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), Lisa DeKeukelaere (Brown University), Annette Emerson (AMS)


December 2005

"Good news: Numbers are up." The Oregonian, 28 December 2005;
"Researchers discover largest prime number." CNN.com, 4 January 2006;
"CMSU group makes big math find," by Garance Burke. The Kansas City Star, 4 January 2006;
"Math researchers find largest prime." The Associated Press, 5 January 2006;
"One small beep brings prime number glory to Missour," by Ian Sample. Guardian Unlimited, 5 January 2006.

These articles concern the recent discovery of the largest known prime number: 230,402,457 - 1, a number with over nine million digits. (The article in The Oregonian notes that "The newest prime number is so big that it makes the national debt look like a rounding error, rather than an economic one.") The prime number was discovered on computers at Central Missouri State University (CMSU) as part of the Great Internet Mersenne Prime Search. The CMSU team was led by mathematics professor Curtis Cooper and associate dean Steven Boone. There is a US$100,000 prize for the first discovery of a prime number with over 10 million digits.

--- Mike Breen

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"Mathematician/Counterterror Entrepreneur: Jonathan Farley," by Yohannes Edemariam. Seed, December 2005/January 2006.

The theme of the December 2005/January 2006 issue of Seed magazine was the "Year in Science" for 2005, and one section of the magazine highlighted "15 people who have shaped the global conversation about science in 2005." One of the individuals profiled is Jonathan Farley, a mathematician and science fellow at Stanford University. The profile of Farley describes how he became interested in using mathematics to model terrorist networks. He has founded a consulting company, Phoenix Mathematical Systems Modeling, which, the article states, "is developing software the authorities can use to foil terror attacks." The article also notes that Farley distances himself from partisan disputes over how the war on terror is being fought. "This is about studying terrorism and terrorist groups," he is quoted as saying. "It's not about politics. It's about saving lives."

--- Allyn Jackson

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"Siemens Westinghouse Science Winners Announced," by Robert Smith. All Things Considered, National Public Radio, 5 December 2005;
"Boy, 16, Wins Top Award at Math Competition," by Times Staff and Wire Reports. "
Los Angeles Times, 6 December 2005;
"US$100,000 scholarship no problem: 16-year-old mathematics whiz wins prestigious competition," by Elizabeth Fitzsimons. San Diego Union Tribune, 6 December 2005. "16-Year-Old mathematics win $100,000 in Siemens Westinghouse prizes [sic]." NewsFromRussia (Pravda.ru), 6 December 2005;
"Carmel Valley teen wins national math competition," by Philip K. Ireland. North County Times (NCTimes.com), 8 December 2005;
"Person of the Week: Michael Viscardi," by Bob Woodruff. "World News Tonight," ABC News, 9 December 2005;
"Teen Taught by Mom Wins Top Science Competition," by Nancy Steinbach. VOA News, 14 December 2005;
"Rising Stars: Preparing for takeoff," Random Samples---People, Science 16 December 2005.

Michael Viscardi, a 16-year-old home schooled mathematician, won the US$100,000 grand prize in the prestigious 2005 Siemens Westinghouse Science Competition held in December. As Woodruff reports, Viscardi "has updated the late 19th century law by mathematician Lejeune Dirichlet. Viscardi figured out, in excruciating detail, how heat travels across a metal surface, and how the temperature can affect the surface of the metal." This theory can be applied to all metals, and might lead to better airplane wing design. In Viscardi's own words: "I formed a theorem which characterizes all such domains for which the resulting solution is rational---namely in terms of the Riemann maps and their Bergman kernals." The news of the young mathematician's win traveled far and wide because his work was outstanding, the competition and prize are noteworthy, he is home-schooled by his mother, and his mathematics may find important applications. Steven Krantz (professor of mathematics at Washington University in St. Louis), one of the competition's judges, is quoted on Viscardi's work: "His research is profound, substantial and complete, with potentially important applications in heat flow, magnetism, electrodynamics and other branches of physics."

--- Annette Emerson

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"Pulling the Strings": Review of Hiding in the Mirror: the Mysterious Lure of Extra Dimensions, from Plato to String Theory and Beyond, by Lawrence M. Krauss. Reviewed by by Michael Atiyah. Nature, 22 December 2005, page 438.

Is deference to mathematical beauty leading modern physics astray? Lawrence M. Krauss attempts to answer this serious question in Hiding in the Mirror: the Mysterious Lure of Extra Dimensions, from Plato to String Theory and Beyond. The reviewer, Fields Medalist and Abel Prizewinner Sir Michael Atiyah, notes that while many general science books assume the voice of an "energetic protagonist," Krauss takes a different view, casting a critical eye on the separation between beautiful, clean mathematical equations and the physical reality that scientists are attempting to understand and explain. While tackling the philosophical truth versus beauty debate, Krauss presents the ideas behind Einstein's theory of relativity and quantum mechanics, giving historical context and avoiding technical complexity.

