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Math Digest

Summaries of Media Coverage of Math

Edited by Allyn Jackson, AMS
Contributors:
Mike Breen (AMS), Claudia Clark (freelance science writer), Lisa DeKeukelaere (Brown University), Annette Emerson (AMS)


June 2006

Reviews of Unknown Quantity by John Derbyshire: "A Faulty Survey of Algebra's Roots". Reviewed by Victor Katz. Science, 9 June 2006, pages 1473-1474.
"Equal this". Reviewed by Ben Longstaff. New Scientist, 24 June 2006, page 60.

The book under review is a history of algebra. Katz compliments Derbyshire's prose and writes that the author demonstrates that algebra is not at all a dry subject. Yet Katz does not recommend the book. "In general, the book succeeds in its aim of enlightening the non-expert on what algebra is today, giving good summaries of recent work in such fields as algebraic topology, algebraic geometry, and even category theory. Unfortunately, Derbyshire's history of algebra through the 17th century has many shortcomings." The review concludes with: "There is much good reading in Unknown Quantity, and the intended audience can probably learn a lot... I had hoped, on receiving the book, that I could recommend it to my students. Unfortunately, until the major errors are corrected in a new edition, that is not possible."

The review by Longstaff is far shorter, and far more positive. "This really is a history of algebra, but don't be scared," Longstaff reassures readers. The book is "a world away from schoolroom tedium" and provides "a first-rate account that even algebraphobes will struggle to fault."

--- Mike Breen and Allyn Jackson

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"Chinese, English Speakers Vary at Math," by Randolph Schmid (Associated Press). The Washington Post, 26 June 2006.

A recent study ("Arithmetic processing in the brain shaped by cultures," by Yiyuan Tang, Wutian Zhang, Kewei Chen, Shigang Feng, Ye Ji, Junxian Shen, Eric M. Reiman, and Yijun Liu, Proceedings of the National Academy of Sciences, 30 June 2006) has shown that people perform arithmetic differently depending on their native language. Chinese researchers used an MRI to chart the areas of the brain accessed by participants completing simple addition problems and found that Chinese speakers used a region associated with visual processing, while English speakers activated an area associated with language. The researchers believe that language influences computation, but concede that math learning strategies and school training methods could play a role. In this case, this discovery could lead to improved mathematical instruction in the future.

--- Lisa DeKeukelaere

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"He Talks the Talk So Viewers Think He Figures the Figures," by Sean Mitchell. The New York Times, 25 June 2006.

Scene from Numb3rs

The most intelligent, recognizable mathematician on television never graduated from college---and he's not really a mathematician, either. But David Krumholtz, who plays a brilliant, young, crime-solving professor on the hit series NUMB3RS, has succeeded in drawing millions of Americans into the possibilites of mathematics. Casting directors for the show note that Krumholtz was chosen for his unique ability to make intricate, tangled mathematical verbiage sound like normal discourse. Krumholtz, however, admits that he lacks a strong mathematical aptitude. He approached the show instead by placing viewpoint above equations. He wanted to see how mathematicians see the world, to portray the passion of the mathematical community, and to avoid the negative stereotypes of the profession. As a result, Caltech and three mathematical conventions have invited Krumholtz to give speeches this year.

--- Lisa DeKeukelaere

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"Mathematics stepping out of the shadows," by Nicole Strandlund. Business Edge, 22 June 2006.

Canada's Mathematics of Information Technology and Complex Systems (MITACS) is a network of mathematics centers of excellence. MITACS is in its second year of sponsoring a program that places mathematics graduate students (close to 200 in 2006) into internship positions in Canada businesses. Students in the program split their time between grad school and their internship. In this article Arvind Gupta, head of MITACS, tells of the variety of jobs that math students can do and have done, and of how the program has helped keep Canadian math graduate students in Canada after graduation.

--- Mike Breen

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"Schwer fassbare dreidimensionale Sphären (Difficult-to-grasp three-dimensional spheres)," by George Szpiro. Neue Zürcher Zeitung, 21 June 2006.

This article describes the Pauli Lectures presented by mathematician Richard Hamilton of Columbia University. The lectures were delivered at the Swiss Federal Institute of Technology in Zurich. Hamilton discussed the use of the Ricci flow to attack the Poincaré and Geometrization Conjectures. He also described work of Grigory Perelman, which seems to have provided a way of resolving the conjectures.

