# Math Digest

## Summaries of Media Coverage of Math

Edited by Allyn Jackson, AMS
Contributors:
Mike Breen (AMS), Claudia Clark (freelance science writer), Lisa DeKeukelaere (2004 AMS Media Fellow), Annette Emerson (AMS), Brie Finegold (University of California, Santa Barbara)

### December 2006

"Wobblology," by Davide Castelvecchi. New Scientist, 23/30 December 2006, pages 38-39.
"Strange but True: Turning a Wobbly Table Will Make It Steady," by JR Minkel. ScientificAmerican.com, 25 January 2007.
"The Science of Steadying a Wobbly Table": Interview with Keith Devlin. Weekend Edition Saturday, National Public Radio, 17 February 2007.

 If you've ever attempted to steady a wobbly table with four equally long legs, you may appreciate these articles. Ph.D. student Roger Fenn wrote a proof in the late 1960s that "for any smoothly curving floor that bulges upward like a hill, there is at least one way to position the table so that it is balanced and horizontal," but he did not offer a way to find this spot. Now mathematician Burkard Polster and colleagues have proven that rotating the table will solve the problem, an idea that appeared in a column by Martin Gardner in Scientific American over 30 years ago. (Their proof has been accepted for publication by the Mathematical Intelligencer.) This proof applies to both square and rectangular tables, on a floor that has no places that slope more than 35.26 degrees. Note that the table might not be level at the balanced location. Polster and colleagues also suggest a procedure for balancing the table: lift up the table leg diagonal to the wobbly leg so that both legs are about the same distance from the floor, then rotate. A demonstration of the technique is online. --- Claudia Clark

"New math could improve 'invisibility cloak'." CBC News, 27 December 2006.

The article begins by announcing "Mathematicians who came up with a way to explain how a new 'invisibility cloak' hides objects have now developed a theory that could let the technology hide items that emit light." The research described is that of mathematician Allan Greenleaf (University of Rochester, NY) and colleagues Matti Lassas (Helsinki University of Technology in Finland), Yaroslav Kurylev (Loughborough University in Leicestershire, England), and Gunther Uhlmann (University of Wahsington, Seattle). After communicating with David R. Smith (Duke University), whose team recently demonstrated independently the first working invisibility cloak, Greenleaf announced that his latest work "predicts behavior inside the cloak." Greenleaf and team are now working to confirm the relationship between their work and experiments, which have previously included detecting tumors. Detailed information on the research described in the newspaper article is posted on the University of Rochester website.

--- Annette Emerson

"Tsunami Data Points to Value of Reefs in Warming Era," by Christopher Joyce. All Things Considered, National Public Radio, 26 December 2006.

 Joseph Fernando, a mechanical and aerospace engineer at Arizona State Unviersity, was born and raised on the coast of Sri Lanka, one of the places hit hard by the 2004 Indian Ocean tsunami. In his interview on the radio program he explains how he and other researchers created mathematical models to simulate the tsunami, and the results confirm that shorelines behind reefs fared much better. As summarized on the NPR program website, "That raises both the value of reefs as well as alarm over their rapid disappearance. And with climate change expected to raise sea levels, the data also suggest that reefs might help protect low-lying areas from higher wave surges." The research paper co-authored by Fernando, "Episodes of nonlinear internal waves in the northern East China Sea," was published in GeoPhysical Research Letters. --- Annette Emerson

"Major progress in prime number theory", by Krishnaswami Alladi. The Hindu, 25 December 2006.

This article reports on the work of Ben Green and Terence Tao concerning arithmetic progressions of prime numbers, on the occasion of Tao receiving the 2006 SASTRA Ramanujan Prize. This US\$10,000-prize is given every year on the birthday of Srinivasa Ramanujan (December 22) in his hometown of Kumbakonam, India. An arithmetic progression is a sequence of numbers that differ by a fixed amount. For example, 10, 17, 24, 31, 28 is an arithmetic progression of length 5 where the difference between the numbers is 7. Green and Tao made a major advance by showing that there are arithmetic progressions that consist only of prime numbers and that are as long as you choose. This work contributes to a line of research stretching back to the first part of the 20th century and uses results of Ramanujan himself.

--- Allyn Jackson

"Erziehung berechnen (To compute upbringing)", by George Szpiro. Neue Zürcher Zeitung, 24 December 2006.

This article describes a paper by the econometrician Michael Beenstock in which family interactions are modeled. The results are not surprising (e.g., spend more time with kids who cry a lot), but they show how mathematics can be useful even in situations seemingly far removed from the subject.

