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2. How to focus in clutch moments
3. Is the Riemann hypothesis being solved? More here, on de Branges (gated, but excerpted in the comments section).
4. The latest books on happiness
Posted by Tyler Cowen on March 19, 2008 at 04:45 PM in Web/Tech | Permalink
Comments
Can you really say links if its only one?
Posted by: ylight at Mar 19, 2008 4:53:03 PM
Excerpt:
"For nearly 25 years, de Branges has plugged away at the Riemann hypothesis. From time to time, he has posted on his website work he considers approaches a proof. Now he has gone one further and posted what he believes to be a proof of the Riemann hypothesis.
Key to this paper is the idea that there exists a deeper theory behind the zeta function. The type that Riemann studied involves positive whole numbers, but there are also other forms of zeta function that sum over mathematical sets. De Branges says he has found an underlying connection between them and this, he now claims, proves the Riemann hypothesis.
Other researchers are not so sure. The sins of de Branges's youth have not been forgiven, and it does not help that the man is a loner. Getting to grips with his paper requires understanding mathematics that he has developed more or less alone. Yashowanto Ghosh at Aquinas College in Grand Rapids, Michigan, is one of the few mathematicians to have studied de Branges's theory in depth. He says he is "fairly certain" that de Branges's approach is valid. "It differs from a valid proof only in that it lacks some technical details," says Ghosh.
Certainly de Branges knows he has his work cut out convincing his critics. The papers he has previously posted on his website tend to be overlong and seem repetitive, with almost no explanation of what he is trying to do or where he is going. Often he does not even bother to divide documents into sections. De Branges says he is making his Riemann hypothesis paper more readable by dividing it into sensible chunks and emphasising the key steps."
Posted by: Tyler Cowen at Mar 19, 2008 5:36:13 PM
Incidentally, Yashowanto Ghosh is in no way an independent expert. De Branges was not his thesis advisor, but Ghosh was a student at Purdue who studied extensively with de Branges. (See for example Sabbagh's book on the Riemann hypothesis.) Also, Ghosh has never published in this area - his two papers deal with probability theory. So Ghosh's opinion is interesting to know but not all that convincing, especially with the caveat about lacking "some technical details".
Every time de Branges claims to have solved the Riemann hypothesis, someone writes a news article about it. He might be right this time, and I certainly can't prove otherwise, but I wouldn't count on it.
I've never met de Branges, but I've heard him speak. He's an extremely bitter man, who even in his lectures spends a lot of time complaining that nobody takes him as seriously as he deserves. It's a sad situation.
Posted by: Anonymous at Mar 19, 2008 6:05:42 PM
The proof of the pudding is in the tasting, of course. While his habits fit the crackpot model let's not forget that Grigory Perlman also fit that model.
Posted by: Adam Hyland at Mar 19, 2008 8:03:13 PM
As a mathematician, I'll say this:
1. Most mathematicians, fairly or not, view de Branges as sort of a crank. He keeps claiming that he's solved it.
2. He's made false claims of proving other important conjectures before, as well as untested claims.
3. OTOH, he did prove the Bierbach Conjecture in 1984, which is really something. Even then people didn't take that proof seriously at first because of him crying wolf earlier on other results.
4. Most mathematicians don't really understand de Branges's work or methods, and he doesn't make it easy to do so at all. Oftentimes the only people who understand the methods are people who studied at Purdue.
5. Several eminent mathematicians I know have said something along the lines of "Maybe he's proven it, maybe not. I don't care until someone else checks it, but I don't have the time or want to do so myself."
Posted by: John Thacker at Mar 19, 2008 8:34:36 PM
Most mathematicians don't really understand de Branges's work or methods, and he doesn't make it easy to do so at all.
Definitely, in fact he almost goes out of his way to obscure things. He's developed a lot of elaborate theory of Hilbert spaces of entire functions, and it underlies many of his attempted proofs. For the Bieberbach conjecture, people rapidly figured out how to remove de Branges's machinery and give a simpler proof using more familiar techniques. He's still angry about this, since he thinks (correctly) that it removed all the incentive for other mathematicians to study his general theories. Overall, he makes no attempt to make his work accessible to other mathematicians; instead, he tries to bludgeon people into reading as much of his theory as he thinks they should. The net effect is simple: pretty much everyone thinks his Riemann hypothesis proofs are probably wrong, and that if by some miracle they are correct, then once somebody really understands them they'll find a much simpler version that avoids all his machinery. That leaves everyone really reluctant to be the first one to try checking the details, and it leaves de Branges feeling unfairly neglected.
He also really upset people many years ago when he first claimed to have solved the invariant subspace problem. He never said this explicitly, but he made his attitude pretty clear: he had no responsibility to check the details carefully or make his work accessible, while the referees had the responsibility to go through his work with a fine-toothed comb and correct any oversights/gaps. That's just not reasonable, and when the proof turned out to be irreparably flawed it made people even angrier. (You can get away with a lot more if you turn out to be right in the end.)
Posted by: Anonymous at Mar 20, 2008 4:18:39 AM
Today's slashdot post
http://science.slashdot.org/article.pl?sid=08/03/20/1728236
is based on this blog post. Sorry I forgot to link here - hit the submit button too soon.
Posted by: arbitraryaardvark at Mar 20, 2008 4:46:13 PM