--- Allyn Jackson

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"Hawking Takes Beijing; Now, Will Science Follow?", by Dennis Overbye. International Herald Tribune, 20 June 2006.

This article describes a conference on string theory held in Beijing in June 2006, at which the legendary Stephen Hawking was a featured speaker. The event held special significance for China. "China wants to stand up scientifically, as it is beginning to economically, and it is pouring money and talent into the sciences, particularly physics," Overbye writes. The chief organizer of the meeting was Shing-Tung Yau, a Harvard mathematician whose work intersects with physics. "I want to put on a good show," Yau is quoted as saying. Overbye writes: "Dr. Hawking, 64, is always a good show, and his arrival set off a stellar burst of camera flashes worthy of any rock star." The article goes on to talk about the state of physics research in China, where there is plenty of money for research but where training students and hiring outstanding researchers is still difficult.

--- Allyn Jackson

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"Die Ecken und Kanten des runden Balles (The corners and crusts of round balls), by George Szpiro. Neue Zürcher Zeitung, 18 June 2006.

This article appeared during the height of soccer fever as the 2006 World Cup was being played in Germany. The article discusses an intriguing mathematical fact about soccer balls: No matter what the number and shape of the soccer ball's panels, the ball's Euler characteristic is always equal to 2.

--- Allyn Jackson

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"Awards: Kyoto Prize." Newsmakers, Science, 16 June 2006, page 1595.

This short item is about the winners of the 2006 Kyoto Prize. One of the winners is Hirotugu Akaike, a researcher at the Institute of Statistical Mechanics in Tokyo. Akaike won the basic sciences prize for his work that led to "the development of statistical models used in forecasting economic trends and natural phenomena." Akaike and the two winners in other categories will each receive a gold medal and approximately US$446,000.

--- Mike Breen

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"Goal fever at the World Cup," by Michael Hopkin. Nature, 15 June 2006, page 793.
"Scientists send Eriksson the perfect penalty formula," The Daily Telegraph, 22 June 2006.
"Researchers try to formulate the perfect penalty shot," by Luis Andres Henao. The Christian Science Monitor, 6 July 2006.

Soccer action

The first article concerns one of the accepted truths about soccer: Once a team scores, the likelihood of that team scoring many goals increases. Researchers call this effect "self-affirmation." Mathematician Martin Weigel and colleagues analyzed games from previous World Cups and from Germany's premier leagues and found that high-scoring games are more frequent than would be expected if scores were distributed randomly. Weigel's team modeled game outcomes by increasing a team's chance of scoring for each goal that it had already scored and found that the model fit the score distribution "perfectly." England is one team that is historically best at self-affirmation. The paper, Football fever: goal distributions and non-Gaussian Statistics, was posted on the Physics ArXiv. The other two articles deal with research by mathematician David Lewis and scientists at John Moore University in Liverpool (UK), who came up with a formula for the perfect penalty kick. The formula involves quantities like the velocity of the ball, the time between placing the ball and taking the kick, and the striking position of the foot. The formula was sent to England coach Sven-Goran Eriksson, but it is not known whether he used it in the recent World Cup.

--- Mike Breen

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"Mathematician Colors His Numbers into Artworks," by Jennifer Flowers. Shreveport Times, 14 June 2006.

Evolution I

Half of Evolution I, courtesy of Paul Sisson.

It is not unusual to hear mathematicians use the word "beautiful" when describing some mathematical result. Conveying that beauty to non-mathematicians, however, can be a challenge. Paul Sisson, dean and professor of mathematics at Louisiana State University in Shreveport, hopes to do just that with his artworks, multicolored images of complex functions, currently hanging on the walls of a local restaurant. Sisson wrote the programs used to generate these images using Mathematica© software. Many of the images contain a golden ring, "a central mathematical reference point," Jennifer Flowers writes. Around this ring, the rest of the image lies: succeeding, neon-bright colors that represent progressively greater iterations of the original pattern.

Restaurant co-owner Amy Grosz, herself "fascinated" by the images, has observed the patrons’ interest in the works, particularly when they find that they were made by a mathematician. And this is just the kind of reaction Sisson wants: "I hope that people look at my artwork and ask, ‘what is that?’ … Every time they do that, I have five minutes to talk about math."

