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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), Baldur Hedinsson (Boston University), and Adriana Salerno (Bates College)
"Turning Away from High Symmetry," by John C. Crocker. Science, 29 January 2010, pages 535-536.
The packing of a large number of spheres has been well observed in nature and studied by mathematicians and material scientists alike. Small clusters (involving a small number of particles), like crystals, are much less understood. In a recent article published in Science ( "The Free-Energy Landscape of Clusters of Attractive Hard Spheres," pp. 560-563 of the same issue), Meng et al. report on an experimental study of the equilibrium cluster configurations in a model consisting of “sticky” spheres designed to have short-range attraction. This work would help understand the “rules” by which nature self-assembles small structures and ultimately crystals. The main insight is that, in thermal equilibrium, the most common clusters are not those with the lowest internal binding energy, but those with the lowest free energy, which is favored by higher entropy. What Meng and his collaborators observed, through a microscopic experiment involving meticulous observation, was that highly symmetric structures were much less likely to occur. For six particles, for example, two different structures could be formed: an octahedron, and a “polytetrahedron” consisting of three tetrahedra joined by adjacent faces. The latter low-symmetry structure was observed 96% of the time. According to the authors, this difference is almost entirely accounted for by the octahedron’s high rotational symmetry, which induces low entropy. Generalizing their model to non-spherical molecules will probably be a non-trivial extension, Crocker says.
--- Adriana Salerno
Arthur Benjamin in the media:
"Colbert Report with Arthur Benjamin," Comedy Central, 27 January 2010;
"Ta Da!," The New York Times, 30 December 2009.
Arthur Benjamin (Harvey Mudd College) appeared on the Colbert Report Wednesday, January 27 (Comedy Central). Benjamin demonstrated some of his calculation skills (the subject of his book, Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks), doing some instantaneous multiplication and reporting of the day of the week on which Colbert was born. Benjamin responded to Colbert's bombardment of questions about mathematics, saying math is both practical and beautiful, that studies show that more mathematics training is the single best predictor of a person's income, and that statistics teaches people how to think critically, assess risk, and determine randomness. When asked why he loves mathematics, Benjamin replied that he loves solving problems and thinking about various ways to arrive at the same answer. View the video clip to learn what Benjamin's favorite number is and why it's his favorite. (Photo: Richard Faverty/Beckett Studios.)
--- Annette Emerson
In the "Ta Da!" piece, Arthur Benjamin shares some "Math Tricks" that will amuse and impress your friends. Unlike most performers, this mathemagician shares his show-stopping secrets with the public--basic algebra and pattern-finding. Based on their newfound knowledge, readers can calculate more quickly and come up with a few tricks of their own. More tips and explanations can be found in Dr. Benjamin's DVD course The Joy of Mathematics.
--- Brie Finegold
"Doing the Math on Mexican Drug Wars", by Viridiana Rios. New York Times, 25 January 2010.
Viridiana Rios is a PhD student in political science at Harvard University. A native of Mexico, she is trying to use mathematical modeling to understand Mexican drug cartels. The article describes her trepidation in going to Mexico to collect information about the cartels, which have taken violent means to silence those who come asking questions. "They cannot kill me in America," she writes. "In 10 minutes, when I am [in Mexico], they will be able to." But she also claims that speaking up about drugs is not dangerous if you speak in the language of mathematics, "the language of the sigma and conditional expectations". "Math protects me from the violence," she says, but she does not explain how. The article includes an equation that Rios says can predict "the maximum percentage of the Mexican population that could turn to drug trafficking if wage inequality doubled". Just what the equation means is unclear, as none of the terms in it are defined. (The equation does not show up in the online version.) The mystery of this equation, and of exactly how Rios is using mathematics, is compounded when she writes, "I know, I know, this is weird." The article makes some outsized claims for the reliability of mathematical modeling in the social sciences, such as "Mathematics is cold-headed; it cannot go wrong." A letter to the editor in response to Rios's piece noted: "Perhaps mathematics 'cannot go wrong,' but human beings have a remarkable capacity for screwing up in real life." The letter pointed to the 2008 economic meltdown as a case in point.
