Math Drudge

Fields Medals awarded

admin — Thu, 19 Aug 2010 15:26:29 +0000

The 2010 meeting of the International Mathematical Union is being held in Hyderabad, India. At this meeting, Ingrid Daubechies (of wavelet fame) was appointed President, the first woman ever afforded than honor. Also at this meeting the Fields Medal, long regarded as the mathematical equivalent of the Nobel Prize, was awarded to four mathematicians:

Elon Lindenstrauss, of Hebrew University of Jerusalem, received the award for “far-reaching advances in ergodic theory,” namely the study of random processes and the statistical behavior of dynamical systems. Lindenstrauss has achieved progress in what is known as the Littlewood conjecture.
Ngô Bo Châu, of Université Paris-Sud in Orsay, France, received the award for a “brilliant proof” of a long-standing conjecture in number theory known as the “Fundamental Lemma.” This lemma is a central feature of a unifying vision of mathematics, originally sketched by Robert Langlands, now at the Institute for Advanced Study in Princeton, NJ, that ties together numerous aspects of modern mathematics. With this breakthrough, further advances in the “Langland Program” now appear possible.
Stanislav Smirnov, of the University of Geneva, Switzerland, received the award for work in statistical physics, in particular in the lattice models now used as approximations to continuous space. This schemes have assumed that the scaling limits, as these grids become finer and finer, don’t propagate artifacts of the original lattice. Smirnov has affirmed this principle for triangular lattices.
Cedric Villani, of the Henri Poincaré Institute in Paris, received the award for work in mathematical physics, in particular for work in the area of statistical mechanics and entropy. Villani’s work concluded that a highly organized system reaches its equilibrium state at different speeds. Villani also discovered surprising connections between the theory of gas diffusion and problems in the economics of transportation.

Several other awards were also announced at the ICM meeting:

The Nevanlinna Prize was given the Daniel Spielman of Yale University for work in linear programming and error-correcting codes. For example, Spielman and Shang-Hua Teng of Boston University have developed a theory that explains why the simplex method works so well on practical linear programming problems.
The Gauss Prize was given to Yves Meyer of the École Normale Supérieure de Cachan in France. Meyer was instrumental in developing the theory of wavelets.
The first Chern Medal was given to Louis Nirenberg of New York university, for his work in the modern theory of partial differential equations.

Further details are available in a very nice article by Barry Cipra on the Science Now website: Online article.

Workshop to honor Jonathan Borwein’s 60th birthday

admin — Tue, 17 Aug 2010 22:59:35 +0000

In honor of Jonathan Borwein’s 60th birthday in May 2011, a workshop on “Computational and Analytical Mathematics” will be held at the IRMACS Center of Simon Fraser University in Burnaby, BC, Canada.

Here is a synopsis of the upcoming meeting, taken from
SFU conference announcement:

Having authored more than a dozen books and more than 300 publications, Jonathan Borwein is one of the most productive Canadian mathematicians ever. His research spans pure, applied, and computational mathematics as well as high performance computing. His research continues to have enormous impact: MathSciNet lists more than 2500 citations by more than 1250 authors, and he is one of the 250 most cited mathematicians of the period 1980-1999. He has served the Canadian Mathematics Community through his presidency (2000–02) as well as his 15 years of editing the CMS book series.

Jonathan Borwein’s vision and initiative have been crucial in initiating and developing several institutions that provide support for researchers with a wide range of scienti?c interests. A few notable examples include the Centre for Experimental and Constructive Mathematics and the IRMACS Centre at Simon Fraser University, the Dalhousie Distributed Research Institute at Dalhousie University, the Western Canada Research Grid, and the Centre for Computer Assisted Research Mathematics and its Applications, University of Newcastle.

As Dr. Borwein turns 60 in May 2011, a great opportunity arises to celebrate this shining example of excellence through a workshop held in his honour. The profound impact his research has had on Optimization, Functional Analysis, Operations Research, Mathematical Programming, Number Theory, and Experimental Mathematics is certain to attract high-caliber scientists from a wide range of mathematical fields. The workshop will be an excellent opportunity to survey the state-of-the-art in these areas, and to discuss promising research directions and approaches.

