# Math Digest

## Summaries of Articles about Math in the Popular Press

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

### November 2004

"Getting the Message Across": Review of Information Theory, Inference, and Learning Algorithms by David J.C. MacKay. Reviewed by David Saad. American Scientist, November-December 2004, pages 578-579.

The reviewer gives a positive review of this textbook, which is concerned with the application of probability and statistics to communication. Saad writes, "This is primarily an excellent textbook in the areas of information theory, Bayesian inference and learning algorithms. Undergraduate and post-graduate students will find it extremely useful for gaining insight into these topics; however, the book also serves as a valuable reference for researchers in these areas. Both sets of readers should find the book enjoyable and highly useful."

--- Mike Breen

"Amateur puts maths riddle to its stiffest test," by Jenny Hogan. New Scientist, 27 November 2004, page 11.

This short article describes two different efforts to verify the Riemann Hypothesis, one of the main outstanding problems in mathematics. It is possible to test the Riemann Hypothesis in specific cases, and although such tests can never definitively prove or disprove the hypothesis, many have been carried out. Two of the latest ones were done by people in France and Germany. The researcher in France had an especially good algorithm, while the researcher in Germany had more computer power available. The two are now joining efforts to do yet more testing.

--- Allyn Jackson

"Math prizes." Random Samples, Science, 26 November 2004, page 1471.

Ben Green, Gérard Laumon and Bao-Châu Ngô are the recipients of the 2004 research awards from the Clay Mathematics Institute. Most of this short piece in the "People" section of "Random Samples" is about Green who, along with Terence Tao, proved a conjecture about arithmetic progressions of primes in early 2004.

--- Mike Breen

This piece discusses an article in Nature that stirred a good deal of controversy. In that article, researchers used the statistical tool of regression analysis to predict that women would surpass men in the 100-meter sprint in just a few years. The author explains why the reason in the article is faulty.

--- Allyn Jackson

"Father of Fractals," by Jim Giles. Nature, 18 November 2004, pages 266-7.

 When Benoit Mandelbrot turned 80 in November, writer Jim Giles marked the occasion with an article about this famous mathematician. From his Ph.D. work in mathematical linguistics, to his 1963 paper on cotton-price fluctuations, to the publication of his 1982 book containing his work on fractals---which would bring him wide recognition---to the present, Mandelbrot's career has been marked by unusual methods, "remarkable insights, and no small amount of feuding". He led a nomadic academic existence for many years, and is known for his combativeness, possibly due, in Giles' opinion, to lack of recognition through the first three decades of his unorthodox career. Giles offsets examples of Mandelbrot's "aggressive" behavior (in the words of one colleague) with evidence of the undeniable impact his work has had on mathematics and science. In the words of mathematician Ian Stewart, Mandelbrot " has changed the questions we ask." --- Claudia Clark

"Grape ripening as a past climate indicator," by Isabelle Chuine, Pascal Yiou, Nicolas Viovy, Bernard Seguin, Valerie Daux and Emmanuel Le Roy Ladurie. Nature, 18 November 2004;
"Medieval harvests reveal climate change," by Alanna Mitchell. The Globe and Mail, 18 November 2004.

 French scientists have measured the global climate change by researching 600 years of harvesting the pinot noir grape in Burgundy. Using meticulously-recorded harvest dates, mathematical models were used to figure out variations in temperature. The researchers, who included applied mathematician Pascal Yiou, expected to find that temperatures in the 1990s were higher than any France had endured for hundreds of years, "but," as Mitchell notes, "when the French scientists crunched their grape numbers, they found that the land of the pinot noir had been about as warm as the 1990s in the 1380s, 1420s and 1520s, and then through the 1630s to the 1680s...While individual decades or years have been warm in Burgundy, the anomaly now is that the warming trend has kept going for more than a century" and 2003 was an unpredictably warmer year. Yiou is quoted in the Globe and Mail article as saying that this "could be a coincidence, or troubling evidence that climate is becoming more variable and therefore more unstable." --- Annette Emerson

"A Watchdog Follows the Money in Iraq," by Erik Eckholm. New York Times, 15 November 2004, page A6.

This article is about the career of Bunnatine H. Greenhouse, an African-American woman who is the contract director at the Army Corps of Engineers. Her job is to ensure that contracting by the Corps follows government rules and is carried out with integrity and without favoritism. Recently she has taken heat for asking hard questions about contracts given to companies, such as Halliburton, that are doing reconstruction work in Iraq. Greenhouse studied mathematics at Southern University and was a high school teacher. After joining the government, she earned master's degrees in business management, engineering, and national resources strategy. Of her work on contract management, the article quotes her as saying: "It appealed to my love of mathematics. I like structure and rules. I don't ever want to feel like I am in La-La Land."

