# 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), Adriana Salerno (Bates College)

### December 2009

"Why certain shapes are more pleasing to the eye," by Steve Connor. Independent, 22 December 2009.

Theoretical mathematician Adrian Bejan of Duke University proposes that there is an evolutionary basis for why humans find shapes in the "golden ratio" proportion (approximately 1.618) so appealing. For centuries mathematicians and other have tried to figure out why humans perceive this proportion to be so aesthetically pleasing--in architecture, art and nature. Bejan's paper in The International Journal of Design and Nature and Ecodynamics explains how "the visual scene that is easiest to scan is one where the horizontal axis is wide than the vertical. This is true for a gazelle scanning the African horizon for predators, or early human hunter-gatherers searching their territory for food." Our eyes are positioned such that we absorb information more efficiently side-to-side rather than up and down. "When the proportions allow this to be done, it should be a source of pleasure because of its past evolutionary associations."

--- Annette Emerson

"Weather pioneer was well ahead of his time," by Charles Perry. Times & Transcript, 21 December 2009.

 Lewis Fry Richardson "was the first to apply mathematics to predicting weather." He outlined his concept in 1910 but his work didn't gain recognition until about a decade later, when his work, "Weather Prediction by Numerical Process," was published. "He proposed a means of weather forecasting built around the solution of different equations. It is the method used today by meteorologists, although when Richardson published it in 1922, there were no computers to carry out suitable, fast computing of the weather data."

--- Annette Emerson

"For real: Mukilteo High teacher wins country music contest," by Molly Rosbach. The Seattle Times, 20 December 2009.

 Chance McKinney (pictured at left), a math teacher at Kamiak High School in Washington, won Country Music Television's Music City Madness contest for his song "Be Real." McKinney got the idea for the song as he was boarding a plane and surreptitiously recorded it on his phone so that he wouldn't forget it. His prize is a trip to Nashville to record songs and audition for a recording contract. Some of McKinney's students were torn as to whether to vote for him in the online poll, "I [didn't] know if I should vote for him because I want him for my teacher next year." (Photo by Stephen Sexton.) --- Mike Breen

"Alice's adventures in algebra: Wonderland solved," by Melanie Bayley. New Scientist, 16 December 2009.

"The 19th century was a turbulent time for mathematics, with many new and controversial concepts, like imaginary numbers, becoming widely accepted in the mathematical community. Putting Alice's Adventures in Wonderland in this context, it becomes clear that Dodgson, a stubbornly conservative mathematician, used some of the scenes to satirise these radical new ideas." Bayley was inspired to pursue this line of examination after reading a 1984 paper by Helena Pycior (University of Wisconsin-Milwaukee), who linked the Trial of the knave of Hearts with a Victorian book on algebra. Bayley writes that Dodgson (aka Lewis Carroll, author of Alice's Adventures in Wonderland), a mathematician at Oxford University, incorporates projective geometry, quaternions, non-commutative algebra and other concepts into the book in fantastical ways. Bayley cites, for example, "The parallels between William Rowan Hamilton's maths and the Hatter's tea party--or perhaps it should read "t-party"--are uncanny."

--- Annette Emerson

"Rekindling the gender-bias debate," by Karen Kaplan. Nature, 17 December 2009, page 947.

The Science on Women in Science, a recent book of nine essays, examines several viewpoints in the debate on whether the low representation of women in the sciences has resulted from bias or a lack of innate ability. Christina Hoff Sommers, an essay author and the editor of the compilation, argues against government-driven affirmative action to boost female numbers in the sciences because, she claims, the research in departments that institute such policies is inferior to those that do not. Another essayist cites differing test results between young boys and girls as evidence that men prefer to analyze while women instead lean toward empathy. In contrast, other essays argue that boys and girls show similar aptitude for mathematical thinking and that the policies of academia historically have hindered women's success. One author compares this debate to that in the medical profession, which forty years ago believed that women could not be doctors--a belief that has long since dissipated.

--- Lisa DeKeukelaere

Articles on a formula for perfect parallel parking:
"British Mathematician Perfects Parallel Parking," Renee Montagne. National Public Radio Morning Edition, 15 December 2009; and
"Scientists create formula for perfect parking," by Murray Wardrop. Telegraph, 11 December 2009.

