Not Even Wrong

Louis de Branges is a mathematician at Purdue who has had a long history of claiming proofs of the Riemann hypothesis. His latest claim has lead to a press release from Purdue. The press release points to what seems to be an older manuscript by de Branges outlining some of the history of the Riemann hypothesis and his work on it. This also includes some history of his ancestors, and de Branges has taken to calling himself “Louis de Branges de Bourcia”. He more or less promises that if he wins the Clay million dollar prize for solution of this problem he would use it to restore the ruined chateau de Bourcia for use as a mathematical research institute.

The actual purported proof is here. One mystifying thing about it is that in the abstract and introductory paragraph it repeatedly refers to relations to quantum mechanics, but there seems to be nothing about this in the body of the paper. Weyl’s book on quantum mechanics and group theory appears in the references, but nothing in the text seems to refer to this.

de Branges has a checkered history as a mathematician, with several of his claimed proofs of the Riemann hypothesis and other problems turning out to be incorrect. On the other hand, he did produce a correct proof of one well-known problem, the Bieberbach Conjecture. In that case his initial manuscript was pretty impenetrable, but after he explained his ideas to a group of Russian mathematicians, they gave a more understandable version of the proof and it became clear that de Branges really did have a proof. It looks like this one may also take some major effort to see what he really has.

For more about de Branges and the Riemann hypothesis, see the recent popular book “The Riemann Hypothesis: the Greatest Unsolved Problem of Mathematics” by Karl Sabbagh. A review of this book has some interesting comments about de Branges and his NSF funding.

A couple weeks ago a preprint appeared on the arXiv by R. A. Arenstorf, a mathematician at Vanderbilt University, claiming a proof of the twin prime conjecture. I asked one of my colleagues who is an expert on the subject about it and he said he didn’t believe it and would bet $100 it was wrong. Today I see that Arenstorf has withdrawn the preprint, saying that a serious error has been found.

A couple years ago two French brothers, Igor and Grichka Bogdanov, managed to get Ph.Ds in France and publish several nonsensical papers about quantum gravity in refereed physics journals, several of them rather well-known and prestigious ones. John Baez has a useful web-page about this story.

This whole thing seemed to me strong evidence of how in recent years there has been a collapse of any real intellectual standards in this part of theoretical physics, and I ended up being quoted about this in various places. The “Affaire Bogdanov” died down fairly quickly, and the scandal doesn’t seem to have lead to much in the way of higher standards.

I recently heard from Fabien Besnard, who wrote to tell me that the Bogdanovs have a new book out, called “Avant le Big-bang” (Before the Big Bang), in which they quote me as endorsing their work. Besnard has a web-page (in French) on the latest developments in the L’affaire Bogdanoff.

The Bogdanovs wrote me last year, here’s a copy of their e-mail. I made the mistake of thinking “maybe these guys aren’t so bad, just overly-enthusiastic sorts who could use a little helpful advice”, and wrote this back to them. In their book they use part of my e-mail, mis-translating:

“It’s certainly possible that you have some new worthwhile results on quantum groups..” (I was being too polite here; while possible, it is unlikely)

as

“Il est tout a fait certain que vous avez obtenu des resultats nouveaux et utiles dans les groupe quantiques” (It is completely certain that you have obtained new worthwhile results on quantum groups).

One lesson from this is not to write back to crackpots. Another strange part of this story: late last year I received an e-mail purporting to be from a “Prof. L. Yang” at the “International Institute of Mathematical Physics” at Hong Kong University. It appeared to come from

th-phys.edu.hk

a domain name that is registered with the Hong Kong DNS, supposedly by the Hong Kong University of Science and Technology. I connected to the web-site at this address, which at the time contained an official-looking web-page for this Insitute. It now contains just a listing of directories, one of which is full of .pdf files of the papers of Arkadiusz Jadczyk.

This web-site is hosted by a US web-hosting company “Everyone’s Internet, Inc.” If you look carefully at the header for this e-mail you see that while it purports to be from

“liu-yang.imp@th-phys.edu.hk”

it really comes from

th-phys.edu.hk (ATuileries-117-1-27-138.w193-253.abo.wanadoo.fr [193.253.192.138])

which appears to be a machine connecting to the internet from Paris, set to claim to be “th-phys.edu.hk”.

It’s looking more and more like the original idea that the Bogdanovs were hoaxers, putting on the physics community, was closer to the truth than the idea that they are serious, just not very good, researchers.

Update: The comment section received a message from a supposed mathematician named “Roland Schwartz” defending the Bogdanov’s work on quantum groups. The source of the comment was
IP number 217.128.255.129. The DNS shows

nslookup 217.128.255.129

Name: ATuileries-117-1-29-129.w217-128.abo.wanadoo.fr
Address: 217.128.255.129

Funny, this seems to be a very close neighbor in Paris of Prof. L. Yang…..

I also just noticed that Jacques Distler has posted an account of his experiences with “Prof. L. Yang” et. al.

I was visiting the math department at Dartmouth the past couple days, and gave a colloquium talk there. It’s now available online.

