# 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)

### March 2007

Math Blogs on the Internet

Math enthusiasts itching to share their daily/weekly insights are looking to the blogosphere for an outlet. For a little over two years, Professor Mark Bridger of Northeastern University has commented on the TV show NUMB3RS in his blog of the same name. He often uses the show's quick mention of a mathematical topic as a prompt for more detailed descriptions accessible to readers with an elementary understanding of mathematics.

Ivars Peterson, a writer for Science News, began Math Trek in 1996. This blog envelops readers in the puzzle-like and artistic aspects of mathematics ranging from Sudoku to knitting patterns. Often these subjects provide a forum of common interest between mathematicians and aficionados. With Peterson leaving Science News to work for the Mathematical Association of America, Julie Rehmeyer inherits Math Trek, and Peterson will create a new blog, The Mathematical Tourist.

American Scientist writer Brian Hayes titles his blog Bit Player, emphasizing the applied and computer-based sides of mathematics. His entries infuse quotidian activities with mathematical interest. One of his most recent entries discusses the everyday schoolyard problem of picking teams fairly.

Even "mainstream blogs," like the Houston Chronicles SciGuy by Eric Berger, are sprinkling a little mathematics between global warming and medical issues. The square-wheeled bicycle devised by Macalester mathematician Stan WagonÊis pictured and in the ensuing commentary some applications are discussed in the in the January 2007 blog.

Also worth remarking on is the community of more informal bloggers, such as those who post on the Carnival of Mathematics page, a newly created monthly anthology of submitted entries. Contributed titles include "Unapologetic Mathematician," "A Math Less Traveled By," and "Abstract Nonsense." These entries range in viewpoint and are often slightly more technical in nature, requiring a college-level understanding of mathematics.

Although blogs are not vetted or particularly scholarly, these venues allow for feedback from readers and interaction between diverse types of people. For example, over 100,000 people have visited Mark Bridger's NUMB3RS blog since its inception. The writers of these blogs often give their time freely, providing a public service whose effects we will surely see in the future.

--- Brie Finegold

"Meet Mr. Polytope": Review of King of Infinite Space, by Siobhan Roberts. Reviewed by Tony Rothman. American Scientist, March-April 2007.

 This hyperbolic tiling represents the kind of mathematics Donald Coxeter enjoyed. Image by Jos Leys. King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry is a biography of the legendary mathematician H.S.M. Coxeter, whose lifelong love affair with with classical geometry ended with his death in 2003 at the age of 96. The book grew out of an award-winning profile Roberts wrote for the magazine Toronto Life. The review discusses the daunting challenge Roberts faced in making an interesting story out of Coxeter's life, which was not especially eventful. In fact, the reviewer writes, Coxeter is "upstaged" throughout the book by more colorful characters such as Ludwig Wittgenstein, John von Neumann, and John Horton Conway. The book is also enlivened by a description of the Bourbaki group, which had a major impact in mathematics that was quite different from the impact of Coxeter's work, and by discussions of Coxeter's interactions with artists such as M.C. Escher. "Even if Roberts's title character is a slightly wan hero," the reviewer writes, "King of Infinite Space supplies ample grist for the mills of anyone pondering the state of modern mathematics, its sociology and its interaction with other pursuits." --- Allyn Jackson

"Multiscale Modeling in Biology," by Santiago Schnell, Ramon Grima, and Philip K. Maini. American Scientist, March-April 2007, pages 134-143.

Mathematical modeling can help biologists in two ways. First, scientists can determine the factors driving a biological process---the domination of normal cells by cancerous cells, for example---by comparing observed reality to the predictions of models based on different sets of underlying criteria. Scientists can use a good model to test theories on how to alter that process, such as how to stop the cancerous cells. One way to model a biological process involves stringing together smaller models that predict behavior at each level of complexity, from building block cells to entire populations of organisms. This approach may be too cumbersome to implement effectively, however, and lacks predictive value because it ignores interdependence between the levels. This article provides an accessible look into the theory behind developing mathematical models of biological processes and gives examples of how these models are being used in cancer research and how mathematical modeling has progressed since the early days of Euler.

