September 07, 2004

True to media type

It's surprising that something becomes news, sometimes. But once it does, the treatments are pretty much predictable. At least, they often tell you as much as about the information sources as about the information provided.

Back on April 15, this article by Eric Weisstein appeared in MathWorld Headline News:

Russian mathematician Dr. Grigori (Grisha) Perelman of the Steklov Institute of Mathematics (part of the Russian Academy of Sciences in St. Petersburg) gave a series of public lectures at the Massachusetts Institute of Technology last week. These lectures, entitled "Ricci Flow and Geometrization of Three-Manifolds," were presented as part of the Simons Lecture Series at the MIT Department of Mathematics on April 7, 9, and 11. The lectures constituted Perelman's first public discussion of the important mathematical results contained in two preprints, one published in November of last year and the other only last month.


Stripped of their technical detail, Perelman's results appear to prove a very deep theorem in mathematics known as Thurston's geometrization conjecture. Thurston's conjecture has to do with geometric structures on mathematical objects known as manifolds, and is an extension of the famous Poincaré conjecture. Since Poincaré's conjecture is a special case of Thurston's conjecture, a proof of the latter immediately establishes the former.

Perelman's work had been reported in Science News back in June of 2003, Mark Kleiman blogged about it in December of 2003, the Boston Globe had a story on December 30, and Charles Kuffner blogged about it on January 2, 2004, among other things that you can find on the first page that Google returns for {Perelman Poincare}.

But yesterday, Keith Devlin talked about Perelman's proof at the British Association for the Advancement of Science's Festival of Science 2004 (main program here), and this (or the associated publicity) was taken by some journalists as an announcement of something newsworthy.

So Reuters ran a piece in its "Oddly Enough" category, exclaiming about how Perelman "has simply posted his results on the Internet and left his peers to work out for themselves whether he is right". Since the proof is not news, I guess some Reuters editor decided to treat it as a human interest story. At least, that's the charitable interpretation. Apparently the fact that Perelman traveled to MIT to give a series of lectures doesn't matter, perhaps because it happened last year, and in any case spoils the story line.

The Reuters story also indicated its reporters' and editors' deep appreciation of practical mathematics by adding an extra three orders of magnitude in the currency conversion process from dollars to pounds:

A reclusive Russian may have solved one of the world's toughest mathematics problems and stands to win $1 million (560 million pounds) -- but he doesn't appear to care.

Though perhaps they had the Lebanese pound in mind, in which case the error is only a factor of three.

At the Guardian, Tim Radford combined Pereman's work with Louis de Branges' alleged proof of the Riemann Hypothesis to predict doom and disaster for life as we know it, or at least for the internet. Some lesser outlets have picked up Radford's disaster-mongering, so in case you feel the urge to stockpile drinking water and check your ammunition supplies, here's what MathWorld said about de Branges a couple of months ago:

Riemann Hypothesis "Proof" Much Ado About Nothing
A June 8 Purdue University news release reports a proof of the Riemann Hypothesis by L. de Branges. However, both the 23-page preprint (from 2003) cited in the original release and a 124-page preprint (from 2004) cited in a back-dated modified release seem to lack an actual proof. Furthermore, a counterexample to de Branges's approach by Conrey and Li has been known since 1998. The media coverage therefore appears to be much ado about nothing.

The BBC manages to quote Keith Devlin as (apparently) stating that Poincare's conjecture for n=3 -- what Perelman seems to have proved -- is false:

"One of the odd things about this conjecture is that if you go even higher in dimensions - four, five, six manifolds, the Poincare Conjecture is true as it is for two manifolds (dimensions)," said Dr Devlin.

But it fails for three manifolds. The one case that is really of interest in physics is the one case in which it fails."

What he meant, of course, was not that the conjecture fails for the case of n=3, but that it had remained open for n=3, and has now apparently been shown to be true in that case as for other values of n. Here's a detailed account, from MathWorld, some version of which Devlin no doubt explained to the BBC's reporter:

In the form originally proposed by Henri Poincaré in 1904 (Poincaré 1953, pp. 486 and 498), Poincaré's conjecture stated that every closed simply connected three-manifold is homeomorphic to the three-sphere. Here, the three-sphere (in a topologist's sense) is simply a generalization of the familiar two-dimensional sphere (i.e., the sphere embedded in usual three-dimensional space and having a two-dimensional surface) to one dimension higher. More colloquially, Poincaré conjectured that the three-sphere is the only possible type of bounded three-dimensional space that contains no holes. This conjecture was subsequently generalized to the conjecture that every compact n-manifold is homotopy-equivalent to the n-sphere if and only if it is homeomorphic to the n-sphere. The generalized statement is now known as the Poincaré conjecture, and it reduces to the original conjecture for n = 3.

The n = 1 case of the generalized conjecture is trivial, the n = 2 case is classical (and was known even to 19th century mathematicians), n = 3 has remained open up until now, n = 4 was proved by Freedman in 1982 (for which he was awarded the 1986 Fields Medal), n = 5 was proved by Zeeman in 1961, n = 6 was demonstrated by Stallings in 1962, and n >= 7 was established by Smale in 1961 (although Smale subsequently extended his proof to include all n >= 5).

The BBC also has Devlin saying that "manifolds" are "dimensions", but at least they left telepathy out this time.

People on Slashdot took the opportunity to argue about attitudes towards money and fame. There was also some discussion about the question of whether putting papers up on the internet constitutes "publication" (as required by the terms of the Clay prize) or not.

The recent story was also picked up by many other outlets, though not yet by many in the blogosphere -- perhaps because it's not really news. There are just four references in Technorati so far, all simply pick-ups of a wire service story.

Devlin's talk seems to have been part of a session entitled "Million Dollar Maths", introduced in the Festival's program this way:

Million dollar maths
The Clay Mathematics Institute's seven prize problems are providing exciting challenges for mathematicians in the new Millennium. This event looks at the problems: the Riemann Hypothesis,Navier Stokes equations, Poincare conjecture, Yang-Mills theory, P vs NP and the Birch and Swinnerton-Dyer conjecture which hold eternal fascination for mathematicians, and also for those who follow the story of their solution.

The speakers were Marcus du Sautoy on the Riemann Hypothesis (he doesn't mention de Branges' claimed proof in his abstract, but perhaps discussed it in his talk), Simon Singh on the Clay $1M challenge, and Keith Devlin on the Poincaré Conjecture.

[Update: If you're interested in the (very interesting) background of the Louis de Branges story, there's a July 2004 London Review of Books article by Karl Sabbagh, and a paper by Louis de Branges himself entitled " Apology for the Proof of the Riemann Hypothesis", dated 8/10/2004.]


Posted by Mark Liberman at September 7, 2004 08:12 AM