Has the “P not NP” problem been solved?

admin — Wed, 11 Aug 2010 12:01:52 +0000

On 6 August 2010, Vinay Deolalikar, a mathematician working at Hewlett-Packard Laboratories in Palo Alo, California, distributed a note to some colleagues claiming that he had solved the “P not NP” problem, a most famous and potentially far-reaching question at the nexus of mathematics and computer science. Deolalikar’s manuscript is available here: Deolalikar paper.

The Clay Mathematics Institute describes this problem as follows (Clay):

Suppose that you are organizing housing accommodations for a group of four hundred university students. Space is limited and only one hundred of the students will receive places in the dormitory. To complicate matters, the Dean has provided you with a list of pairs of incompatible students, and requested that no pair from this list appear in your final choice. This is an example of what computer scientists call an NP-problem, since it is easy to check if a given choice of one hundred students proposed by a coworker is satisfactory (i.e., no pair taken from your coworker’s list also appears on the list from the Dean’s office), however the task of generating such a list from scratch seems to be so hard as to be completely impractical. Indeed, the total number of ways of choosing one hundred students from the four hundred applicants is greater than the number of atoms in the known universe! Thus no future civilization could ever hope to build a supercomputer capable of solving the problem by brute force; that is, by checking every possible combination of 100 students. However, this apparent difficulty may only reflect the lack of ingenuity of your programmer. In fact, one of the outstanding problems in computer science is determining whether questions exist whose answer can be quickly checked, but which require an impossibly long time to solve by any direct procedure. Problems like the one listed above certainly seem to be of this kind, but so far no one has managed to prove that any of them really are so hard as they appear, i.e., that there really is no feasible way to generate an answer with the help of a computer. Stephen Cook and Leonid Levin formulated the P (i.e., easy to find) versus NP (i.e., easy to check) problem independently in 1971.

If Deolalikar’s solution were to stand scrutiny, he could receive a prize of US$1 million that has been offered by the Clay Mathematics Institute for the solution. Some initial response was cautiously optimistic, but now there are indications that the tide may be turning against it.

In any event, the episode has highlighted the emergence of a new mode of collaboration for research mathematics. Here is an excerpt from a commentary by John Markoff of the New York Times (see URL below):

Some of the researchers said that until now such proofs had been hashed out in colloquiums that required participants to be physically present at an appointed time. Now, with the emergence of Web-connected software programs it is possible for such collaborative undertakings to harness the brainpower of the world’s best thinkers on a continuous basis.

In his recently published book “Cognitive Surplus: Creativity and Generosity in a Connected Age” (Penguin Press), Clay Shirky, a professor of interactive telecommunications at New York University, argues that the emergence of these new collaborative tools is paving the way for a second scientific revolution in the same way the printing press created a demarcation between the age of alchemy and the age of chemistry.

“The difference between the alchemists and the chemists was that the printing press was used to coordinate peer review,” he said. “The printing press didn’t cause the scientific revolution, but it wouldn’t have been possible without it.”

Now, he says, the new tools are likely to set off a similar transformation.

“It’s not just, ‘Hey, everybody, look at this,’ ” he said, “but rather a new set of norms is emerging about what it means to do mathematics, assuming coordinated participation.”

Along this line, the following Scott Aaronism article lists “Ten Signs that a Claimed Result is Wrong,” which are good to keep in mind for any new mathematical result of this sort: Online article.