--- Allyn Jackson

"Quantum decoys create uncrackable code," by Mark Buchanan. New Scientist, 13 November 2004, page 8.

This short article describes a recent breakthrough in quantum cryptography by researchers at the University of Toronto. One reason quantum codes were initially thought to be so powerful is that eavesdropping would disturb the photons used to carry the messages and therefore could be detected. Then researchers found a way whereby an eavesdropper could cover up his or her tracks. The new research shows how a message-sender can send out decoy photons that would foil an eavesdropper.

--- Allyn Jackson

"A fractal life": Interview with Benoit Mandelbrot. Interviewed by Valerie Jamieson. New Scientist, 13 November 2004, pages 50-53.

No mathematical object has become so well known among the general public as has the fractal. Benoit Mandelbrot coined the term and was the first to systematically explore this geometric phenomenon. In the interview, he talks about his views on the popularity of fractals, his background growing up in France, and the influence of his uncle, Szolem Mandelbrojt, who was a mathematician at the Collège de France in Paris. He also talks about his latest research on the concept of "negative dimension" and on the dynamics of financial markets. His book The (Mis)Behavior of Markets: A fractal view of risk, ruin and reward, written with Richard Hudson, came out in 2004.

--- Allyn Jackson

On November 14, 2004, an organization that has been working to get girls in the United States to take more challenging high school math and science courses celebrated its 30th anniversary. The organization is called the Math/Science Network. It was founded in San Francisco by a group of female "math whizzes and scientists" who were troubled by a study showing that female college freshmen didn't have the same math training as their male counterparts. In this article, Teri Perl, one of the founders of the organization, speaks about their history. In 1976, they organized their first "Expanding Your Horizons" all-day conference at Mills College. The conference offered girls the opportunity to perform hands-on experiments in mathematics, science, and engineering, and to hear inspiring presentations by women working in these fields. Today there are 90 conferences held each year in 31 states for middle and high school girls. Perl says that although studies show that the conferences have made a difference, the need to interest girls in mathematics and science continues.

--- Claudia Clark

"Verifying Art With Math." Random Samples. Science, 3 December 2004, page 1678;
"Putting science to work solving art's whodunits," by Geoff Edgers. The Boston Globe, 23 November 2004;
"Con Artist: Scanning program can discern true art," by Erica Klarreich. Science News, 27 November 2004, page 340;
"Computer Analysis Is Bringing Science to Art," by Rick Weiss. Washington Post, 29 November 2004, page A8.

Three researchers at Dartmouth College have devised a method to detect art forgeries. A statistical model, using wavelets, is made from high-resolution scans of of works known to be painted or drawn by an artist. The work in question is also scanned and compared to the known works. The method was put to the test on 13 slides of works: eight originals by Pieter Breugel and five imitations of his work, and it correctly categorized all 13. The lead researcher, Hany Farid, agrees that the method is preliminary but foresees that more testing will lead to its improvement. The team's technique is described in "A digital technique for art authentication," published in the Proceedings of the National Academy of Sciences.

--- Mike Breen

Articles on Fibonocci numbers and markets:
"Crude Oil Falls as Report Expected to Show U.S. Supplies Rose," by Gavin Evans.
Bloomberg.com, 16 November 2004;
"The Market Powers Ahead," by Mark Arbeter, BusinessWeek Online, 15 November 2004;
"Discovering How to Use the Elliott Wave Principal," Elliott Wave International, FXStreet.com, 10 November 2004;
"Oil Little Changed After Falling on Adequate Supply Speculation," by Gavin Evans. Bloomberg.com, 8 November 2004.

 Each of these articles gives a brief explanation of how Fibonacci numbers apply to markets: "A Fibonacci graph of the increase from June 20 to the peak of US$55.67, identifies US$45.485 a barrel as the 50 percent retracement of the rise. Fibonacci analysis is a tool, named for a 13th century mathematician, which is used by technical traders who chart historical prices and volumes to discern trends and turning points in a market." (Evans, November 16 and 8.) "The second technical technique to identify potential targets [for indexes as well as individual stocks] is with the use of Fibonacci retracement levels...The most common Fibonacci retracements are 23.6%, 38.2%, 50%, 61.8% and 100%. It has been found that after a large market move, prices will often retrace a portion of the original move." (Arbiter, November 15.) "Many investors today know that Fibonacci ratios are used for market forecasting...The use of Fibonacci ratios requires a valid Elliott wave interpretation as a starting point" (Elliott Wave International, November 10.) --- Annette Emerson