--- Lisa DeKeukelaere

"248-dimension maths puzzle solved" BBC, 19 March 2007.
"Success in mapping 248-dimensional object: Until now, no one thought structure could ever be understood", by Sara Goudarzi. MSNBC, 19 March 2007.
"Une vingtaine de chercheurs percent l'un des plus grands secrets mathématiques (Twenty researchers crack one of the greatest secrets in mathematics)". Le Monde (with Agence France Presse), 19 March 2007.
"Journey to the 248th dimension: Map of weird mathematical entity may point way for string theory," by John Whitfield. Nature, 19 March 2007.
"Mathematicians finally map 248-dimension structure," by Hazel Muir. New Scientist, 19 March 2007.
"Is this the fabric of the universe?", by Roger Highfield. Daily Telegraph, 19 March 2007.
"Mathematicians Team Up with Supercomputer to Crack 248-Dimensional Object". Scientific American, 19 March 2007.
"The Scientific Promise of Perfect Symmetry," by Kenneth Chang. New York Times, 20 March 2007.
"Century-old math puzzle is solved", by Julie Sevrens Lyons. San Jose Mercury News, 20 March 2007.
"Team Cracks Century-Old Math Puzzle". Associated Press, 21 March 2007.
"The theory of everything in 248 easy steps," by Steve Connor. The Independent, 21 March 2007.
"It took 100 years, but key maths conundrum is finally cracked," by James Randerson. The Guardian, 22 March 2007.
"Mapping the 248-Fold Way," by Dana Mackenzie. Science, 23 March 2007, pages 1647-1649.
"Checking the Math on a Huge Theoretical Problem," by Keith Devlin and Scott Simon. NPR Weekend Edition, 24 March 2007.
"His mind is on the eighth dimension" (profile of David Vogan), by Billy Baker. Boston Globe, 26 March 2007.
"Struktur einer komplizierten Gruppe berechnet: Resultat eines vierjährigen Forschungsprojekts (Structure of a complicated group calculated: Result of a four-year research project)", by George Szpiro. Neue Zürcher Zeitung, 28 March 2007.
"Fearful Symmetry," by Alex Stone. Discover, June 2007, page 18.

 This computer-generated two-dimensional representation of E8 was made by John Stembridge and is based on a hand drawing made in the 1960s by Peter McMullen. Can E8 have become a household word? This listing of articles represents only a handful of the worldwide media coverage of the calculation of all the irreducible representations of the exceptional Lie group E8. Four years in the making, this enormous calculation represents a milestone in mathematics and in computing. Many of the articles emphasize the possible role that the new calculation might play in string theory. See also Tony Phillips's comments on the media blitz in "Tony's Take" in the current issue of the AMS web feature Math in the Media. --- Allyn Jackson

"Spezialist für Statistik in den USA erhält den Abel-Preis (Statistics specialist in the USA receives Abel Prize)," by George Szpiro. Neue Zürcher Zeitung, 22 March 2007.
"It All Adds Up to a Big Prize For Math Professor at NYU," by Gary Shapiro. The New York Sun, 23 March 2007.
"Abel Prize." Newsmakers, Science, 30 March 2007, page 1775.
"Big prize for unlikely research," by Erica Klarreich. Science News, 31 March 2007, pages 205-206.
"Science of chance," by R. Ramachandran. Frontline, 7-20 April 2007.
"Equal to Nobel," by R. Ramachandran. Frontline, 7-20 April 2007.
"Indian mathematician awarded Abel prize, thanks motherland." Bureau Report in Zee News Limited (India Edition), 30 April 2007.