References

New York Times
New Scientist
Nature article
Richard Lipton’s blog
U.K. Telegraph

Why I love my Telco

Jon Borwein — Mon, 09 Aug 2010 06:16:52 +0000

I am a great fan of the intelligent use of technology. Indeed, I like David Bailey have spent a great deal of my career advocating just such use. The story below is an unexaggerated description of one of the most frustrating encounters I have ever had with a major company. I am left wondering whether Telstra has ever learned what it means to be a private company; to offer genuine service, honest quality assurance, and knowledgeable assistance; to use modern databases or train competent assistants. There again, when the main competition in Oz is Optus what choice does a consumer have? Certainly my experience must have been a tad unusual or Telstra would I imagine no longer be in business. That said, I am left scratching my head at such profligate and repeated waste of time, energy and resources by everyone involved.

See what you think (http://carma.newcastle.edu.au/jon/telstra.pdf).

Jonathan Borwein (half of Math Drudge)

Borwein to present lecture on “The life of Pi”

admin — Fri, 06 Aug 2010 20:25:25 +0000

Prof. Jonathan Borwein of the University of Newcastle, Australia, will give the “public lecture” at the upcoming meeting of the Australian Mathematical Society on “The life of Pi.” Here are some details: Announcement

Abstract: The desire to understand pi, the challenge, and originally the need, to calculate ever more accurate values of pi, the ratio of the circumference of a circle to its diameter, has captured mathematicians——great and less great——for many many centuries and, especially recently, pi has provided compelling examples of computational mathematics. Pi, uniquely in mathematics, is pervasive in popular culture and the popular imagination. In this lecture I shall intersperse a largely chronological account of pi’s mathematical status with examples of its ubiquity.

Time: 6:30pm Tuesday 28 September 2010

Place: Abel Smith Lecture Theatre (Blg 23), University of Queensland, St Lucia Campus, Brisbane, Australia. Parking is available on the St Lucia campus; please check the UQ Website about parking zones, costs and locations.

Viewgraphs: Borwein’s viewgraphs for this lecture are available here: Online presentation.

Japanese and U.S. researchers compute pi to 5 trillion places

admin — Fri, 06 Aug 2010 15:03:33 +0000

Online article

Details of methods used

Synopsis:

A pair of Japanese and US computer whizzes claim to have calculated pi to five trillion decimal places — a number which if verified eclipses the previous record set by a French software engineer.

“We believe our achievement sets a new record,” Japanese system engineer Shigeru Kondo said, adding that the Frenchman’s calculation to nearly 2.7 trillion places was believed to be the previous record. …

It took 90 days to calculate pi at Kondo’s home using a desktop computer with 20 external hard disks. It ran on the operating system Windows Server 2008R2 and used powerful Intel microprocessors. Verification took 64 hours.

Kondo built the computer by himself, procuring parts from local electronics shops and via the Internet. “I don’t really want to say how much it cost me as my family may hear it… it’s about 18,000 dollars,” he told AFP by telephone. …

Latest research indicates we unconsciously pursue goals

Jon Borwein — Mon, 05 Jul 2010 04:18:44 +0000

The notion that humans often take actions and pursue goals due to subconscious desires and instincts dates back to Sigmund Freud, who suggested, among other things, that repressed sexual urges underlay some human behavior. Freud’s theories were later judged unreliable and largely nonfalsifiable. In any event, until recently it was assumed that conscious decisions are essential for the mental processes involved in setting and pursuing a goal. Indeed, goal pursuit has been considered nearly synonymous with conscious thought.

But a number of recent studies suggest otherwise. In one of the first studies of this sort, some U.S. students were seated at a table to work on two apparently unrelated puzzles. For some students, the first puzzle included words related to achievement (such as “win” or “achieve”), but for others it did not. The researchers found that students who were exposed to the achievement-oriented words outperformed the other group of students on the second puzzle. Interviews with students after the test showed that the students were not aware of any influence of the first task on the second. Somewhat disconcertingly this works equally well with subliminal cues.

In some other studies, researchers found that subjects reading words related to money-making occupations (e.g., “stockbroker”), or even watching another person’s actions such as operating a slot machine, are more likely to work harder on tasks where money is at stake.

Even subtle cues in a working environment can influence behavior. For example, upon entering an office, people become more competitive when they see a leather briefcase placed on a desk. They talk more softly when there is a photo of the interior of a library on the wall. They clean their table more often when there is vague scent of cleansing agent in the air.