--- Allyn Jackson
Articles on girls and math anxiety:
"Study: Female teachers' math anxiety affects girl students," by Kristen Mack. Chicago Tribune, 25 January 2010;
"Girls may learn math anxiety from female teachers." Boston Herald, 25 January 2010;
"Female teachers may pass on math anxiety to girls, study finds," by Karen Kaplan. Los Angeles Times, 26 January 2010.
A study of first and second grade students found that girls taught by females who had math anxiety were more likely to believe that boys are "hard-wired" for math--and girls aren't--and those girls who had that belief scored significantly lower on a math achievement test than those who didn't. The research was done by a team led by Sian Beilock (University of Chicago pyschology department) and involved seven female teachers with math anxiety and more than 100 first and second grade students. The study, Female teachers' math anxiety affects girls' math achievement, by Sian L. Beilock, et al, in the Proceedings of the National Academy of Sciences, is the first both to examine teachers' math attitudes and show that those attitudes can be transmitted to students and affect their performance.
--- Mike Breen
Four math articles in the 22 January edition of The Chronicle of Higher Education.
*Two Commentary pieces relate to proof and the importance of mathematics in other courses. In the first, "The Poetry is in the Proof," Charles Coppin (Lamar University) tells of a proof course that is required of all liberal arts students at Lamar (the "poets" are those who major in the humanities or the arts). He explains that the course gives non-math students a much better insight into mathematics than do traditional math courses for humanities majors. "When original proofs are presented, conjectures are made, and examples and couterexamples are given, the imagination is engaged, excitement abounds, and on a good day, pure poetry flows." Some of Coppin's explanations and reasoning is based on former AMS President Felix Browder's article "The Relevance of Mathematics" (American Mathematical Monthly, Vol. 83, No. 4, April 1976, pp. 249-254). In the second article, "Improve Math Education, Improve Student Retention," Tao Pang, chair of the physics and astronomy department at the University of Nevada Las Vegas, writes that the real problem for students who struggle in science courses is their lack of mathematical skills. He recommends revamping remedial courses so that students learn math before they can take more demanding courses. Pang says that current remedial courses don't help students graduate and are a burden on those enrolled. He states that getting remedial courses "right" will lead to more student retention and more graduation. The article concludes with "The troubling problem of America's poor student retention may be resolved only when society takes a great leap forward. But for today's educators, working to improve our students' math background is a good start."
*In "The Rocky Transition From High-School Calculus," David Bressoud, current MAA president, examines the Advanced Placement (AP) calculus program and recommends changes. Currently about 300,000 students take the AP calculus exam while at least 200,000 other students take calculus in high school but do not take the exam. Bressoud writes that for most of these students, AP calculus may be more of a stumbling block than a stepping stone. Furthermore, he states that a mis-alignment between AP calculus content and the college math curriculum is part of the cause for declining enrollments in math courses beyond Calculus I. Bressoud makes specific recommendations for high schools and colleges and ends his article with: "If we want to facilitate a smooth transition from high-school calculus into college mathematics, then we must get more information about the true difficulties students face, ensure that students are ready before they begin calculus, and rethink the college mathematics curriculum. We need engaging, intellectually satisfying courses that will inspire students to continue their study of mathematics."
*Finally in "Math + Women + MIT = Dramatic Tension," Carolyn Mooney and Sara Lipka write about the play Truth Values: One Girl's Romp Through M.I.T.'s Male Math Maze. The play is written by Gioia De Cari, who is also the sole actress in the play, and was performed three times during the Joint Mathematics Meetings in San Francisco. The play's prologue begins with a discussion of Lawrence Summers' remarks in 2005 about women's science and math aptitude. Then the play follows De Cari's journey "including math nerds who wanted to paw her and professors who asked her to bring cookies to the meeting or wondered why she wasn't at home raising children." Critics and audience members (including people from MIT) are very positive about the play. Hear a podcast about the play from its run in New York. (Photo courtesy of Gioia De Cari.)
--- Mike Breen
"Ties That Bind," by Lisa Grossman, Science News, 16 January 2010.
Laughter often seems contagious, and perhaps the emotions of our friends affect our emotions more than we know. Some social scientists are building scientific evidence that traits like happiness, loneliness, and obesity can spread much like disease. In an attempt to understand why even people with a large social network can feel lonely, a recent paper, "Alone in the crowd: The structure of loneliness in a large social network", traces the trajectory of loneliness through a group of 5,000 people on whom social data had already been collected. This new study by psychologist, political scientist, and sociologist suggests that loneliness is most prevalent on the edges of networks, propagates through the social network in clumps, and extends through three degrees of separation. In other words, the mental state of a man and his mother's boss's girlfriend are linked, even if they've never met.
