# 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 (University of Texas, Austin)

### June 2009

"Attack of the Toaster Oven," by Michelle Slatalla. The New York Times, 25 June 2009.

 Slatalla had an extended series of unfortunate events, among them: the clothes washer stopped working, the oven door wouldn't close, the toaster oven didn't toast, the dishwasher made ominous noises, the shower head broke off, and her car had a flat tire. She began to feel as if someone were out to get her, so she consulted Michael Starbird (University of Texas at Austin), co-author along with Edward Burger of Coincidences, Chaos, and All That Math Jazz, to see if her misfortunes could be attributed to chance. Starbird told her that the events were indeed coincidences and explained that what people think of as random is often an even distribution of events, which isn't random at all. He related an experiment he does with students in which they write what they think of as a random sequence of 200 heads and tails, and then write a sequence of heads and tails from flipping a coin 200 times. Starbird can always tell which sequence is which. Once Slatall understood that the failures were arbitrary, she no longer felt oppressed: "And when the clothes dryer broke the other day, I thought, what a marvelous coincidence that the appliance repairman was already here." --- Mike Breen

"Animals that count: How numeracy evolved," by Ewen Callaway. New Scientist, 23 June 2009.

 Elizabeth Brannon tests the number sense of a ring-tailed lemur from the Duke Lemur Center with a touch-screen computer. (The animals prefer to push buttons with their noses.) Photo Credit: Duke University Photography While the supposed counting ability of a certain horse by the name of Clever Hans was debunked over a century ago, most people now believe that at least primates have some understanding of number. Elizabeth Brannon (Duke University), pictured at left with a ring-tailed lemur, is one researcher who has done experiments to test the numerical cognition of primates. In this article, Ewen Callaway describes some of the work that has been done by her and others to determine the numerical abilities of animals and to determine where this ability comes from—early training or innate ability. According to a number of studies, some animals appear to share our basic ability to distinguish between a smaller number and a larger number. For example, in an experiment performed by Jurgen Tautz and colleagues, bees were able to distinguish up to four shapes. Other researchers have found that both red-backed salamanders and mosquitofish distinguish between quantities when one quantity is at least twice as large as the other. Some animals even demonstrate the ability to perform very simple addition and subtraction, as demonstrated by Rosa Rugani and Lucia Regolin in their work with three- and four-day-old chicks. --- Claudia Clark

"The mathmagicians," by Gordon Farrer. The Age, 19 June 2009.

Marty Ross and Burkard Polster, the “mathmagicians” from the title of this article, are determined to expose Australia to the beauty and fun in mathematics. They met eight years ago at Monash University, and now tour schools and run an annual Mathemagical Mystery Tour to regional Victoria. They publish math puzzlers in Vinculum magazine, write math columns for The Age, and each year they have a public lecture series at Melbourne Museum (the current series started June 21 with the topic “How to Become a Human Lightning Calculator”). Ross emphasizes that the fun aspect is just as important as the learning aspect of each lecture: “If people aren’t enjoying themselves, then it’s failed. It simply has to be as much fun as possible, then you slip in some mathematics.” Their school tours therefore involve juggling, soap bubbles, tricks, and setting children on fire (!). Polster dismisses the notion that mathematics is just a game which is not applicable to real life, by stating flatly that “We don’t really care about that. Maths is justification in itself. It’s beautiful and it’s fun.” The Maths Masters web page has some fun math resources, including links to the pair's columns.

"Serpentine Steps," by Andrew J. Clark and Adam P. Summers. Nature, 18 June 2009, page 919.
"Scales provide a smoother slither," by Rachel Ehrenberg. Science News, 4 July 2009, page 7.

 Gravity propels human walking motion, and inertia propels human running motion, but what about snakes’ motion? Based on research by Andrew Clark and Adam Summers, serpents are more like walkers than runners; from a scientific perspective, their smooth slither results primarily from friction, a gravitational force. The frictional coefficient of a snake’s belly scales allows it to move more quickly in some directions—forwards and sideways—than others. The scientists computed this coefficient by measuring the angle at which a flat board must be tilted before an (anesthetized!) snake lying upon it began to slide downward. This measurement, combined with observations about the snake’s distribution of weight between the straight and curved portions of its slither, allowed the scientists to build a more accurate model of snake motion. In the past, such models have helped in designing snake-like robots for rescue missions in dangerous environments. --- Lisa DeKeukelaere

"A Calculating Web Site Could Ignite a New Campus 'Math War'," by Jeffrey R. Young. The Chronicle of Higher Education, 12 June 2009.
"Sum Help: New Search Engine for Mathletes," by Carl Bialik. The Wall Street Journal, 17 June 2009, page A14.

Does Wolfram Alpha "make graphing calculators look like slide rules" as Jeffrey R. Young writes, or is it just one more computational aid to add to an ever-growing list? The president of the MAA, David Bressoud, says, “Most math instructors now realize that the end-all and be-all of math instruction is not to give students algorithmic facility, but is really to understand the mathematical ideas and understand how to use them.” However, a student's success is often judged by his/her ability to properly perform algorithms on homework, and a site like Wolfram Alpha provides quick answers complete with "steps" that "show work" for students of calculus and other areas of undergraduate mathematics. For instance, typing in "What is the integral of x2y dy?" yields "x2y2/2." However, it might be somewhat comforting that "What is the integral of yx2 dy?" yields "Wolfram Alpha isn't sure what to do with your input."

Stephen Wolfram, creator of Wolfram Alpha and Mathematica, sees computational tools as a means to experiment and build intuition and recalls how he benefited from such tools as a young man. The broader question of whether professors should condone or encourage students' use of computational aids is also discussed. Some consider using such tools as cheating, while others require their use. For those who wish to discuss how to use (or not use) Wolfram Alpha in their classrooms, Derek Bruff, an instructor at Vanderbilt University, has started a discussion forum.