It is important to note that in many of these studies, subjects were asked afterwards whether they felt motivated to pursue the goal in question. These retrospective checks indicate that while subjects may become conscious of their motivation after the behavior is performed and when they are explicitly asked to reflect on it, they were generally not aware of it when they participated in the test.

In short, a large and growing body of research indicates that the pursuit of specific goals can be initiated or amplified outside of our conscious awareness. Understanding how this happens is not well understood at the present time, but is an area of active research. At one level this growing body of research confronts our current understanding of consciousness and challenges conventional notions of free will.

One intriguing question is whether the productivity of scientific research can be enhanced by subtle cues in the research environment. If so, how can one take advantage of such subtle effects in a positive way?

More details on these intriguing findings can be found in an informative and readable article [Custers2010] in a recent issue of Science, from which the above note is summarized. The authors do propose a mechanism to explain recent findings and emphasize that attention and consciousness are not synonyms. The review article contains a reproduction of Ruebens painting Achilles Slays Hector and notes that in the Iliad no reference is ever made to either consciousness or intention. Current discoveries make Julian Jaynes’ thesis in The Origin of Consciousness in the Breakdown of the Bicameral Mind [Jaynes1976] seem less audacious. Likewise they are highly consonant with the developing sophistication of behavioral economics in recent best-selling books such as Richard Thaler and Cass Sunstein’s Nudge: Improving Decisions about Health, Wealth and Happiness [Thaler2009] and Dan Ariely’s Predictably Irrational [Ariely2008].

References

[Ariely2008] Dan Ariely, Predictably Irrational: The Hidden Forces That Shape Our Decisions, Harper Perennial, 2008. See also Amazon listing and Wikipedia article.
[Custers2010] Ruud Custers and Henk Aarts, “Unconscious Will: How the Pursuit of Goals Operates Outside of Conscious Awareness,” Science, vol. 329, no. 5987 (2 Jul 2010), pg. 47-50, available at Online article (for fee).
[Jaynes1976] Julian Jaynes, The Origin of Consciousness in the Breakdown of the Bicameral Mind, Houghton Mifflin, 1976. See also Wikipedia article.
[Thaler2009] Richard Thaler and Cass R. Sunstein, Nudge: Improving Decisions about Health, Wealth and Happiness, Penguin, 2009. See also Amazon listing and Wikipedia article.

Perelman rejects $1 million Clay award

admin — Thu, 01 Jul 2010 16:48:23 +0000

Russian mathematician Grigory Perelman announced today that he is rejecting the $1 million Clay Mathematics Institute prize for his recent solution of the Poincare conjecture. Perelman has been quoted saying he believes his contribution in proving the conjecture was no greater than that of a U.S. mathematician named Richard Hamilton, who first suggested an approach that Perelman utilized in his solution. He also indicated that his great dislike for the “organized mathematical community” was a large factor.

For more details see: AP News report | Washington Post report | New York Times report | MAA report. A fascinating and quite convincing portrait of Perelman is drawn in Masha Gessen’s 2009 book Perfect Rigor.

IBM’s “Watson” to compete against Jeopardy champs

admin — Thu, 17 Jun 2010 22:02:02 +0000

Many readers will be familiar with the Jeopardy! television show, which is the most popular quiz show in North America. One of the present bloggers confesses to watching it almost every weekday evening when not on travel (and hardly any other television program). The other blogger is also a keen armchair contestant.

In this show, clues are presented on a video screen to the three contestants, and after Canadian host Alex Trebek completes reading the clue, contestants must first ring in with a handheld button. The first contestant to ring in then has five seconds to provide the answer, which must be phrased in the form of a question. If he/she is correct, then he/she wins the amount of money attached to the question, which varies from $200 to $1000 in the first round and $400 to $2000 in the second round; if wrong, this same amount is deducted from his/her score.

