# 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)

### June 2005

"Paper Detailing Milk Contamination Released," reported by Joe Palca. National Public Radio's "All Things Considered," 28 June 2005;
"PNAS Publishes Botulinum Paper," by Jocelyn Kaiser. Science, 1 July 2005, page 31;
"Biosecurity," an interview with Lawrence Wein. National Public Radio's "Talk of the Nation," 1 July 2005;
"If you want to poison the US, read on," by Anjana Ahuja. The Times Online, 4 July 2005;
"Huge costs of terror attack on US milk supply," by Chris Mercer. DairyReporter.com, 4 July 2005;
"Spilled Milk," by Richard Monastersky. The Chronicle of Higher Education, 8 July 2005, page A1.

 The National Academy of Sciences (NAS) in Washington DC published "Analyzing a Bioterror Attack on the Food Supply: the Case of Botulinum Toxin in Milk," by Lawrence Wein and Yifan Liu (Institute for Computational and Mathematical Engineering, Stanford University), despite pleas by the US government not to do so. The researchers used probabilistic mathematical models to present how the nation's milk supply could be sabotaged. The government claimed that the paper was in essence a how-to guide for terrorists, and others simply criticized the quality of the paper. The NAS claimed that information on mass-poisoning could be found freely on the web and that this is a scientific paper worthy of publication. The paper ended up being published online only. Various media covered the story, focusing not on the content of the paper, but on the issue of the division between science and security. --- Annette Emerson

"Landmarks on the Road to Modern Calculus": Review of The Calculus Gallery: Masterpieces from Newton to Lebesgue, by William Dunham. Reviewed by Judith V. Grabiner. Science, 24 June 2005, page 1872.

Grabiner calls The Calculus Gallery: Masterpieces from Newton to Lebesgue, by William Dunham (Princeton University Press, 2005), "a wonderful book" for teachers "wanting a clear sense of where ideas came from", and for mathematicians, scientists, and historians, who "can learn much that is interesting, much that is mathematically significant, and a good deal that is both".

--- Annette Emerson

"Probing Performance Gaps": Review of Gender Differences in Mathematics: An Integrative Psychological Approach, edited by Ann M. Gallagher and James C. Kaufman. Reviewed by Debra Lewis. Science, 24 June 2005, page 1871.

Lewis reviews the book Gender Differences in Mathematics: An Integrative Psychological Approach, edited by Ann M. Gallagher and James C. Kaufman (Cambridge University Press, 2005). The volume "offers a collection of self-contained chapters investigating this perceived gender gap in mathematics achievement, particularly the mismatch between course grades and scores on standardized tests." Lewis describes the writing and contents as uneven, but does say that most of the chapters are well written and provocative "in the best sense of the word." She concludes with some as yet unanswered questions and thoughts of her own.

--- Annette Emerson

 Photograph by Gilbert Jain Photography. The Chronicle's Magazine & Journal Reader focuses on "Interview with Martin Gardner" in the June/July issue of Notices of the AMS. The summary quotes a bit from the article, and gives a brief overview of Gardner's life and works---which to date include more than 50 books and the "Mathematical Games" column that ran in Scientific American for 25 years. --- Annette Emerson

"Grassroots Math Guide." NetWatch, Science, 17 June 2005, page 1721.

The PlanetMath website currently has over 5000 entries in its encyclopedia of mathematics topics. Nathan Egge and Aaron Krowne began the site about five years ago when another website they used as a math reference went offline. Users write and review the content at PlanetMath. Krowne estimates that mathematics graduate students are the biggest contributors.

--- Mike Breen

"Trade secret." Random Samples-People, Science, 17 June 2005, page 1739.

In April, Alexis Lemaire broke his own record for calculating in his head when he found the 13th root of a 200-digit number in under five minutes. The 24-year-old informatics student said that he would like to set his next record in the U.S. because, "In France almost everybody knows me now."

--- Mike Breen

 A group of researchers, César A. Hidalgo, Alejandra Castro, and Carlos Rodriguez-Sickert, have devised a mathematical model that approximates a film's box-office earnings in the weeks after its release. The three major factors in the model are: "the size of the possible audience, the initial desire of audience members to see the film (which is often dictated by the amount spent on marketing and publicity), and audience response to the film." Hidalgo and his colleagues compared their model with the weekly earnings of the 44 highest-budget films of 2003. They say that their model and the data were a good match. A researcher who studies Hollywood marketing points out that the model does not consider factors such as a film's availability, which affects the number of people who see it. The paper "The effect of social interactions in the primary life cycle of motion pictures," is posted online. --- Mike Breen

"A perfect fit." Random Samples-People, Science, 10 June 2005, page 1547.

Wayne Daniel has created a puzzle which is a nested set of the five platonic solids: the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. The puzzle has 41 interlocking pieces. Daniel is a former physicist who first became interested in making geometric objects when he first made a tetrahedral kite for his son. This short article indicates that his next challenge is to design a puzzle based on the surface of a soap bubble.

--- Mike Breen

"Can Get Satisfaction," by Carla P. Gomes and Bart Selman. Nature, 9 June 2005.

In this article, Carla Gomes and Bart Selman begin by discussing constraint-satisfaction problems, a class of optimization problems used in the scheduling of airline or train crews and computational biology, to name a few applications. These types of problems contain a set of variables with a finite number of possible values, as well as a set of constraints. Although "computer scientists conjecture ... that there is no algorithm that can do substantially better [at finding solutions to these types of problems] than can an exhaustive search, ... certain sets of constraints are actually surprisingly easy to satisfy." For example, problems with many variables that can take many values and have only a few constraints, will have many solutions. On the other hand, problems with few variables and many constraints may have no solution. What about the constraint-satisfaction problems that fall between these two situations, problems at the "phase transition" which "occurs at a certain ratio of constraints to variables"?

Here Gomes and Selman discuss the work of Dimitris Achlioptas, Assaf Naor, and Yuval Peres. These three researchers present "a new approach to determining the lower bound on this phase transition in [a type of constraint-satisfaction problem, known as a] k-SAT problem." Achlioptas, Naor, and Peres also offer a technique for determining the solution of graph-coloring problems, another type of constraint-satisfaction problem.

The work of these researchers highlights, in the words of Gomes and Selman, how "the quest for a deeper understanding of phase-transition phenomena in computational problems has been a catalyst to a productive interchange of ideas and concepts between statistical physics, mathematics and computer science."

--- Claudia Clark

"Game for some road-trip fun?," by Lynn Petrak. The Chicago Tribune, 5 June 2005.

The new hand-held game, 20Q, amuses families on car trips as it uses algorithms to correctly guess most word choices. Canadian mathematician Robin Bergener turned entrepreneur by allowing a commercial toy company to develop and sell the device based on his 20Q.net. Petrak notes that "although the so-called neural network that drives the game is complex, the premise is simple: Think of a word, press a button to start and answer the ensuing series of questions scrolled along a small screen as yes,' no,' unknown,' or sometimes.' Three out of four times the game is likely to win." The Chicago Tribune's editor notes that "the toy is amazing. And addictive."

--- Annette Emerson

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