--- Allyn Jackson

"What a Flake: Computers get the hang of ice-crystal growth," by Peter Weiss. Science News Online, 23 December 2006.

 Several mathematicians have recently made progress in accurately modeling how a snowflake develops its shape. Such models have been studied by scientists since the 1600s and can be used to better understand how clouds affect climate and the likelihood that airplanes flying through clouds will gather dangerous ice formations on their wings. Earlier models, based on partial differential equations or simple computer algorithms, produced results that looked like snowflakes but did not account for the physical factors that impact how a snowflake develops. The new models look at multiple properties like temperature, humidity, and even randomness, since most real snowflakes are imperfect. They succeeded in mimicking both the final shape and the developmental stages in two dimensions, but modeling the process in three-dimensions remains a challenge. --- Lisa DeKeukelaere

"Breakthrough of the Year: The Poincaré Conjecture--Proved," by Dana Mackenzie. Science, 22 December 2006, pages 1848-1849;
"Math takes Science's spotlight in 2006," by Alan Boyle. MSNBC, 22 December 2006;
"Maths solution tops science class," by Paul Rincon. BBC News, 22 December 2006;
"Journal Science selects top 10 scientific breakthroughs of 2006," People's Daily Online, 22 December 2006.

Each year Science looks back and chooses ten significant breakthroughs from the past year, labelling one "The Breakthrough of the Year." This year, for the first time, a mathematical breakthrough is the Breakthrough of the Year---the proof of the Poincaré Conjecture. Mackenzie explains the conjecture's history and some of the controversy surrounding Grigory Perelman's proof. Poincaré proposed the conjecture about the properties of three-dimensional manifolds in 1904. In 2002 Perelman posted on a preprint server the first of three papers providing the means to prove the conjecture as well as a more general result, the Thurston Geometrization Conjecture. The usual process of verifying this work was not followed because the papers weren't submitted to a refereed journal. It was only recently that the mathematics community has come to a consensus that the Poincaré Conjecture has been proved. Mackenzie writes that "While bringing new results to topology, Perelman's work brought new techniques to geometry." Other breakthroughs in 2006 include the sequencing of Neandertal DNA and the documentation of the accelerated shrinking of ice sheets in Greenland and Antarctica (these are described in an article beginning on page 1850). As of this writing, Science's breakthrough articles were available online.

--- Mike Breen

"Master Class in Evolutionary Modeling": Review of Evolutionary Dynamics: Exploring the Equations of Life, by Martin Nowak. Reviewed by Steven A. Frank. Science, 22 December 2006, page 1878.

In this article, University of California, Irvine, professor of ecology and evolutionary biology Steven Frank reviews the book Evolutionary Dynamics: Exploring the Equations of Life. Frank notes that author Martin Nowak is not the only person to claim that "evolution is the single most significant idea in biology." But where "almost all mathematical syntheses of evolution have been confined to population genetics," Frank writes, Nowak shows "the many ways in which the mathematics of evolution led to advances in diverse subjects, including cancer, game theory, and language."

While most of the theory presented in the book has been previously published, Frank states that "the lucid presentation, drawing frequently on the author's own research, provides a uniquely compelling introduction to mathematical biology." Indeed, Frank suggests that the book can be used as a starting point for one's own research; he concurs with this statement of Nowak's: "I will start with the basics and in a few steps lead you to some of the most interesting and unanswered research questions in the field. Having read the book, you will know what you need to embark on your own journey and make your own discoveries."

--- Claudia Clark

"Measures for measures," by Sune Lehmann, Andrew D. Jackson, and Benny E. Lautrup. Nature, 21/28 December 2006.

Universities and grant foundations try to dole out promotions and funding based on the quality of an academic's work---but how robust are their measures of quality? Three Danish scientists compared three methods for ranking academics: number of papers published, mean number of citations received per paper published, and a score called the Hirsch index that takes both factors into account. The methodology for the comparison, involving conditional probability and Bayes' theorem, may be somewhat difficult to decipher as detailed in the article, but the results and warnings appear clearly. Mean number of citations per paper published is the best choice, followed by the Hirsch index, while number of papers published fares little better than random score assignment. The authors caution that, "unable to measure what they want to maximize (quality), institutions will maximize what they can measure" and conclude by noting that actually reading an applicant's papers is still the best way to go.

--- Lisa DeKeukelaere

"Painting by numbers," by Scott LaFee. The San Diego Union Tribune, 21 December 2006.