As technological advances provide more avenues by which to collect personal data, social scientists are more prone to carry out large-scale studies of how emotion spreads through social networks. The new field of computational social science brings concepts from statistical mechanics and computational biology to bear on these large banks of data. However, some argue that using this type of analysis could be used to make it seem like less mutable characteristics like height and acne are also contagious. Meanwhile, since no social network is completely closed, it is difficult to decide when a data set is complete. Still, as this area of study develops, it will become a hotbed for collaboration across traditionally distant disciplines.
--- Brie Finegold
"In a Series: Nickelodeon Will Focus on Math," by Elizabeth Jensen. The New York Times, 11 January 2010.
Nickelodeon, which produces television shows that "focus on social skills as much as letters and numbers, will move squarely into the academic realm, with the introduction of 'Team Umizoomi,' which it said is the only preschool series centered entirely on teaching math to children." The half-hour program will mix animation and live action--along the lines of other shows--but will integrate concepts of problem solving, shapes, counting, computation and measuring. The program--of which 20 episodes have been produced--was set to begin airing on the Nickelodeon network on January 25.
--- Annette Emerson
"Branded as Scholars," by Peter Monaghan. The Chronicle of Higher Education, 8 January 2010, page A6.
Monaghan writes of professors and students who have been tattooed with snippets of their work or formulas related to their work. Nicole L. Ackerman, who's a doctoral student in physics at Stanford University, has the first few terms of the Maclaurin series for the sine function tattooed on her left arm, calling the series "the most beautiful thing I've ever learned." She says that she has achieved some fame for the tattoo: Strangers approach her at parties and say, "Oh, you're that girl..." Although many people recognize the expansion, Ackerman says that "they can't always place off the top of their head whether it's the expansion of sine or cosine." (Does a tan obliterate the sine?)
(Image courtesy of Nicole L. Ackerman.)
--- Mike Breen
"Maths genius is youngest to go to Cambridge University," Telegraph (UK), 7 January 2010.
Home-schooled 14-year-old Arran Fernandez is set to become the youngest student to attend Cambridge University since William Pitt the Younger went to the university at the same age in 1773. Arran has "A-levels" in advanced mathematics, needs to pass an A-level physics exam before being admitted, but it was widely predicted that he would do so. He loves mathematics and tells the media, "There are a few things I want to work on; I'd like to solve the Riemann hypothesis."
--- Annette Emerson
"$250 million initiative for science, math teachers planned," by Nick Anderson. The Washington Post, 6 January 2010, page A3.
The U.S. government along with businesses, foundations, and universities, is spending $250 million dollars to improve science and math education. The money will be spent over a five-year period to prepare 10,000 new math and science teachers and for in-service training for existing teachers. Secretary of Education Arne Duncan says, "If we're going to be economically competitive and continue to innovate and create jobs, we have to get much, much better in STEM [science, math, technology, and engineering] education."
--- Mike Breen
Media coverage of the national Who Wants to Be a Mathematician game:
"Fairview math standout competes in national competition," by Laura Snider. Boulder Daily Camera, 6 January 2010;
"Knows His Sums." Fairfax Connection, 7 January 2010;
"2007 Spelling Bee winner wins math competition," by Wayne Freedman. KGO-TV, 14 January 2010;
"Danville teen, national spelling bee champion, wins national math contest," by Robert Jordan. San Jose Mercury News, 15 January 2010.
Pictured, Front (left to right): Kathy Lin, Los Alamos High School (NM); Kevin Yin, San Marino High School (CA); Rohit Agrawal, Wayzata High School (MN); Rebecca Easterwood, Shades Valley High School (AL); Back (left to right): Charles Xu, Fairview High School (CO); Ofir Nachum, Algonquin Regional High School (MA); Daniel Li, Thomas Jefferson High School for Science and Technology (VA); Evan O'Dorney, Berkeley Math Circle (CA); Brian Freidin, Glenbrook North High School (IL); and Ben Zauzmer, Upper Dublin High School (PA). (Photo by Annette Emerson.)