 Formula for perfect parallel parking by Simon Blackburn. Simon Blackburn, mathematics professor at University of London's Royal Holloway College, has devised a formula that ensures perfect parallel parking. He tells reporter Wardrop, "This was the perfect opportunity to show how we can apply mathematics to understanding something that we all share. If you understand the angles and the dimensions of your own car then you can work out how to park in a nice, confident way." NPR's Montagne points out, however, that one probably shouldn't be doing the calculations while driving. The formula is the result of collaboration between Blackburn and Vauxhall Motors in the U.K. The story was picked up by Fox News and other media. Read a different solution of the problem, complete with applets, courtesy of Math Digest reader Jerome White of the Lusher Charter High School in New Orleans.

--- Annette Emerson

"The 9th Annual Year in Ideas," The New York Times Magazine, 13 December, 2009.

The following mathematics-related ideas were included in the The New York Times Magazine's annual issue devoted to newsworthy ideas:

• "Black Quarterbacks Are Underpaid," by Jason Zengerle. In an article from the February issue of Journal of Sports Economics, economists David J. Berri and Rob Simmons found that black quarterbacks are paid less than their white counterparts. The difference is even more dramatic when comparing the best quarterbacks from each group. A difference which might be attributed to simple racism is actually, according to Berri and Simmons, more linked to statistical bias. Basically, the numbers used for the N.F.L.'s quarterback rating (which affects the quarterback's salary) don’t include rushing yards, a "key offering" of many black quarterbacks according to the authors.
• "Random Promotions," by Clive Thomson. Common sense would dictate that the best way of deciding promotions in a company is by merit. Unfortunately, according to Canadian psychologist Laurence J. Peter, that might be a surefire way to end up with a company full of incompetents. The reasoning behind his "Peter Principle" is that being good at one job does not guarantee the same type of performance at a new, more challenging position. In fact, many people reach a sort of "level of incompetence" and they stop being promoted. A trio of Italian scientists tested two models, one in which a firm promoted the best workers and they had a random likelihood of performing well at a new job, and a second model in which promotions were decided randomly. Counter-intuitively, the latter was shown to improve the overall efficiency of the firm. They also tried alternately promoting the best and worst workers, and that also worked better that just promoting on merit. According to Andrea Rapisarda, one of the coauthors, this phenomenon is well-known in physics and game theory: the idea that you win more often by alternating between two losing strategies. This study was recently published in the journal Physica A.
• "Reverse-Engineering Social Security Numbers," by Mark van de Walle. Some years ago scientists figured out how to determine the date of birth of an applicant and state of issue given a particular Social Security Number, but the other direction had remained pretty elusive, until now. This year, economist Alessandro Acquisti and computer scientist Ralph Gross developed an algorithm to predict someone's S.S.N. given a state and birth date. They were able to predict correctly all nine digits in an S.S.N. in 1,000 attempts or fewer, 8.5 percent of the time. Paradoxically, what gave these scientists the data pool necessary to discover the patterns in S.S.N.'s were measures developed by the government to prevent identity theft and fraud.
• "Forensic Polling Analysis," by Christopher Shea. Results published on polls during the 2008 presidential race by the firm Strategic Vision L.L.C. have recently been called into question. In September, the American Association for Public Opinion Research publicly denounced the fact that Strategic Vision would not reveal how it conducted these polls. Strategic Vision's response was to threaten to sue. This prompted scientists to analyze these results and determine whether the firm had anything to hide. Nate Silver, proprietor of fivethiryeight.com and political blogger, noticed that there was a highly abnormal distribution of trailing digits, an indication that the data was fabricated rather than naturally obtained. "Tell a human to come up with a set of random numbers, and they will be surprisingly inept at trying to do so," says Silver. Michael Weissman, a retired physics professor at the University of Illinois, used Fourier analysis to conclude that the data was suspicious at best. Strategic Vision's response to these results: threaten to sue Nate Silver, too.

--- Adriana Salerno

"Mammogram Math," by John Allen Paulos. The New York Times Magazine, 13 December 2009.

 Mammogram image by Dr. Dwight Kaufman. National Cancer Institute. In light of the public outcry over the recent recommendations by a panel of scientists to decrease the frequency of mammography for breast cancer screening, John Allen Paulos does the arithmetic to show why the recommendations make sense. If, for example, a very large portion of the population is healthy, then even a test with a very low probability of drawing a false positive will result in a sizeable number of healthy people misdiagnosed—more people, in fact, than the number of people correctly diagnosed with the disease, because so few people have it in the first place. Paulos also calls upon a mathematical technique called reductio ad absurdum, which involves taking an argument to an extreme. If mammograms can save lives by detecting cancer in women in their 40s, why not screen all women, starting with little girls? This approach would result not only in more misdiagnoses, however, but also inflict harmful doses of radiation on the population. Paulos’ ultimate goal is to show that the scientists’ recommendations are, in fact, based on scientific evidence, and attackers should rely similarly on evidence instead of psychological biases. --- Lisa DeKeukelaere

"A 19th-Century Mathematician Finally Proves Himself," by Laura Sydell. National Public Radio Morning Edition, 10 December 2009.