 Cheshire cat, by Kerry Mitchell (copyright Kerry Mitchell). This article was accompanied by some stunning fractal pictures (including "Cheshire Cat" by Kerry Mitchell, at the top of the Math Digest page). LaFee gives some mathematical background on fractals and examples of occurences in nature (such as blood vessels). He also explains how the images are generated with modern software: Pixels are assigned numbers and are colored based on the number's behavior in an iterative process. Churning through numbers doesn't guarantee a beautiful picture, however, an artist must understand both form and function to create such images. --- Mike Breen

"2006 in Review," by Nicola Jones. news@nature.com, 20 December 2006;
"Top 10 stories of 2006." news@nature.com, 28 December 2006.

In her "romp through ten of this year's big science developments", Jones includes "Russian recluse spurns prize," the story of Perelman's refusal of the Fields Medal (link to article) and speculation on whether he would also decline the Clay Math Institute's US\$1 million award for his proof of the Poincaré conjecture. Making second place on the top 10 Readers' Choice list (of most clicked-on stories) of 2006 was a mathematics-related article, "Geometric whirlpools revealed" ("recipe for making symmetrical holes in water is easy," 19 May 2006). Mathematics stories did not make the top 10 Editor's Choice or top 10 Most Talked About lists, but eighth place on the top 10 News Features (longer tales worth another read) was "Fractals in art: In the hands of a master" ("fractal analysis has been used to assess the authenticity of paintings purporting to be the work of Jackson Pollock. Alison Abbott reports," 8 February 2006).

--- Annette Emerson

"A prime example," by Karen Gold. Guardian Unlimited, 19 December 2006;
"Making mathematics music to their ears," by Alexandra Frean. Times Online, 23 December 2006.

Mathematician Marcus du Sautoy is one of the great popularizers of mathematics and often appears in media in the U.K., Australia, and New Zealand. The article by Gold notes that "he recently landed the landmark British TV scientist slot---the Royal Institution (London) Christmas Lectures. With the title The Num8er My5teries, and subjects ranging from codes, magic tricks, and the shape of the universed, he hopes to turn a generation of young teenagers on to maths." du Sautoy recalls that other mathematicians laughed at the notion of his trying to explain the Riemann hypothesis to general readers, and his response is that because mathematics is "a totally logical subject, and a pathway has been marked out" he can---if he himself completely understands it---explain it so other people get it. The article by Frean focuses on du Sautoy's efforts to engage students between the ages 11 and 14, the period when young people often lose enthusiasm for math. du Sautoy, "who often plays a trumpet during lectures to illustrate the similarities between harmonics and the sine waves used to predict prime numbers, suggests that maths teaching should be similar to music teaching," and that teenagers struggling with the subject might benefit from learning a musical instrument.

The Guardian story was also published under the titles "Think math isn't sexy?," Taipei Times 23 December 2006; and "The magic of maths," Mail and Guardian Online, 15 January 2007.

--- Annette Emerson

"Die Berechnung der Bedeutung: Die Mathematik hinter Googles Webseiten Klassifizierung (The calculation of meaning: The mathematics behind Google's website classification)", by George Szpiro. Neue Zürcher Zeitung, 15 December 2006.

When you use Google to search for information on the Internet, how does Google decide which pages to put at the top of the list? Szpiro describes Google's "Page Rank" system, which is a mathematical way of classifying web pages. The article is based on the December 2006 installment of the AMS "Feature Column", by David Austin. Austin's column proved to be extremely popular, accumulating so many hits that it slowed down the entire AMS web site for a period in December.

--- Allyn Jackson

"Mathematician numbers don't add up," from AAP newswire. Herald Sun (Australia), 14 December 2006.

The Australian Academy of Science released a review saying that "underinvestment in maths and statistics is jeopardizing the competitiveness of Australian industry." Mathematician Hyam Rubinstein (University of Melbourne) tells the reporter that Australia's reputation as a leader in mathematics and statistics has served as a magnet for experts in these fields, but that the reputation is being upheld by an older generation. He also noted that since 1995 math and statistics departments in Australia have lost one-third of their permanent faculty. Several of the country's newspapers picked up the report: The Australian, The Age, The Melbourne Herald Sun and The Sydney Morning Herald.

--- Annette Emerson

"Nick Patterson; A Cold War Cryptologist Takes a Crack at Deciphering DNA's Deep Secrets" by Ingfei Chen. New York Times, 12 December 2006.