"Paul Joseph Cohen, 72; leading mathematician." Associated Press, 31 March 2007.
"Paul J. Cohen, Mathematics Trailblazer, Dies at 72," by Jeremy Pearce. New York Times, 2 April 2007.

Fields Medalist Paul Cohen died 23 March 2007 in Palo Alto, California, at the age of 72. Cohen proved that the Continuum Hypothesis could not be proved from the axioms of Zermelo Fraenkel set theory, which established the hypothesis' independence (Kurt Gödel had proved earlier that the negation of the Continuum Hypothesis could not be proved) and settled David Hilbert's first problem. Cohen developed the technique known as forcing, used for constructing set-theoretic models. Cohen received the AMS Bôcher Memorial Prize in 1964 for his work on the Littlewood conjecture. He also won the National Medal of Science in 1967 and was a member of the National Academy of Sciences. Cohen joined the Stanford faculty in 1961 and although he retired in 2004, he was still teaching until the spring quarter 2007. Peter Sarnak (Princeton University), a former student of Cohen's, called him "one of the most brilliant mathematicians of the 20th century."

--- Mike Breen

"Math Circles Inspire Students," by Julie J. Rehmeyer. Science News Online, 31 March 2007.

In an effort to raise the popularity of mathematics among school-age kids, professors and educators are starting Math Circles, which originated in Hungary, all over the U.S. In her article, Rehmeyer profiles two such groups, one in California and one in Massachusetts, where kids are literally jumping out of their seats to answer mathematical questions and discuss their ideas outside of the traditional classroom. Whether the approaches used are more competitive or more cooperative, the end result seems to be that students are inspired to return week after week to explore beautiful mathematics. Much like art or sport, mathematics becomes participatory in these contexts and is no place for the idle spectator. In this spirit, Rehmeyer ends the article with a problem for the reader to consider, inviting us to step into the Math Circle.

--- Brie Finegold

"The chance of a lifetime": Interview with Persi Diaconis. Interviewed by Justin Mullins. New Scientist, 24 March 2007.

Persi Diaconis is a magician-turned-probabilist and a professor at Stanford University. In the interview he talks about connections between magic and mathematics, about what statistics is, and about his work debunking claims of extrasensory perception. He offers a simple question about shuffling decks of cards whose question is completely unknown. "It's linked to the Riemann hypothesis, one of the fanciest open problems in mathematics," Diaconis says. "That's the kind of thing that makes the mathematician and magician in me rather happy."

--- Allyn Jackson

"Euler's revolution," by Ian Stewart. New Scientist, 24 March 2007, pages 48-51.

This article starts out discussing the question of whether power lines could be used to carry communication signals, such as internet or television signals. The problem is that power lines are rife with noise. Despite this problem, a recent survey of research has concluded that "power line communication" is, as Stewart quotes the survey, "an idea whose time has come". The advances that make PLC feasible center on error-correcting codes, which allow one to clean communications signals of noise. These codes are based on the work of Leonhard Euler, who was one of the greatest mathematicians who ever lived; the 300th anniversary of his birth is being celebrated with worldwide events during 2007. Euler studied Latin squares, which are square arrays of numbers, similar to Sudokus, that obey certain rules. It turns out that his work on Latin squares has led to new ideas for constructing error-correcting codes.

--- Allyn Jackson

"The True Price of a Human Organ," by Susan Brown and David Glenn. Chronicle of Higher Education, 23 March 2007.

This article includes a sidebar "A Mathematician Matches Donors with Recipients," which discusses a scheme devised by Sommer Gentry, a mathematician at the US Naval Academy. She is married to a transplant surgeon, who explained the problem to her. Suppose a husband is willing to donate a kidney to his wife, but his kidney is incompatible, and suppose further that another person needing a kidney has a sister who is willing to donate, but the sister's kidney is also incompatible. If the donors are swapped and compatibilities match, then both patients receive the transplants they need. This kind of swapping has become more commonplace---and more complicated. One case involved swapping among five donors and patients. In such situations doctors realized that there are many different swapping schemes, and they wanted a way of choosing the best one. Gentry used graph theory to devise a method for finding a swapping scheme that maximizes the number of patients helped. "Several transplant centers have already used her scheme to sort through potential matches within their own groups of patients," the article says.