--- Claudia Clark

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"The N.B.A.'s Secret Superstars," by David J. Berri. The New York Times, 10 June 2006.

Basketball

There's a new way to judge the performance of N.B.A. basketball players: "whether a player's actions---both scoring and non-scoring---help his team win or not." Unlike the sabermetrics used in baseball (where it is easier to separate the contributions of individual players), the numbers in a team sport such as basketball are not so obvious. The author David Berri points out that most of the players are not like Michael Jordan, who excelled at every aspect: Most players have diverse talents and may contribute in only one or two aspects of the game. Berri, an economist at California State University at Bakerfield, and two other economists, Martin Schmidt (College of William and Mary) and Stacey Brook (University of Sioux Falls), have developed an algorithm that takes each statistic in terms of how it contributes to wins and that "measures a player's wins produced for his team." The researchers went back over an entire 82-game season and found that their calculations of all the statistics (free throw attempts, blocked shots, assists, turnovers, personal fouls, etc.) brought results of standings "shockingly close to the official." Key factors were "efficiency" and the importance of some of the non-stars. The system shows that "it is possible for a non-scorer to produce high numbers of wins."

--- Annette Emerson

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"The Style of Numbers Behind a Number of Styles," by Daniel Rockmore. The Chronicle of Higher Education, 9 June 2006.

Dartmouth College professor of mathematics and computer science, Daniel Rockmore, discusses the field of "stylometry," the use of statistics to determine the originator of a literary or visual work by measuring some feature(s) of the work. With literary works, where the field had its first "notable success," such "features" typically include the percentage of words of different lengths, or the frequency of particular types of words (particularly of what Rockmore refers to as "function words," including prepositions and conjunctions). But while literary works consist of "discrete, countable entities," Rockmore notes, there’s no obvious corollary for visual works. Or is there? Nineteenth-century Italian statesman and art aficionado Giovanni Morelli wrote that "As most men who speak or write have verbal habits and use their favorite words or phrases involuntarily ... so almost every painter has his own peculiarities, which escape him without being aware of them." Morelli used these "peculiarities"—the way a painter depicts such small details as fingernails, earlobes, and draperies—to distinguish the work of one painter from another.

Rockmore then describes how he and colleagues Hany Farid and Siwei Lyu are making use of current technology to perform "wavelet analysis" on artworks to identify an artist’s "numerical signature." As Rockmore tells it, "wavelets permit the reconstruction of a small patch of a picture as an accumulation of lines of horizontal, vertical, and diagonal orientation, and of varying resolutions." The resulting statistical summaries they have extracted have, so far, "reproduced the classifications made by connoisseurs." On the other hand, physicist Richard Taylor is interested in the fractal dimensions of art. He has applied his analysis to Jackson Pollock’s poured paintings in an attempt to validate or invalidate the authenticity of some works that have more recently appeared. (One of Taylor’s discoveries, Rockmore reports, is that "there appear to be fractal dimensions that are specific to particular periods of Pollock’s work ... Pollock’s early drip work has a fractal dimension near 1.4 and rises past 1.7 late in his career.")

For Taylor, as for Rockmore, the use of mathematics to look at art is both valid and valuable. "Both mathematics and art are all about pattern," says Taylor. "It would be unusual that you would not apply mathematical analysis to the question."

--- Claudia Clark

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"Charting an Arabic course": Review of Mathematical Geography and Cartography in Islam and their Continuation in the Occident, Vol. I by Fuat Sezing, translated by Guy Moore and Geoff Sammon. Reviewed by A. M. Celâl Sengö. Nature, 8 June 2006, pages 696-697.

According to the review, conventional treatments of the history of mathematical cartography and geography have neglected almost half of the available material. Fuat Sezgin has remedied this in a work of three volumes originally published in German. Volume 1 has now been translated into English. Seng starts the review with "Few books in the historiography of science have single-handedly created a revolution in their subject, but this one just might." and near the end writes that "The abundance of material brought together in this book is truly awesome."

--- Mike Breen

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"Eine Hommage an Kurt Gödel (A Homage to Kurt Gödel)," by George Szpiro. Neue Zürcher Zeitung, 7 June 2006.