--- Lisa DeKeukelaere

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"Busted: The gold standard of digital security lies in tatters," by Celeste Biever. New Scientist, 17 December 2005, pages 44-47.

Security in electronic communications is crucial in today's world. That's why so many researchers are concerned about the vulnerabilities recently exposed in an algorithm called SHA-1. SHAs, "secure hash algorithms", are used pervasively in cryptographic systems that protect electronic communications. "Hash algorithms are mathematical procedures that have a seemingly magical, and extremely useful, ability to `digest' a file of any length ... to produce a fixed-length string of 1s and 0s," the article explains. The cryptographer Xiaoyun Wang, who is at Tsinghua University in Beijing, has now shown that SHA-1, the secure has algorithm used for the most secure applications, can be compromised with many fewer calculations and much less computing power than experts had predicted. This has increased the urgency to develop new, stronger SHAs---or maybe some completely different tool that would replace SHAs altogether. Read more about SHAs in the article "Find Me a Hash" (PDF, 700KB), by Susan Landau, in the March 2006 issue of Notices of the AMS.

--- Allyn Jackson

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"Math class proves Smarties fun fact isn't true." CBC News, 16 December 2005.

A fact printed on Smarties candy packages sold in Canada claims that the Smarties consumed annually (in Canada) laid end-to-end would circle the globe 350 times. Tanja Coghill's sixth grade math class checked out the claim and found that it wasn't true. Canadians eat four billion Smarties annually, which the class calculated would circle the globe about once. (The distance around the earth at the equator is about 40,000 kilometers, which makes the calculations fairly easy in the metric system.) The class contacted the maker of Smarties, Nestlé Canada, and on the third try they got a response. The company agreed to change the fun fact. For the current fun fact to be true, the earth would have to be much smaller (or the circling done very near the poles), or the candies would have to be 3.5 meters wide.

--- Mike Breen

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"NUMB3RS gets real 'Science Guy'," by Kate O'Hare. The Indianapolis Star, 15 December 2006.

Bill Nye, whose "Bill Nye the Science Guy" television program aired on PBS and in syndication, appeared on the crime show NUMB3RS on 16 December 2005. One of the show's creators, Cheryl Heuton, never forgot a three-hour interview with Nye in which he talked a lot about inspiring young people to study math and science. In this NUMB3RS episode the mathematician character turns to the character played by Nye to track down a serial arsonist; Nye's character re-creates a backdraft in a lab. In this article Nye says "I'm thrilled" about NUMB3RS, agreeing with other scientists that it's about time scientists are portrayed on a primetime TV program. He notes that he is "on this Committee on Public Understanding of Science and Technology (COPUST)" and regarding NUMB3RS he reports that "they love it at COPUST", and they love it at the American Association for the Advancement of Science.

--- Annette Emerson

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"The Rembrandt Code," by Bijat Trivedi. Wired Magazine, 13 December 2005.

Can a computer judge the authenticity of a painting as well as a trained art historian? Curators at New York's Metropolitan Museum of Art are doubtful, but computer scientist Dan Rockmore has already shown success in developing a computer algorithm that examines photos of paintings pixel by pixel and correctly separates the real from the fake. Rockmore likens the uniqueness of a painter's style to person's handwriting, and his algorithm forms a statistical model of a painting by quantifying characteristics such as brushstroke length and thickness. While his initial algorithm tackled the works of Bruegel, his new challenge is paintings purportedly created by Rembrandt. In this business the stakes are high: the value of a true Rembrandt is a full order of magnitude higher than that of a work by one of his students.

--- Lisa DeKeukelaere

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"Researcher says math can protect border," by Louie Gilot. El Paso Times, 12 December 2005.

As different ideas are proposed in Washington for improving United States border security, at least one team of researchers is proposing the use of mathematics to address the costly business of guarding the border. This month, a reporter for the El Paso Times interviewed Stefan Schmidt, a researcher at New Mexico State University's Physical Science Laboratory and co-founder of a company that develops mathematical models to address homeland security issues. Schmidt and research partner Jonathan Farley are using Reflexive Theory to create a prototype for improving border security. According to Reflexive Theory, "the behavior of the adversary can be controlled through the selective release of information and disinformation," Gilot writes. By applying this theory, he adds, the Border Patrol could direct drug smugglers to attempt border-crossings at "points that are cheaper for the agency to guard."

Farley notes that their research could be applied to a range of problems, such as dealing with roadside bombs in Iraq, as well as other tasks including placement of campaign ads.