--- Brie Finegold

"New Yorker Glen Whitney quits hedge fund job to create math museum," by Oren Yaniv. New York Daily News, 9 June 2009.
"The Math Midway Takes Shape. Go Figure," by Dominick Tao. The New York Times (city Room Blog), 15 June 2009.
"Stony Brook man hopes math museum plan adds up,"
by Josh Seidman, Newsday.com, 2 July 2009.
"Math-Hattan," by Nick Paumgarten, The New Yorker, 3 August 2009.

 Glen Whitney with an exhibit, "The Ring of Fire," courtesy of Glen Whitney. Glen Whitney is a Long Island man who quit his hedge fund job to create a series of exhibits designed to get people excited about mathematics. The 20 displays were unveiled at the World Science Festival Street Fair in Washington Square Park on June 14, and the exhibition, the Math Midway, is set to travel across the country. Whitney says he wanted “to get people started in seeing the interesting side of mathematics,” which inspired him to create presentations like a tricycle with square wheels that offers a smooth ride thanks to a track with dips and bumps based on the catenary curve, and an interactive map that allows visitors to play with traffic-light patterns. He claims that “any time people get excited about something, it’s much easier to learn about it.” Whitney hopes to turn this endeavor into a more permanent math museum, preferably in Manhattan, currently called the Math Factory, which would be geared towards middle and high school students. The article in The New Yorker mentions the museum, but is primarily concerned with a tour Whitney gave pointing out mathematics while walking through Manhattan. --- Adriana Salerno

“Revenge of the Nerd,” by Matthew Philips. Newsweek, 8 June 2009.

In this article, Matthew Phillips profiles Oxford-trained mathematician Paul Wilmott, whom he calls “arguably the most influential quant today.” What is the “revenge” sought by this “nerd?” It is to reform quantitative finance, particularly the idea that human behavior can be predicted by mathematics. Wilmott argues that models must be tested, not revered. He concedes that “that’s hard work, but this idea that there are these great principles governing finance and that correlations can just be plucked out of the air is totally false.” In pursuit of this goal, Wilmott has written several textbooks, published over 100 research articles, publishes a bi-monthly journal, and has a website with 65,000 registered users. But, Phillips notes, “the key, [Wilmott] hopes, to saving the quants from themselves” is a six-month training program, the Certificate in Quantitative Finance, “designed to break them of the abstract, theoretical approach to finance they learned in their Ph.D. or financial engineering programs, and replace it with a more practical set of skills that are actually used on Wall Street.” Since the schools founding in 2003, 1,273 people have graduated from the program. In addition to describing Wilmott’s work, Phillips describes some of the key moments in the history of the use of quantitative methods in finance. For example, he discusses how quants’ reliance on the Gaussian copula function to predict default rates led to an explosion of buying and selling in the collateralized debt obligation (CDO) market, and an eventual financial disaster.

--- Claudia Clark

"Connecticut District Tosses Algebra Textbooks and Goes Online," by Winnie Hu. The New York Times, 8 June 2009.

Students' backpacks may lighten as schools like those in Westport, CT decide to create their own online curricula and ditch the 1,000-page Algebra I textbooks currently in use in most of the nation. Finding the textbooks offered to be too dense, the school district paid a total of $70,000 to in-house teachers and web site designers to develop their own online text complete with animations and graphics. The site is maintained by a company in Singapore, and will save the school an estimated$25,000 per year in textbooks for years to come.

The school district has better test scores now than prior to the implementation of the online materia, and the number of students taking multivariable calculus at Westport's Staples High School skyrocketed from 4 students to 44 in just three years. A representative of Houghton-Mifflin, whose texts are being phased out of use at Staples, questions the teachers' abilities to create an adequate text. But only time will tell whether textbooks will go the way of penmanship instruction.

--- Brie Finegold

"The Thinkers: RMU professor finds beauty in math," by Mark Roth. Pittsburgh Post-Gazette, 1 June 2009.

 Photo courtesy of Monica VanDieren. Monica VanDieren, a mathematics professor at Robert Morris University, is unique not just for the rarity of her gender within the profession, but also for her chosen field of research. Model theory, VanDieren’s specialty, involves construction of special “mathematical universes” based on specific axioms, and she estimates only about 10 other people worldwide look at the same problems. While research in many scientific disciplines has become dependent on computers, VanDieren makes progress with simple pen and paper, often working at her dining room table with other members of her small research community, and some wine. This article offers a window into VanDieren’s professional life not just as a researcher, but also as an active mentor for prospective young female mathematicians and as a woman who watched her own female classmates drop away as she advanced through school. VanDieren also offers interesting examples of modern technology, such as cell phones and iPods, made possible by the application of research in pure mathematics. --- Lisa DeKeukelaere

"Game Theory Meets Darwin," by Andrew Grant. Discover, June 2009.

In 2002 mathematical ecologist Sasha Dall used game theory, a branch of mathematics often associated with economics, to predict the behavior of ravens. Game theory is typically used to predict the course of action a person will choose when the outcome depends not only on his choice, but that of others, and Dall's work marked the first time these theories have been applied successfully to animals. His models explained why young ravens scavenge alone but later invite others to share the findings. They also predicted that some ravens would scavenge in groups---a behavior that a field ecologist discovered within a year of Dall's findings by tracking ravens in North Wales. The behavior, published in a paper with Jonathan Wright in February 2009, demonstrates the importance of the stability that cooperation provides, even when individuals can achieve success alone.

--- Lisa DeKeukelaere