hi mom!

September 7, 2004 2:21 AM

Russian may have solved Riemann hypothesis. Financial disaster ensues.
posted by Espoo2 (17 comments total)

DOH.

I meant Louis de Branges, a French-born mathematician.

Mind was warped by this older /. article about the russian who recently claimed that he solved the Poincare Conjecture.
posted by Espoo2 at 2:45 AM on September 7, 2004

Well, it's possible to have an application of a mathimatical principle without having proved it works. A lot of crypto and other computers are things like that. We think it works, and it works in practice, but know one actualy knows if it works in theory.

So it's not like having a proof of this would break eccommerce any more then thinking that this would break eccommerce.

On the other hand, there is some speculation that proving this might yeild some new kinds of math, which could then be used to do quicker prime factorization. The article dosn't really explain why it would, however, so who knows.
posted by delmoi at 3:12 AM on September 7, 2004

* brain explodes *

Interesting stuff....thanks espoo2
posted by mattr at 3:14 AM on September 7, 2004

People shouldn't use the word "spectrometer" in simplifying analogies.
posted by Pretty_Generic at 3:45 AM on September 7, 2004

Would it have killed the Guardian to include a link to the Clay Mathematics Institute?
posted by gi_wrighty at 4:25 AM on September 7, 2004

That's the most overwrought article on RH ever. "The sky is falling! We'll never be able to use prime numbers again!" Nimrods.

Short version: Perelman's proof of Poincare is almost certainly correct (people I know at Utah have worked through it), and de Branges' proof of RH is almost certainly not.
posted by gleuschk at 4:39 AM on September 7, 2004

Eh. P vs. NP was always more interesting to me.
posted by paladin at 5:04 AM on September 7, 2004

Way over my head, but a fascinating read. Thanks Espoo2!
posted by shoepal at 7:01 AM on September 7, 2004

Scary to think that so much is placed on the Riemman Hypothesis, but then they're nowhere close to solving it.
posted by destro at 7:28 AM on September 7, 2004

It seems like the article is stretching for a reason why non-math-geeks should care.

"Someone claimed to have solved the Riemman Hypothesis."

"So what."

"Well, if this highly suspect proof is true, and some more as yet unforseen breakthroughs in mathematics happen, ALL OF INTERNET COMMERCE COULD COME SCREECHING TO A HALT!"

"Oh shit!"

Cryptography is to a large degree built on finding functions that are easy to solve if you know the secret, and difficult to solve if you don't. Any analytical techniques produced by the proof might still be so expensive that they are not of practical use to cryptoanalysis. And remember, the product of two primes is only one possible function that can be used for cryptography. It seems like journalists' understanding of cryptography frequently does not go much beyond RSA.
posted by KirkJobSluder at 9:37 AM on September 7, 2004

I'd wait a while... this is not the first time de Branges has claimed a proof of the RH...
The deal with De Branges can be found here, written by the author of a popularizing book on the subject. Here is his proof (pdf file - obviously technical!), and here's a rather quaint "Apology for the Proof of the Riemann Hypothesis" (pdf) combining serious mathematics with the hypothesis' history and some personal mathematical autobiographical notes...
It's probably impossible to understand the allure and the importance of the RH without some mathematical background, but if you have a decent first year college mathematical background, Derbyshire's Prime Obsession, is excellent reading (worked for me)...
posted by talos at 9:52 AM on September 7, 2004

de Branges supposed proof has been floating around math circles for a while, so this isn't really news. Nor is it clear at all how a proof of the Riemann hypothesis would provide much of any immediate leverage for attacks on factoring large numbers.

I mean, go ahead and make the assumption that Riemann was correct and that the nontrivial zeros of his extended zeta function all lie on the critical line (they all do as found to date through mass number munching). What new attacks on factoring, for example, RSA-640, does that assumption provide?
posted by fold_and_mutilate at 11:23 AM on September 7, 2004

As a non-expert, I have always been led to believe that what protected your internet transactions was not cryptography, but the fact that "hackers" probably already had your credit card number, along with ten million other credit card numbers in a big text file, but that, statistically, they would never get around to using yours, specifically. Somehow, statistics is more reassuring to me than prime number cryptography. Dunno why.
posted by Hildago at 11:25 AM on September 7, 2004

fold and mutilate: More than that, I believe that it has been proven that all of the nontrivial zeros fall within an infinitetismal strip next to the line. However going from saying that the maximum distance away from the line approaches zero and that the maximum distance away from the line equals zero seems to be a difficult step.

From my admittedly casual understanding of the problem, it is not hard to find easier ways to factor. However it is hard (perhaps even impossible) to find easier ways to factor that don't scale up exponentially with each added digit (or bit).
posted by KirkJobSluder at 2:12 PM on September 7, 2004

And of course, for some reason this little bit of journalistic hyperbole somehow rose to the top of my memigo list.

Is is just me, or should journalists be forced to read at a minimum Singh's The Code Book and at best crack open Kahn's seminal but very readable The Codebreakers before typing one word about cryptography?
posted by KirkJobSluder at 3:03 PM on September 7, 2004

Slightly OT, but the real security in ecommerce is provided by credit card policies which allow line-by-line repudiation of charges on your bill - you can simply say, "I didn't authorize this" and they will eat the charges. And it's a good thing, because SSL is just a digital Maginot Line - it protects against something that isn't likely to happen (an attacker gaining complete control of the communication channel and running a man-in-the-middle attack) and not at all against what is in fact very likely, which is that one of the hosts at either end of the transaction is compromised. (through for eg. a phishing expedition, or any number of MS-related vulnerabilities.)
posted by dinsdale at 3:10 PM on September 7, 2004

“Nimrods?” Is being called a hunter derogatory these days?
posted by bz at 5:01 PM on September 7, 2004