These stories are about the national Who Wants to Be a Mathematician contestants (pictured at left). The first profiles Charles Xu of Boulder, Colorado, who says that studying math is "probably the purest intellectual activity that you can have." The second is about Daniel Li, a student at Virginia's Thomas Jefferson School for Science and Technology, who is going to use some of his winnings to help create a math and science library at the school. The other two stories were about the contest itself-which involved 10 contestants from across the county-and the winner, Evan O'Dorney, who won $10,000 in the contest. As a ninth grader, he won the national spelling bee and has twice been on the U.S. International Mathematical Olympiad team, earning silver medals both times. His goal is to become a math professor. In the nearer future, he hopes to go to Harvard University. His competition in the finals was Ben Zauzmer, from Pennsylvania. Ben's mother, Jan, said, "If he had a piece of paper when he was 2, instead of scribbling, he was making up mathematical formulas." Ben, who earned $3000 for himself and $3000 for the math department at his high school, was very gracious after losing in the finals, "Evan did a great job and he really deserves it. He is an impressive mathematician and it was a lot of fun up there." (Read more about the competition and an earlier article about Ben.)
--- Mike Breen
Articles on Pi:
"Pi calculated to 'record number' of digits," by Jason Palmer. BBC News, 6 January 2010;
"The Big Question: How close have we come to knowing the precise value of pi?" by Steve Connor. The Independent, 8 January 2010.
Fabrice Bellard used a desktop computer running Linux to calculate pi to nearly 2.7 trillion digits (the previous record was about 2.6 trillion digits). Bellard says, "I got my first book about Pi when I was 14 and since then, I have followed the progress of the various computation records." The calculation takes over a terabyte of space on his computer's hard drive. Connor has other questions and answers posted, including this from Ian Stewart (Warwick University) about why people are interested in pi: "All numbers are interesting but some are more interesting than others and pi is the most interesting of the lot."
--- Mike Breen
"The Best and Worst Jobs," The Wall Street Journal, 5 January 2010.
The job of actuary rose to the top spot on a 2010 study ranking of 200 best and worst jobs in the U.S. (The job of mathematician, which ranked #1 in 2009, has dropped to #6 on the list due to the recession's impact on hiring.) "Actuaries, who evaluate the financial impact of risk on an organization, fared best because they work during standard business hours and in favorable conditions--indoors and in places free of toxic fumes or loud noise... and they also aren't expected to do any heavy lifting, crawling or crouching." The study also takes into account compensation and growth potential. To qualify as an actuary one must have a minimum of a bachelor's degree in a field such as statistics or economics, and pass a series of exams. The other best jobs following actuary on the 2010 list are software engineer, computer-systems analyst, biologist, historian, and mathematician. Media that picked up the study's job ranking report include the San Francisco Chronicle, Kansas City Star, and CBS Money Watch.
--- Annette Emerson
Science News of the Year. Science News, 2 January 2010, page 19.
Seven math stories from the year 2009 were chosen as the top math stories by the Science News. The seven include (the following links are to previous Digests on the stories, while the dates refer to the appropriate Science News issue) new statistics to measure fielding ability in baseball (29 Aug. issue), using quantum computation to solve large systems of linear equations (7 November issue), and evidence of fraud in the June 2009 election in Iran (10 July issue).
--- Mike Breen
"A Tisket, A Tasket, an Apollonian Gasket," by Dana MacKenzie. American Scientist, January-February 2010, pages 10-14.
The author explores the history of the Apollonian gasket, a geometric construction in which three adjacent circles have a fourth circle drawn into the space between them and a fifth circle drawn that surrounds and is tangent to the original three. Continuing this process indefinitely produces an object akin to a foam, in which the space between the circles reduces to zero but the length of the foam expands to infinity. Mathematicians and physicists have worked with this construct since at least the time of ancient Greece, when the Greek geometer Apollonius devised a method for drawing the surrounding circle. Descartes later picked up the problem of determining the size of the surrounding circle. Subsequent mathematicians did not work out the location of such a circle until the 1990s, however. The author also relates Apollonian gasket problems to other shapes, such as squares and triangles, and examines the fractal nature of the construct. (Image courtesy of Jos Leys.)
--- Lisa DeKeukelaere
Three stories about mathematics, and one mathematician’s obituary, made Discover Magazine’s annual issue covering the top 100 science stories published in 2009:
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