--- Allyn Jackson

"Is Beauty Truth and Truth Beauty?": Review of Why Beauty is Truth: A History of Symmetry, by Ian Stewart. Reviewed by by Martin Gardner. Scientific American, 18 March 2007.

Martin Gardner, the founder of Scientific American's "Mathematical Games" column, which he wrote from 1956 until 1981, reviews a book by one of his successors in the quest to popularize mathematics. Both Gardner and Stewart have published over sixty books on mathematics, a feat few others can claim. Gardner, whose review focuses on the philosophical aspects of Stewart's book, praises its historical content and narrative but disagrees with Stewart when it comes to the title. "In mathematics, beauty must be true---because anything false is ugly," writes Stewart. But Gardner points to elegant yet false statements, as well as simply stated theorems with ugly proofs. Of course, anyone intimate with a subject may be blinded by love for it. In 1963, the famous mathematician Dirac was quoted in Scientific American as saying: "[I]t is more important to have beauty in one's equations that to have them fit experiment. It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one's work and experiment, one should not allow oneself to be too discouraged, because. That will get cleared up with further development of the theory." So perhaps even if all beautiful mathematics is not necessarily true, the search for beauty may prove the best path to truth.

--- Brie Finegold

"The Next Generation," by Aimee Cunningham. Science News, 17 March 2007, page 166.

 John Vincent Pardon. Three mathematics projects finished in the top six in the 2007 Intel Science Talent Search. John Vincent Pardon from Durham Academy in Chapel Hill, NC, won second place and a US$75,000 scholarship for proving that "a closed curve can be made convex without permitting any two points on the curve to get closer to one another." Third place and a US$50,000 scholarship went to Dmitry Vaintrob, from South Eugene High School in Eugene, OR, for proving that, in an important class of spaces, loop homology and Hochschild cohomology coincide. Gregory Drew Brockman, of Red River High School in Thompson, ND, won sixth place and a US$25,000 scholarship for his project on Ducci sequences. The top award, a US$100,000 scholarship, went to Mary Masterson of Oklahoma City who built an accurate spectrograph for about US\$300. --- Mike Breen

"U.S. Math Tests Don't Line Up," by Jeffrey Mervis. Science, 16 March 2007.

A standardized math test given to 12th graders nationwide in 2005 by the Department of Education's National Center for Educational Statistics offered mixed messages on progress. Because the 2005 test emphasized different topics and was administered with different rules than the previous exam---given in 2000---the results are difficult to compare to those from the past. Some argue that 2005 scores should not be used to gauge progress since 2000 due these differences, but other researchers claim to have found evidence of probable gains that appear to track with improvement levels for lower grades. Many educators, however, are disappointed by a lack of major steps forward.

--- Lisa DeKeukelaere

"There Ought to Be a Lawsuit," by Josh Keller. The Chronicle of Higher Education, 16 March 2007, page A6.

A student at the University of Colorado at Boulder sued her calculus teacher after she got a C- in the course. The teacher had allowed her extra time on tests, because of her test anxiety, and exempted her from some quizzes. None of her test scores were above 65 percent, and she fell asleep halfway through the final exam. Still she sued, claiming that she had been discriminated against on the basis of her race and her disability (test anxiety). A district court and appeals court ruled against her.

--- Mike Breen

"'Jeopardy': What is a three-way tie, Alex?," MSNBC.com, 16 March 2007.
"Jeopardy! has a first three-way tie," The West Australian, 18 March 2007.

These were among the many news media that picked up an AP (Associated Press) report on the rare occurrence of a three-way tie on the TV game show, Jeopardy!. A mathematician was consulted who calculated the odds of such a three-way tie happening to be 1 in 25 million.