 An overview of the structure of DNA. Image created by Michael Ströck. This article profiles Nick Patterson, a mathematician and cryptographer who applies his code-breaking expertise to problems in genomics. He started his career at the GCHQ, the British government's code-breaking organization. Patterson then moved to the Center for Communications Research, which is the cryptography branch of the Institute for Defense Analysis and which is based in Princeton, New Jersey. In the 1990s, he was persuaded by James Simons, a former mathematician and cryptographer himself, to join Simons' investment company Renaissance Technologies, which relies heavily on mathematical techniques. "But by 2000, [Patterson] was restless," the article says. That's when he took a job at the Whitehead/MIT Center for Genome Research, which later became the Broad Institute. Both cryptography and genome research require the development of pattern recognition to make sense of large quantities of data. This is what Patterson excels at. Eric Lander, a mathematician turned geneticist who is the director of the Broad Institute, is quoted as saying that Patterson has the statistical insight to tell whether a signal is "simply random fluctuation or whether it's a smoking gun." This same article appeared under the title "A whole new breed of biologists" in the International Herald Tribune, 14 December 2006, page 10. --- Allyn Jackson

"One Last Mission for Ship Sunk in Pearl Harbor Attack," by Michael E. Ruane. Washington Post, 7 December 2006, page A3.

Ruane explains how a mathematical model is being used to simulate deterioration of sunken ships. The ship discussed most in the article is the USS Arizona, which was sunk in the attack on Pearl Harbor (the article was published on the 65th anniversary of the attack). The day before the attack, the Arizona took on over one million gallons of thick oil. The question addressed by the model is: When will the oil in the ship erupt to the surface? Much of the oil has slowly leaked to the surface, but about half of it still remains in the ship. The model predicts that nothing serious will happen for at least 10 years. The Arizona Memorial National Park Superintendent thinks that any collapse of the ship and subsequent leak will continue to take place gradually.

--- Mike Breen

"Relatively Small Number of Deaths Have a Big Impact in Pfizer Drug Trial," by Carl Bialik. Wall Street Journal Online, 6 December 2006.

 After Pfizer announced it was withdrawing a cholesterol drug after some patients died during its clinical trials, "Numbers Guy" Carl Bialik shed some light on the role statistics play in medical trials. He explains that a "statistical boundary" or "p value" is set up for each clinical trial, where "p measures the probability that a particular result---in this case, the difference in the rates of death between the two drug groups---can be chalked up to a statistical anomaly... Calculating p in this case is complex, and takes into account several factors, including the number of people in the study." He expands on the explanation and includes quotes from a couple doctors. --- Annette Emerson

"Siemens High School Science Awards," by Robert Smith. All Things Considered, National Public Radio, 4 December 2006;
"Student Wins Top Math Award," by Anne Williams. The Register-Guard (Eugene), 5 December 2006;
"High school senior wins scholarship," by Karen Matthews. The Associated Press, 4 December 2006.

 Dmitry Vaintrob wins Siemens Competition. In a high-school science competition that pitted a student who studied Parkinson's disease by studying its effect on worms against a high-achiever who discovered new pulsar stars in outer space, a young mathematician recently walked away with the top honors. Dmitry Vaintrob from Eugene, Oregon, won the US\$100,000 Grand Prize scholarship in the individual category of the 2006-2007 Siemens Competition in Math, Science, and Technology for his work in string topology. His project, which presents a formula for describing the way shapes combine in string theory, may help physicists to understand electricity, magnetism, and gravity. Though Vaintrob is only a high school senior, Harvard mathematics professor and competition judge Michael Hopkins says that his achievement is impressive at the Ph.D.-level. The Siemens Foundation press release includes more details. --- Lisa DeKeukelaere

"Never mind the Pollock's [sic]," by Dan Vergano. USA Today, 3 December 2006;
"Jackson Pollock Fractals," a discussion with guest Richard P. Taylor. Talk of the Nation, National Public Radio, 15 December 2006.

Both pieces explore how science, specifically the use of fractals, is a tool to authenticate (or spot faked) art works. The unique style of paintings by Jackson Pollock is the subject. The researchers are Richard P. Taylor (University of Canterbury, New Zealand and University of Oregon, Eugene), and Katharine Jones-Smith and Harsh Mathur (Case Western Reserve University, Cleveland). Their respective efforts seem to present different results. The key, according to Mathur, may be that "in statistical physics, a debate is going on over the proper use of the term `fractal' as a way to designate shapes." Papers and responses of Taylor and Jones-Smith have appeared in Nature. Taylor is interviewed on the NPR program.

--- Annette Emerson

"The Monty Hall Problem," by John Allen Paulos. Who's Counting, abcnews.com, 3 December 2006.