 Charles Babbage was a brilliant mathematician living in Victorian England. To navigate the seas of its vast empire, captains relied upon books of tables containing hand-calculated solutions to equations. Babbage is thought to have conceived of his Difference Engine--which would automatically calculate the solutions to polynomials with the turn of a crank, then print out the resulting values--as a result of finding large numbers of errors in these calculations. For all of his brilliance, however, Babbage was unable to raise the money needed to build this early calculating machine. Over 150 years would pass before Difference Engine No. 2 (Babbage's update to his first design) would become a reality. Using Babbage's designs, and limiting themselves to materials available in Babbage's time, a team headed by Doron Swade of the Science Museum of London built two of these machines. The first, which took 17 years to build, was completed in 2002 and is on display at the museum. The second machine was finished in March 2008 and currently resides at the Computer History Museum in San Jose, California. Tim Robinson, a docent at this museum, notes that the completed machine proves Babbage’s brilliance, but, along with Swade, can only imagine the impact Babbage could have had if the Difference Engine had been built during Babbage's lifetime. Learn more about Difference Engine No. 2, including how it calculates the values of polynomials using the method of finite differences. See also: "Ada Lovelace, Charles Babbage and The Difference Engine that Made a Big Difference," by Nazte Burgos. MetalMiner, 18 December 2009. --- Claudia Clark

"Grigori Perelman's Beautiful Mind": Review of Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century, by Masha Gessen. Reviewed by Jascha Hoffman. The New York Times, 10 December 2009.

This book is an unauthorized biography of Grigory Perelman, who was the subject of headlines around the world in 2002 after he made public his work containing a proof of the Poincaré Conjecture and Thurston's Geometrization Conjecture. He made headlines again in 2006, when he refused to accept the Fields Medal that was awarded him at the International Congress of Mathematicians in Madrid. By then he had become a recluse and had resigned from his position at the Steklov Institute in St. Petersburg. The author of the book was not able to get any information from Perelman himself, so she relied instead on recollections from his colleagues, some of whom "see him as a righteous noncomformist, others as a cranky purist," the reviewer writes. The book provides a "thorough account of the circumstances that led to Dr. Perelman's rise in the `vicious, backstabbing little world' of Soviet mathematics and a brilliant reconstruction of the twisted logic that might have led to his mysterious exit."

--- Allyn Jackson

Articles on the 2009 Siemens Competition winners:
"Paly senior takes second place in math competition," by Diana Samuels. Mercury News, 9 December 2009; and
"Austin Student's Team Wins National Science Competition," Austin American-Statesman, 8 December 2009.

 Lynnelle Ye, awarded US$50,000 in the 2009 Siemens Competition. Left to right: Thomas McCausland, Chairman, Siemens Foundation; Jim Whaley, President, Siemens Foundation; Lynnelle Ye; Jennifer Harper-Taylor, Vice President, Siemens Foundation, and Tom Jones, Lead Judge. Photo courtesy of the Siemens Foundation. Mathematics projects won US$200,000 in prizes this year at the Siemens Competition in Mathematics, Science, and Technology. The research in Graph Theory that Dan Liu, Sean Karson, and Kevin Chen began at a Texas math summer camp earned them first place in the team competition and $100,000 to share amongst themselves. Lynelle Ye started her project in Game Theory over the summer at a research institute at MIT and ended the year with second place in the individual competition and$50,000. In addition, three other students who completed research in mathematics were national finalists. This is the eleventh year that the Siemens Competition has awarded prizes to outstanding high school mathematicians and scientists. Ms. Ye's research focused on the game Graph Chomp, a cousin of the more popular Chomp. Graph Chomp is a combinatorial game played on a graph in which each player takes turns deleting either an edge of the graph or a vertex and all incident edges. The last player to make a move wins the game. Although the rules are easy, determining a winning strategy is not. Ms. Ye began by determining winning strategies for playing Graph Chomp on bipartite graphs. Although the Siemens website does not discuss the details of her results, there are slides available outlining some of her results. The winning team project made progress on a 30 year old problem in graph theory. Entitled "Relating Missing and Decycling Edges in Directed Graphs," the group's project describes improvements to a recently discovered upper bound on the number of edges that must be removed in order to eliminate cycles from a graph. You can read the preprint on arxiv that the three students wrote with Professor Jian Shen, their mentor. --- Brie Finegold

"Mathematics By Collaboration," by Julie Rehmeyer. Science News, 8 December 2009.

