understate the content and the bad ones do the opposite. :D