Recently IBM presented the Jeopardy! show with the opportunity to compete on the show with a computer system they have been developing that answers questions presented to it in English. The system is based on IBM’s “BlueGene” supercomputer, which at present costs (in a configuration sufficient to this task) well over USD$1,000,000. After completion of the project, IBM intends to market this system, say as a tool for user support personnel. Potential uses range from medicine to online government. Some applications, particularly medical applications, also entail various ethical problems.

This development underscores the tremendous advances that have occurred recently in the field of artificial intelligence, or, as it is more commonly now known, “machine learning.” The key breakthrough in the field occurred about 15 years ago, when researchers switched to probabilistic (i.e., Bayseian) schemes instead of the strict rule-based schemes that had been attempted in the past. Researchers began using statistical schemes to analyze large volumes of documents, many of them available on the Internet. Their algorithms process any topic and automatically “learn” what words are statistically most closely associated with it. These ideas parallel developments in neurobiology and even neurophilosophy (see [Churchland]). Unlike progress in computer chess, Watson may even tell us something about human cognition.

IBM’s “Watson” system is a premier example of this new technology. IBM project manager David Ferrucci is himself an artificial-intelligence researcher specializing in question-answering systems. When Ferrucci approached IBM’s management about taking on Jeopardy!, initially he was told to forget it. But he persisted and was finally given the go-ahead to start a development effort.

The initial results were “dismal,” according to Ferrucci, but after a year, Watson’s performance had moved halfway up to the “winner’s cloud,” namely the level of effectiveness achieved by many Jeopardy! champions (some of whom have been invited to come to IBM’s research lab to compete against the system, as part of the development effort). In 2008, when Watson had achieved a level roughly comparable with the “winner’s cloud,” IBM approached Harry Friedman, the executive producer of Jeopardy! with the possibility of having the “Watson” system compete on the air with some former Jeopardy champions. The competition is scheduled for Fall 2010.

Here are some examples of some of the question that the Watson system is currently capable of handling (faster than human contestants):

[Category: "Postcards From the Edge”]: “Toured the Burj in this U.A.E. city. They say it’s the tallest tower in the world; looked over the ledge and lost my lunch.” [Answer: "What is Dubai?"]
“He was presidentially pardoned on Sept. 8, 1974.” [Answer: "Who is Nixon?"]
“In 1594 he took a job as a tax collector in Andalusia.” [Answer: "Who is Cervantes?"]
“Thousands of prisoners in the Philippines re-enacted the moves of the video of this Michael Jackson hit.” [Answer: "What is 'Thriller'?"]
[Category: "All-Eddie Before & After"]: “A ‘Green Acres’ star goes existential (& French) as the author of ‘The Fall.’” [Answer: "Who is Eddie Albert Camus?"]

But many questions that are simple for good human competitors still flummox Watson. Additional information may be found in an excellent, in-depth article that appeared recently in the New York Times [Thompson2010], from which the information above was summarized.

[Thompson2010] Clive Thompson, “What Is I.B.M.’s Watson?”, New York Times, 14 Jun 2010, available at Online article.
[Churchland2008] Paul Churchland, Neurophilosophy at Work, http://www.amazon.com/Neurophilosophy-at-Work-Paul-Churchland/dp/0521692008.

Bailey to give three talks in Spain

admin — Thu, 27 May 2010 17:34:09 +0000

David H. Bailey will present three talks in Spain in June 2010:

“High-Precision Computation: Mathematical Physics and Dynamics,” Joint
SIAM/RSME-SCM-SEMA Meeting on Emerging Topics in Dynamical Systems and Partial Differential Equations, University of Catalona, Barcelona, Spain (June 2010) PDF
“Computing as the Third Mode of Scientific and Mathematical Discovery,” Barcelona Supercomputer Center (3 Jun 2010): PDF
“High-Precision, Highly Parallel Numerical Integration,” University of Zaragoza (Dept. of Mathematics), Zaragoza, Spain, invited seminar (Jun 2010), PDF