--- Claudia Clark

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"Mathematiker mit poetischer Begabung (Mathematician with poetic talent)," by George Szpiro. Neue Zürcher Zeitung, 11 December 2005.

This profile of Hermann Weyl, one of the outstanding mathematicians of the twentieth century, was published to mark the fiftieth anniversary of his death.

--- Allyn Jackson

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"Proof that roundabouts drive us round the bend." Life Style Extra, 10 December 2005.

Roundabout

According to Anne Skeldon of the Surrey University (UK) Mathematics and Statistics Department, "a roundabout presents drivers with the most complex challenge they will encounter." The challenge is to get on and off while others are trying to do the same thing, but at different places, so that drivers' paths cross. A study done at the university proved that getting into and out of a roundabout smoothly is not easy. It also found that one in four roundabout accidents occurred while changing lanes and that one in five accidents occurred while one of the cars was stationary.

--- Mike Breen

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"BCS Schemers Are Looking Out for No. 1," by Sally Jenkins. The Washington Post, 10 December 2005, page E1.

The rankings in the Bowl Championship Series (BCS) determine who plays in the most important college football bowl games, including the championship game. In the past season there was no dispute about which teams belonged in the championship game---the University of Texas and the University of Southern California---but there has been dispute in previous seasons. Jenkins writes about the flaws in the BCS system and about research done by Thomas Callaghan, Peter J. Mucha, and Mason Porter, who analyzed how random walks could be used to rank college football teams. The three found that random-walk rankings were just as good as those of the BCS. Their research, including analysis of the BCS system, is in "The Bowl Championship Sereies---A Mathematical Review" in the October 2004 issue of Notices of the American Mathematical Society.

--- Mike Breen

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"The Numbers Guy," by Brad Wolverton. Chronicle of Higher Education, 9 December 2005, page A33.

Football

In 1971, Jeff Sagarin developed the first computerized sports rankings system. His refined systems are now used to rank college football and basketball teams, which has him in trouble with some fans who often don't like the rankings' results or the fact that they involve computers. He receives nasty e-mail messages, which have gotten worse over the years, even threatening, and rarely leaves his home town. Sagarin's rankings are one of the components used in determining which college football teams play in the biggest---and most lucrative---bowl games. His basketball rankings are used to help order teams in the 65-team NCAA Division I Men's Basketball Tournament. Sagarin, a former math major at MIT, keeps his formulas secret but plans eventually to give them to his alma mater so others can study his algorithms.

--- Mike Breen

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"Shining early." Random Samples-People, Science, 9 December 2005, page 1613.

Manjul Bhargava (Princeton University) and Kannan Soundararajan (University of Michigan) are the inaugural recipients of the Shanmugha Arts, Science, Technology, and Research Academy (SASTRA) Ramanujan Prize. The pair was cited for their "pioneering work in number theory." The US$10,000 prize is given annually to mathematicians 32 years old or younger and was awarded on 22 December, Ramanujan's birthday.

--- Mike Breen

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"Warped geometry speeds airline boarding," by Philip Ball. News@nature.com", 9 December 2005;
"Israeli researchers fly by the numbers," by Allison Kaplan Somer. Israel21c 18 December 2005.

boarding pass

Eitan Bachmat and his team of researchers at Ben-Gurion University of the Negev "have proved mathematically what computer simulation models by airline companies---and the gut feelings of passengers---have already demonstrated. Back-to-front row boarding is not the best way to fill airplanes with passengers." Their work has determined that the most efficient way is already used by Southwest and EasyJet airlines: "let the quickest customers get on first and choose their own seats---with unassigned seating." The Israel21c article provides extensive background about Bachmat, who explains that "Lorentzian geometry was invented for the sole purpose of describing relativity theory. This seems to be the first application of this theory outside physics." Ball notes that "the mathematics [used in Bachmat's research] of permutations gets pretty hairy, involving concepts such as `two-dimensional Lorentz geometry' and `random matrix theory' that are likely to boggle airline companies," and Bachmat admits that "human behavior and psychology would have to be factored into his mathematical equations before making any substantive changes." So for now most travelers can simply observe the boarding process to see which methods seem to work.

--- Annette Emerson

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"Old muskie record catching attention," by Dale Bowman. Chicago Sun-Times, 7 December 2005;
"Muskie math: World-record story just doesn't add up," by Chris Niskanen. St. Paul Pioneer Press, 11 December 2005.

Fish

There is controversy in the fishing world about the world-record for a muskie (muskellunge). Currently the record is a 69 pound, 11 ounce fish caught in 1949 by Louis Spray, but the World Record Muskie Alliance has filed a challenge to the record. Part of the challenge is based on a photgraph taken of Spray with his catch. The fish was reportedly 63 1/2 inches long but in the photo the fish appears to be much shorter. A member of the board of the National Fresh Water Fishing Hall of Fame asked Doug Arnold, director of the Institute for Mathematics and its Applications at the University of Minnesota, to analyze the photo and determine the length of the fish (which would help in determining its weight) using math. Arnold can't be sure but used simple proportions to conclude that the fish is shorter than 63 inches, perhaps much shorter. He posted a demonstration of his conclusion. (Photo from the National Fresh Water Fishing Hall of Fame.)