Witten has contributed an essay to the latest issue of Nature about electroweak symmetry breaking. He describes the main conventional ideas about this, ending with the latest anthropic ones. Here are his comments about those:

“One approach is the anthropic principle, according to which the dark energy and the Higgs particle mass take different values in different parts of the Universe, and we inevitably live in a region in which they are small enough to make life possible. If so, many other properties of the Universe that we usually consider fundamental — such as the mass and charge of the electron — are probably also environmental accidents. Although I hope that this line of thought is not correct, it will inevitably become more popular if experiment shows that electroweak-symmetry breaking is governed by the textbook standard model with a Higgs particle and nothing else.”

He ends with the eminently reasonable summary:

“As yet, none of these theoretical proposals about electroweak-symmetry breaking are entirely satisfying. Hopefully, by the end of this decade, experimental findings at the Tevatron and the LHC will set us on the right track. But the diversity and scope of ideas on electroweak-symmetry breaking suggests that the solution to this riddle will determine the future direction of particle physics.”

Sean Carroll has some comments about the anti-big bang petition. He also points to Ned Wright’s explanation of what is wrong with various proposed alternatives to the big bang scenario. In particular this explains in detail what the problems with Irving Segal’s “Chronometric Cosmology” are, something I’d always wondered about.

Segal was a very good mathematician, who did serious work on quantum field theory in the 50s and 60s. He’s the “Segal” in what is sometimes called the “Segal-Shale-Weil” representation. Segal is a counter-example to Carroll’s observation that, for the most part, opponents of the big bang are not very smart. Unfortunately, it seems that quite smart and otherwise reasonable people can have unshakable faith in ideas that don’t work. Segal’s student John Baez wrote up some of his memories of his advisor and his cosmological research.

Slides used by many of the lecturers at the recent Davis mathematical physics conference in honor of Albert Schwarz are now online.

It’s always a little worrying when this happens, but sometimes I find myself very much agreeing with at least parts of what Lubos Motl has to say. For example see this recent posting to sci.physics.strings. In it Motl argues that

“I think it is premature to try to construct this major framework that would explain the character of vacuum selection and very early cosmology in string theory”

and

“So my belief is that we will have to understand the nonperturbative structure of the stringy arena using some new universal definition of string theory – a definition that is both non-perturbative (reaches the strongly coupled regions) as well as background-universal (reaches the geometries and non-geometries that are different from the starting one), and only afterwards, we will be able to start answering the stringy cosmological questions in a better context. Without this new tool, everything is just vague guesswork.

In my opinion, the research of string cosmology; stringy inflation; de Sitter space in string theory; scattering in backgrounds with non-standard causal diagrams; and all similar things that have essentially be started by the observation of accelerating Universe back in 1998 – has led to a very small number of intriguing results. There is almost nothing non-trivial and mathematically intriguing going on here; there is as much output as much input we insert. It remains a combination of phenomenology and speculations where conjectures can rarely be clearly ruled out.”

I’ve never really understood why there are fields of “string phenomenology” and “string cosmology” when the theory is still in a state that it can’t reliably calculate anything. While I think it is wishful thinking to believe that if you understood string theory better it would reproduce the real world, at least Motl’s is a consistent scientific position.

Motl is also a fierce opponent of the “anthropic” arguments that have become popular among string theorists. For the latest example of anthropic argumentation, see this posting at Jacques Distler’s weblog.

For many years now the SPIRES database at SLAC has been used to produce a list of the most frequently cited papers during each year. Since 1997 Michael Peskin has been doing this, while at the same time writing up a description of what is in the 40 or so most popular papers, together with comments on what this data shows about trends in particle physics. The 2003 edition of Peskin’s review has recently appeared.

Peskin notes that SPIRES has begun indexing more astrophysical papers during the last two years, and many particle physicists have turned their attention to cosmology. He has expanded the number of top papers he reviews from 40 to 50 to take into account the greater coverage of the database.

The most frequently cited article, this year and every year, is the Particle Data Group’s “Review of Particle Physics” compilation of experimental particle physics data. It is conventional for experimental papers to often refer to this instead of to the original papers. This year the number two and three positions are held by papers from the WMAP experiment, with number four the original results on high redshift supernovae that indicated a non-zero cosmological constant.

The first particle theory paper is the Randall-Sundrum one at number five, and Maldacena’s AdS/CFT paper is at number seven. For many years the top part of this list was heavily dominated by relatively new string theory papers, but the situation is now dramatically different. The highest-ranked post-1999 paper is one about PP-waves at number 18, the next is one at number 37 by Ashoke Sen about time-dependent backgrounds. The only other post-1999 paper in the top 50 is the Dijkgraaf-Vafa paper about supersymmetric gauge theories, which is at number 39.

This list provides pretty conclusive evidence that the field of particle theory more or less flat-lined about 5 years ago, with only a small number of minor blips of brain activity since then.

There’s also a cumulative list of the most highly cited papers of all time. Here the dramatic movement one can watch is the speed with which Maldacena’s paper accumulates citations. At the end of last year it was at number 6 on the list of all-time most frequently cited papers; it has now moved to number 5 and soon will overtake number 4. Within a couple of years it should be at number three, only outranked by the Review of Particle Properties and Weinberg’s original paper on the Weinberg-Salam model.