This article talks about an album based on an exhibition about the mathematician Kurt Gödel, which was created on the occasion of the Austrian logician's centenary. The album, published by the German publishing house Vieweg, is edited by mathematicians Karl Sigmund and John Dawson, together with director of the University of Vienna archives Kurt Mühlberger.

See also the Math Digest entry about other stories in connection with the Gödel centenary.

--- Allyn Jackson

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"Das höchste Porto, das auf einen Brief passt (The highest postage that fits on a letter)," by George Szpiro. Neue Zürcher Zeitung, 4 June 2006.

This article discusses the "postage stamp problem": What postages can be affixed to an envelope if only stamps of certain denominations are available and if there is limited space on the envelope? The Journal of Integer Sequences recently published a solution for a special case. Closely related is the "coin problem": Which amounts can be paid exactly, with coins of certain denominations?

--- Allyn Jackson

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"Walk of the Locusts," by John Nielsen. All Things Considered, National Public Radio, 3 June 2006.

Locust

Locust swarms have a devastating effect on farmers all over the planet. This segment on NPR is about recent research published in Science ("From Disorder to Order in Marching Locusts," by J. Buhl et al, 2 June 2006, p. 1402), in which the scientsts used a "wealth of mathematical and simulation-based understanding of SSP models." Science summarizes the news: "The results match predictions from models of phase transitions from disorder to order in statistical physics. These models can permit scaling from laboratory experiments to large populations in the field." The work may result in better prediction of movements of locust swarms and therefore help control the outbreaks. Nielsen notes that forecasting complex behavior patterns of large groups could also be of use in overseeing fishing, controlling crowds of people, and coordinating robots, to name a few applications.

--- Annette Emerson

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"String Trio," by Peter Weiss. Science News, 3 June 2006, page 342.

The tritare

Image courtesy of Samuel Gaudet.

In this issue of Science News, Peter Weiss writes about a new instrument designed by University of Moncton mathematicians Samuel Gaudet and Claude Gauthier. The "tritare" (rhymes with "guitar") is a result of their work analyzing the vibrations of string networks. The tritare looks like a guitar with two additional necks. In Weiss’s words, each of the 6 y-shaped strings "runs from a tuning peg along the fretted neck," then branches "at an unanchored juncture point," where "one string segment runs along each of the two extra, unfretted necks."

But as different as this instrument looks, its sound may be considered even more unusual. As Weiss explains, the plucking, bowing, or striking of a string tightly strung between two points (such as on a guitar) produces harmonic overtones as well as the fundamental sound. But the tritare also produces nonharmonic overtones, more typically heard with percussion instruments such as bells or gongs, "which vibrate in more complicated patterns than simple strings do."

Gaudet describes the tritare’s sounds as “richer and less safe harmonically.” And this is just the first in a family of stringed instruments they are exploring. You can hear the tritare for yourself online. (The tritare was also reported on in Math in the Media in 2004.)

--- Claudia Clark

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"The Forgotten Mathematician": Review of Arthur Cayley: Mathematician Laureate of the Victorian Age by Tony Crilly. Reviewed by A. W. F. Edwards. Nature, 1 June 2006, page 576.

We’ve read about Lord Kelvin, heard about James Clerk Maxwell, and talked about Augustus DeMorgan, but what about their compatriot Arthur Cayley? In Arthur Cayley: Mathematician Laureate of the Victorian Age, author Tony Crilly goes beyond the basics of the Cayley-Hamilton theorem learned by many a devoted linear algebra student. Though Cayley achieved noteworthy mathematical success, the reviewer believes the highlight of the book is its portrayal of life in nineteenth century British mathematical circles. The reviewer also finds that Crilly comes up short in bridging the gap in desired levels of detail between readers who are mathematicians and lay people.

--- Lisa DeKeukelaere

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"The Science behind Sudoku," by Jean-Paul Delahaye. Scientific American, June 2006, pages 80-87.

The rules of Sudoku, its history and strategies, as well as methods of generating Sudoku puzzles are all in this article. Delahaye also deals with the maximal and minimal number of given starting squares that still guarantee a unique solution: 77 and 17, respectively (the latter has not been proven, but no one has found a Sudoku puzzle with 16 squares filled in that has a unique solution). Variations on the standard 9 x 9 Sudoku puzzle are given at the end of the article, including one that uses letters and non-3 x 3 subgrids and whose starting filled-in squares spell "Martin Gardner."

--- Mike Breen

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