Do great ideas come from one individual's flash of genius or from the tireless educated guesses of many? Suspecting the latter, Cambridge mathematician Tim Gowers invited readers of his blog to participate in the "Polymath Project" in January, 2009. The term polymath refers to a person such as Da Vinci with a wide knowledge base, not necessarily restricted to mathematics. The "Polymath Project" provided a forum for many experts all over the world to share their ideas concerning a particular problem in real-time in the same way an true modern-day polymath might bounce ideas around in the privacy of his/her own brain. To kick off the project, Dr. Gowers presented his intuition concerning the Density Hales-Jewett theorem, a difficult-to-prove theorem that is simple to understand for those who study combinatorics. Although already proven, many mathematicians suspected a simpler proof existed, and Dr. Gowers felt that this massive collaboration might be a path towards that simpler proof. So he opened the discussion, put into place a few guidelines for participants, and started a wiki page to record progress.

Rehmeyer explains the theorem loosely in terms of the game tic-tac-toe, and points the interested reader to a friendly and detailed exposition given at the Number Warrior, a blog written by high school math teacher Jason Dyer. Dyer's class tried working on problems related to the theorem, such as the Moser cube problem, which he describes. Just 37 days after the project began, comments from 27 contributors led to a proof of a special case of the Density Hales-Jewitt theorem. This case has now been generalized by a core group of contributors and is much simpler than previous proofs. A preprint of the work is available on arxiv (with author listed as D.J.H. Polymath) courtesy of Ryan O'Donnell, a Theoretical Computer Scientist at Carnegie Mellon University. Discussion is currently underway on Gowers's Weblog concerning the subject and structure of a Polymath 2 Project, which he hopes will attract contributors at a variety of skill levels.

--- Brie Finegold

"The Circular Logic of the Universe," by Natalie Angier. The New York Times, 8 December 2009.

In this article, Natalie Angier honors renowned Russian artist Vasily Kandinsky's love affair with the circle, which he wrote is "the most modest form, but asserts itself unconditionally." Inspired by the Guggenheim exhibit on the artist and by the fact that December is the month of both his birth and his death, Angier writes a poetic and touching survey of the many forms in which we encounter the circle and the sphere, and relates it to Kandinsky’s interpretation of these shapes as "simultaneously stable and unstable," "loud and soft," "a single tension that carries countless tensions within it." Tracey Bashkoff, curator to the Guggenheim's exhibition on Kandinsky's work, says that for Kandinsky the circle was part of a "cosmic language" and a link to a grander, more spiritual plane. From heavenly bodies and raindrops to eyeballs, eggs, and breasts, from physics to biology, near-spherical objects are easily encountered in nature. Our eyes are drawn to these shapes, maybe as a way to search for faces, but also as a way to search for human manufacture, as perfect spheres and circles are hard to find naturally. These shapes are also representations of the divine: mandalas, rose windows, the lotus pad of the Buddha, the halos of Christian saints. And so Angier explores these shapes as a part of nature, art, and the human experience.

--- Adriana Salerno

"The Fundamental Lemma, Solved," by Eben Harrell. Time, 8 December 2009.

Time magazine has named the proof of a mathematical lemma one of the top ten scientific discoveries of 2009. Canadian-American mathematician Robert Langlands posited an important theory in 1979 linking number theory and game theory, and mathematicians have since then worked off of the principle that the “fundamental lemma” of Langlands’ theory was correct—although no one had proved it. Ngo Bau Chau, a Vietnamese mathematician at Université Paris-Sud, found a proof of this lemma over the past few years, and mathematicians this year verified that his proof was correct. His work has drawn deep appreciation from all those already using Langlands' theory.

--- Lisa DeKeukelaere

"Scientific Observations." Science News, 5 December 2009, page 4.