--- Annette Emerson

"Journeys to the Distant Fields of Prime," by Kenneth Chang. New York Times, 13 March 2007.

Chang writes about Terence Tao (UCLA), who won a Fields Medal in 2006 and currently holds a MacArthur Fellowship. The article begins by describing Tao's work with prime numbers and the overflow crowd that came to hear his public lecture on primes. Chang also writes about Tao's research in compressed sensing, which is data compression, as in digital photography, but does not have so much computer power associated with the sensors. Also in the article is Tao's early history as a child prodigy. Included is an eight-question test he was given the day before his eighth birthday. It was designed as a written test, but Tao solved all the questions without pencil and paper---and got them all right. His parents' philosophy with him and his two brothers: " All along, we tend to emphasize the joy of learning, ... The fun is doing something, not winning something."

--- Mike Breen

"Students learn to rhythmic beat of rap," by Shayna Chabner. NCTimes.com, 12 March 2007.

The article profiles Escondido middle school math teacher Alex Kajitani, who transforms into the Rappin' Mathematician. Wearing sunglasses and dancing to several dozen songs he's written, Kajitani has found that his unusual teaching method is helping students commit mathematical concepts to memory. The proof is that for many students "the raps have translated into better test scores and a deeper understanding of the subject." The popularity of rap, combined with the repetition and rhythm of the music form, and Kajitani's lyrics and showmanship, have helped to engage his students. The NCTimes.com article includes a video of Kajitaniin action.

--- Annette Emerson

"Functional Family: Mock theta mystery solved," by Erica Klarreich. Science News, 10 March 2007, page 149.
"A flash of insight brings answers," by Mark Johnson. Milwaukee Journal Sentinel, 13 March 2007, page 1.
"Zahlentheoretiker lösen jahrzehntenaltes Rätsel: Erklärung der `Mock-Theta-Funktionen' (Number theorists solve hundred year old puzzle: Explanation of 'mock theta functions')," by George Szpiro. Neue Zürcher Zeitung, 14 March 2007.

In 1920, as the legendary mathematician Srinivasa Ramanujan lay on his deathbed, he wrote a letter to his British colleague G.H. Hardy about a collection of functions he called mock theta functions. Unfortunately, part of the letter was lost, so through the years although mathematicians had examples of the functions and had seen their uses, there was no definition of them. Now Ken Ono and Kathrin Bringmann, both of the University of Wisconsin-Madison, have defined the functions. George Andrews of Pennsylvania State University says the work is, "just absolutely outstanding. Brilliant. I really didn't expect their achievements to occur in my lifetime." The Journal Sentinel article describes the flash of insight Ono had, while on a flight with Bringmann, that led to the definition. It also gives background on Ramanujan and his work. One mystery does remain: How did Ramanujan discover these functions? Says Ono, "Think of it, 2007 and we're throwing all of our knowledge that we've learned, all of the knowlege accumulated over decades, to figure out what this man was talking about in 1920."

--- Mike Breen

"Numbers Game". The Chicago Sports Review, 6 March 2007.

 With spring training already under way, and baseball season just around the corner, it seems only fitting to discuss a book on the subject of baseball and probability. The book, A Mathematician at the Ballpark: Odds and Probabilities for Baseball Fans, was published in 2004 by University of Oregon mathematics professor and (of course) baseball fan Ken Ross. In this short article, the Chicago Sports Review interviews Ross. They discuss examples of statistically significant events, concepts such the "clutch hitter" and the "streak shooter," and how odds are determined in sports, among other topics. --- Claudia Clark

"Lessons From 'Math Dude' Add Cool to the Equation," by Nancy Trejos. Washington Post, 4 March 2007, page SM 8.