 What's behind the door? Despite the increase in game shows on television, Paulos reports that---based on all the emails he has received over the years about the so-called Monty Hall problem---no game show has aroused as much mathematical interest as Let's Make a Deal. In this show a contestant picks one of three doors for a major prize. Once a door is chosen, host Monty Hall opens one of the two remaining doors to reveal the prize behind it and offers the contestant the chance to switch his or her door choice. Paulos briefly explains probability and then goes on to test the reader's understanding by throwing in a variation of the problem (and he includes the answer at the end of the column). --- Annette Emerson

"Let there be number": Review of How Mathematics Happened, by Peter S. Rudman. Reviewed by Matthew Killeya. New Scientist, 2 December 2006, page 50.

The reviewer writes that this book "charts the evolution of mathematics from early hunter-gatherer cultures to the civilization of ancient Egypt and Babylon." The book also advances the argument that people might learn mathematics better if they take it up after leaving school. "It is an underdeveloped yet intriguing argument," the reviewer writes.

--- Allyn Jackson

"Teacher, students revel in joy of high-level math," by Carrie Sturrock. The San Francisco Chronicle, 2 December 2006.

 Ravi Vakil (near center, in white shirt and jeans) and Stanford University exam-takers, courtesy of Ravi Vakil. The exam for the William Lowell Putnam Mathematics Competition is one of the most difficult taken by undergraduates. On a 120-point scale, the median national score is generally less than 10. Ravi Vakil was one of the top five scorers on the exam for his four years as an undergraduate. Now on the math faculty at Stanford University, Vakil coordinates the Putnam exam at Stanford. This article talks about his own research and the enthusiasm he shows when he works with students. Said Aman Kumar, a Stanford sophomore, "When you learn the Putnam with Ravi, math is a fun, sexy thing." --- Mike Breen

"'Mike's Math': How One Volunteer Is Helping Kids Think Differently," by Kristin Pisarcik. ABC News, 1 December 2006.

In this article, correspondent Kristin Pisarcik interviews "human calculator" and math teacher Mike Byster. Byster has created a system, which he calls "Mike's Math," that enables students to solve complex arithmetic problems rapidly in their head. His system is based upon patterns and memorized shortcuts. He describes his system on his website as a program that "teaches children how to master the art of multitasking by solving problems, memorizing the information, storing the information, being able to recall the information and add to it or modify it." For example, he describes the steps for finding the square of a number in the 50s, in this case 56: start out with 25 and add the one's digit of the number to it (25 + 6 = 31); then square the one's digit of the number (6 x 6 = 36) and tack this onto the 31 for the answer: 3136. Byster intends that students apply his methods to all academic areas. Byster not only gives presentations in Chicago-area schools, but around the world---all as a volunteer. To see Mike and some students in action, go to the story online.

--- Claudia Clark

"Day by day---how a cancer grows," by Frank Urquhart. Scotsman News, 1 December 2006.

Sandy Anderson, a mathematician at Dundee University, has a model for tumor growth that might change cancer treatment strategies. About his model, Anderson said, "The intention of most treatment strategies is to make the environment the tumour is in as harsh as possible, but what you are effectively doing is killing off all the weak cells and leaving all the tough ones behind. My research shows that we need to consider the environment in which the tumour is growing before we attack it." He said that tumors will be less aggressive if they grow in an "oxygen or nutrient-rich environment."

--- Mike Breen

"The Turing Model Comes of Molecular Age," by Philip K. Maini, Ruth E. Baker, and Ceng-Ming Chong. Science, 1 December 2006, pages 1397-1398.

According to the authors of this perspective article, a report by Stefanie Sick et al, "WNT and DKK Determine Hair Follicle Spacing Through a Reaction-Diffusion Mechanism" (beginning on page 1447 of the same issue) provides "the first compelling biological evidence" for Alan Turing's model of how complex spatial patterns arise. In 1952, Turing proposed that "diffusion-driven instability" caused complex biological patterns, but until now no example had been found. Sick and co-authors have identified key compounds in hair follicle growth that appear to behave according to Turing's model. Now, these authors write, it is time to do experiments to measure key parameters in the system to determine which particular model is correct.

--- Mike Breen

"Million Dollar Math," by Stephen Ornes. Discover, December 2006, page 64.

"Mathematics gives some of the most dramatic examples of the glacial but inexorable advance of the human intellect, " begins Ornes. The recent coverage of the 2006 Fields Medal awards prompts him to explore "What problems remain?" He notes that in 1900 mathematician David Hilbert listed 23 outstanding problems for the 20th century, and in 2000 the Clay Mathematics Institute identified seven so-called "Millennium Prize Problems"---with a reward of US\$1 million for each solution. Ornes then summarizes four great problems (two of them identified by the Clay): Riemann Hypothesis, Twin Prime Conjecture, Navier-Stokes Equation, and Traveling Salesman.

--- Annette Emerson