In this regular feature that gives a quote in each issue, Marcus du Sautoy, of the University of Oxford and 2010 winner of the Joint Policy Board for Mathematics Communications Award, says, "I think what drives me as a mathematician are those things which are not seen, the things that we haven't discovered, and it's all those unanswered questions that make mathematics a living subject. I always come back to this quote in the Japanese Essays in Idleness: 'In everything ... uniformity is undesirable. Leaving something incomplete makes it interesting and gives one the feeling that there is room for growth.'"

--- Mike Breen

Articles on Between the Folds:
"Filmmaker Vanessa Gould Goes Between the Folds of Origami World," by Michelle Kung, Wall Street Journal Blog, 5 December 2009;
"Origami and the art of the process," by Joe Maniscalco, New York Post, 30 November 2009; and
"Arthouse films," by Bill Stamets, Chicago Sun Times, 27 November 2009.

 Eric Joisel and some of his origami creations. Photograph courtesty of Green Fuse Films. Throughout the late fall, PBS stations across the country aired Between the Folds, a documentary exploring the science, art, creativity and ingenuity of many of the world's best paper folders, by filmmaker Vanessa Gould. The media give some background about Gould and the individuals--Tom Hull, Erik Demaine, Robert Lang, Eric Joisel, among others--whose stunning works inspired her to make the film. Between the Folds was part of the Independent Lens series and was also screened at the Chicago Cultural Center on November 28.

--- Annette Emerson

The Answer Man,” by Gregory Mone. Popular Science, December 2009.

In May of this year, the internet and newspapers were buzzing about “genius” Stephen Wolfram’s recently unveiled website WolframAlpha.com. Wolfram’s no stranger to the limelight, earning a PhD in physics at age 20, winning a MacArthur genius grant at 21, and then leaving academia altogether to create groundbreaking software (Mathematica) and write a best-selling book (A New Kind of Science). But it seems he has reached new heights by following his dream: to create an artificial intelligence that could solve any number-related problem. In the WolframAlpha website, he has found the first step towards accomplishing this lofty goal. The feature that distinguishes this website from other search engines is that it gives precise answers to any query, rather than a list of websites where the query can be found (a la Google). Any query is interpreted and translated into code by the search engine. Each piece of the query is computed and the system gathers relevant information from previously collected data, and then displays the results in charts, graphs and images. The website draws from more than 10 trillion pieces of curated data from trustworthy sources, which have been in turn compiled by about 200 researchers. But Wolfram believes it can do more: He wants to be able to draw on all of the knowledge humans have compiled about the universe. WolframAlpha was selected by Popular Science magazine as the Computing Grand Award Winner for the Best of What’s New in Computing.

--- Adriana Salerno

"The Year of Living Scientifically," by the editors. Discover, December 2009.

The December 2009 issue of Discover give examples of how "science is burrowing its way into popular culture more deeply than ever this year." The editors select 50 favorite science experiences in the movies, television, books and exhibits from 2009, and note highlights of what we might look forward to in 2010. Those relating to mathematics are: "The Big Bang Theory" (a popular television series about young physicists who love science and that occasionally includes mathematical references); "In the Land of Invented Languages" (a book by Arika Okrent about the origins of languages real and fictional, "including a language based on math"); "Decoding the Heavens" (a book by Jo Marchant that "paints a vivid portrait of both modern code breakers and the wildly creative thinkers of ancient Greece," with a storyline about a group of divers in 1901 who discover a 2,000-year-old-metal wheel, the Antikythera Mechanism, the world's first computer); and "Why Does E = MC2?" (a book by Brian Cox and Jeff Forshaw, who "answer their title question without using math more complicated than the Pythagorean theorem.").

--- Annette Emerson

"Reckoning with Newton---World Premiere of Carl Djerassi's and Isabella Gregor's Play Verrechnet! in Vienna," by Klaus Taschwer. bridges, December 2009.

This is a review of a comedy called Verrechnet!, which was staged in early 2010 in Vienna. One of the playwrights, Carl Djerassi, is a scientist-turned-writer, and the other, Isabella Gregor, is a director. Verrechnet! traces the story of the famous dispute between Isaac Newton and Gottfried Leibniz over which one of them invented the calculus. The main characters in the play are two historical figures who are themselves writing a play about the Leibniz-Newton controversy, and scenes from their work are staged in Verrechnet!, making for a "play within a play". The review also includes a short interview with Djerassi, in which he says that one of his goals in writing pieces like this play is "to smuggle useful information about science and scientists into the mind of a public that may be afraid or ignorant about these aspects."

--- Allyn Jackson

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