 Math Dude Mike DeGraba. The Montgomery County (MD) public school system has a weekly math cable show and podcast to interest today's teenagers in algebra. The star of the show is Mike DeGraba (the Math Dude) a recently retired Montgomery County math teacher, who dresses up as characters such as Groucho Marx to get the math message across. The videos on the school system's website are also on iTunes. (Image courtesy of Montgomery County Public Schools.) --- Mike Breen

"Pi Day celebrated," by Heidi Ledford. news@nature.com, 15 March 2007.
"Happy Pi Day from the Pi Guy," with Marc Umile. All Things Considered on National Public Radio, 14 March 2007.
"A slice of musical pi," by John Zech. Minnesota Publc Radio, 14 March 2007.
"Math mavens unite for International Pi Day," by Misty Harris. CanWest News Service, published in The Windsor Star, Vancouver Island Newspapers, Victorian Times Colonist and Ottawa Citizen, 12 March 2007.
"Pi fans to meet March 14 (3.14, get it?)," by Erin McClam. Associated Press, 11 March 2007.

 Not quite as well-known as 4-20 on college campuses, 3-14 still gets its share of celebration, according to the above article. Pi Day festivities, which also coincide with Einstein's birthday, were even held at the San Francisco Exploratorium, proving that college students are not the only ones who enjoy a little irrational get-together. Math enthusiasts eat pizza pie, recite the digits of pi, sing songs like "American Pi", and show their appreciation for this famous transcendental number, which one article describes as the mathematical equivalent of George Clooney. For those who sometimes ask themselves, Which is better pi or e?: There is no 71st day of February (e = 2.71...). --- Brie Finegold

"Equations as icons", by Robert Crease. Critical Point, Physicsweb, March 2007.

This article is an installment in Robert Crease's monthly column called Critical Point. He discusses two very different equations: Euler's equation relating e, i, and pi, and Einstein's equation relating energy, mass, and the speed of light. Why do some equations become icons?, Crease asks. One reason is that some equations come to symbolize a landmark in scientific inquiry. But perhaps a more important reason is that some equations unify objects or concepts that appear to be quite different. Euler's equation and Einstein's equation are particularly well known and compelling because "they serve as clear and concise examples of what equations and formulas do: they show how seemingly disparate elements are implicated in a unity, and do so concisely, with few moving parts, so to speak," Crease writes.

--- Allyn Jackson

"Graph Theory and Teatime," by Gary Stix. Scientific American, March 2007, pages 37 and 40.

 Christian Borgs and Jennifer Chayes. Photo © Dan Lamont. This article is about Microsoft's Theory Group, especially about the group's founders and leaders, Jennifer Chayes and Christian Borgs. Stix writes that "the pair have succeeded in re-creating the rarefied world of a top university department, right down to the tea ritual." The research is for its own sake, rather than for the sake of new code. Chayes says, "We do research for the day after tomorrow." --- Mike Breen

"Turning the tide," by Jenny Lunnon. Cambridge Alumni Magazine, Number 51, Easter Term 2007, pages 30-33.

This article describes the African Institute of Mathematical Sciences, which gives young people from all over Africa undergraduate-level training in mathematics. The nine-month course of study, culminating in an AIMS diploma, enables the students to bring mathematical skills to further study and then careers in a wide range of areas. Because of the centrality of mathematics to all areas of science and technology, building mathematical capacity in Africa could have a major positive impact on the continent. AIMS was founded by mathematical physicist Neil Turok, and Keith Moffatt, former director of the Isaac Newton Institute for Mathematical Sciences in Cambridge, England, advises AIMS on management issues. Some AIMS students have overcome much adversity to be able to study there, and a couple of their stories are told in the article. For example, Angelina Lutambi is one of nine children. Her parents are small-scale farmers who are themselves uneducated but who encouraged her to go to school. She showed an early facility for mathematics and sold drinks to raise money for her and her siblings' education. After her study at AIMS, she was awarded a Third World Academy of Sciences fellowship that will allow her to study for a PhD. AIMS has a special commitment to helping women.

--- Allyn Jackson