--- Mike Breen

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"Maths stabilises wobbly tables," by Judy Skatssoon. Science Online, ABC News Online (Australia), 5 December 2005.

Researcher Burkhard Polster (Monash Unviersity in Melbourne, Australia) comments that mathematics is usually associated with "ivory tower stuff" but, reports Skatssoon, Polster's team has used mathematics to explain "how to stabilise a wobbly table without needing to jam a beer coaster under one of the legs." They calculate that "turning a rectangular table around on most surfaces will cure the wobble. Alternatively, apply `intermediate value theory' to solve the problem. Intermediate value theory relates to the principle that any curve drawn from above an axis to below will intersect [the axis] at some stage." Other applications? Polster muses that the theory "is useful in positioning items like fridges and washing machines."

--- Annette Emerson

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"Odds are, lotto ticket a wasted dollar," by Gregory Karp. Allentown Morning Call, 4 December 2005.

Lottery

Late last year, the jackpot in the Powerball lottery reached US$340 million---plenty of incentive to pay the measly dollar to play. This article gives the probability of winning Powerball with the purchase of one ticket: 1 in 146 million. Says Doug Arnold, director of the Institute for Mathematics and its Applications at the University of Minnesota, "Basically, if you're talking about the jackpot, you put down your dollar and you never see anything back. That's what the lottery is all about, that captures it almost perfectly." Karp writes that a person is more likely to die from a snake bite than to win Powerball and adds, "The only worse investment than playing the lottery is paying for advice on which numbers to pick." He also points out that 70 percent of the people who receive such windfalls lose the money in just a few years.

--- Mike Breen

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"Risk of severe asthma episodes predicted from fluctuation analysis of airway function," by U. Frey, T. Brodbeck, A. Majumdar, D. Taylor, G. Town, M. Silverman, and B. Suki. Nature, 1 December 2005.

Asthma attacks are often triggered by small, unpredictable environmental events, but researchers recently attempted to calculate the risk of a flare-up by using data on a patient's lung function in both the recent and distant past. By viewing the disease as a dynamical system, the researchers not only computed the probability that an attack would occur within 30 days, but also assessed the efficacy of different treatment methods. They used statistical models and determined the effect of the treatments on the stability of the system. Their findings: oft-prescribed short-term bronchodilators actually increase the risk of an attack, while long-term dilators are associated with decrease in flare-up odds. The researchers believe that success in viewing asthma from this perspective may be groundbreaking when applied to other diseases.

--- Lisa DeKeukelaere

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"A calculated effort," by Vanessa E. Jones. The Boston Globe, 1 December 2005.

Mark Bridger, an associate professor of mathematics at Northeastern University, has found a way to counter the negative impressions that many students and acquaintances have of math: He has started a blog that explains the math explored on NUMB3RS, the number-one TV program on Friday nights. While the show does not and cannot get deeply into the mathematics used to solve crimes, the blog can go into more depth. So far the blog has covered such topics as pi, prime numbers, and algorithms, as well as the Fibonacci sequence, the Riemann Hypothesis, and the Chapman-Kolmogorov equation. Bridger is among the mathematicians consulted on the show, and "his script comments helped prevent the writers from incorrectly using Gödel's Incompleteness Theorem in an upcoming episode." It's hard to judge the effect of NUMB3RS and the blog, but the article reports that both Caltech (the university on which the fictional university is based) and Northeastern have seen an increase in math majors since 2004. And the blog, started in February 2005 at http://www.atsweb.neu.edu/math/cp/blog, has logged more than 4,000 hits since June 2005. Bridger estimates the site receives 50 to 80 hits a day.

--- Annette Emerson

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"Littlest Butterfly," by Jessa Forte Netting. Discover Magazine, December 2005, page 9.

The Sinai baton blue butterfly may seem insignificant (it's only the size of a thumbnail), but mathematical ecologist Martin Hoyle and biologist Mike James have used mapping and models to determine that if average temperatures warmed slightly above a critical threshold the species would become extinct. Their study, published in the August 2005 issue of Conservation Biology, predicts that the world's smallest butterfly could persist---at least for a time---with small increases in grazing and plant collection, but not with increases in temperature. The Discover piece quotes Hoyle's conviction that "there is no reason why this kind of thing wouldn't apply to other endangered endemic species, like polar bears. They don't have anywhere farther north to go."

--- Annette Emerson

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