# 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)

### June 2007

"The hunter and the hunted": Review of Chases and Escapes: The Mathematics of Pursuit and Evasion, by Paul J. Nahin. Reviewed by Justin Mullins. New Scientist, 30 June 2007, page 50.

This book is about the use of mathematics to track and catch prey. Mullins writes that mathematicians were inspired to study this problem starting in the 18th century, because of attacks by pirate ships on merchant vessels. "This is just one of the colorful problems in Paul Nahin's fascinating history of the mathematics of pursuit," Mullins writes, noting that the book requires some college-level background in mathematics.

--- Allyn Jackson

"Scholars juggle dynamics of mathematics at institute," by Martin Snapp. Contra Costa Times, 29 June 2007.

 Photographs courtesy of MSRI. This article gives an overview of the Mathematical Sciences Research Institute (MSRI) in Berkeley, California. In addition to providing an environment for research and collaboration by professors and post-docs, MSRI also sponsors after-school math groups for local kids and a concert series. Even the art on the walls of the institute is mathematically focused, and the address (17 Gauss Way) and furniture in the building allude to the influence of mathematical genius Carl Friedrich Gauss. The mathematicians at work there, however, are often so consumed by their research that they don’t notice the beautiful views of the San Francisco Bay outside their windows. The institute’s funding comes primarily from the National Science Foundation, but universities and private-sector businesses support it as well. --- Lisa DeKeukelaere

"Ein Modell der Internet-Topologie (A Model for Internet Topology)", by George Szpiro. Neue Zürcher Zeitung, 27 June 2007.

This article discusses recent research by five physicists and computer scientists analyzing the topology of the Internet ("A Model of Internet topology using k-shell decomposition", by Shai Carmi, Shlomo Havlin, Scott Kirkpatrick, Yuval Shavitt, and Eran Shir, Proceedings of the National Academy of Sciences, 3 July 2007).

--- Allyn Jackson

"John Todd, math pioneer and Caltech prof, dies at 96." San Francisco Chronicle, 26 June 2007.
"John Todd, 96; Caltech professor pioneered use of computers in math," by Thomas H. Maugh II. Los Angeles Times, 27 June 2007.

John Todd was a pioneer in numerical analysis and in the development of large computers. He died 21 June 2007 in Pasadena, CA. The Los Angeles Times obituary has details about how Todd rescued some mathematicians and the Mathematical Research Institute at Oberwolfach at the end of World War II while he was in the British Admiralty. After finding the mathematicians and many mathematics books at a hunting lodge in the Black Forest, he placed a note on the lodge's door saying that it was the property of the British Navy. A few days later a group of soldiers wanted to seize the lodge but Todd, dressed in an elaborate uniform, stopped them. He later said, "It was like a Gilbert and Sullivan opera, ... [but] this was probably the best thing I ever did for mathematics." Todd and his wife Olga Taussky-Todd came to the California Institute of Technology (Caltech) in 1957 and spent the rest of their careers there. Taussky-Todd was the first woman to receive a formal teaching position at Caltech and later became the first woman to receive a full professorship there. In a Caltech press release, mathematics professor Gary Lorden said, "It was a terrific day for the mathematics department when we succeeded in attracting Jack and Olga to come to Caltech. Not only did we gain eminent scholars, but wonderful colleagues and teachers. They made a remarkably generous commitment to the future of Caltech and the mathematics department."

--- Mike Breen

"A Perfect Match at Mudd," by Paul Fain. The Chronicle of Higher Education, 22 June 2007, page A9.

 (Photo © Kevin Mapp/Harvey Mudd College.) This short article is about Maria M. Klawe, president of Harvey Mudd College, a college that is known not only for its excellence but also---according to the article---for being "a home for eccentrics and pranksters." Klawe, who has a Ph.D. in mathematics from the University of Alberta, says the college's personality matches hers. She juggles, paints, runs marathons, plays video games, and skateboards (as pictured, at left). Last December upon arrival at work she found a 12-foot long "Zen pond" with fountain and plastic fish in her office. Was her response to put the pranksters on double-secret probation? No, she says, "It was fabulous. I loved it. That is so Mudd-like." --- Mike Breen

"'If I have trouble writing, it's a sign that I don't understand,'" by Richard Lea. Guardian Unlimited, 18 June 2007.

Ian Stewart has written 20 popular science and mathematics books, 2 science fiction novels, several short stories, and a radio program. Here he talks about his approach to writing, which has evolved from focusing on a topic to focusing on the story, and the need for all scientists and mathematicians to be good communicators. In the article, Stewart says that writing popular science "has all sorts of benefits---it makes you think about what you're doing, it makes you focus on communication." His most recent book, Why Beauty is Truth, is about groups and symmetry.

--- Mike Breen

"The Story of the Archimedes Manuscript", by Matthias Schulz. Spiegel Online, 22 June 2007.

This article tells the by-now fairly well known story of the Archimedes palimpsest, which was purchased by an American billionaire in 1998 and is now being analyzed by a group at the Walker Museum in Baltimore. The occasion for the article is the upcoming publication of a German edition of the text from the palimpsest in September 2007.

--- Allyn Jackson

"Das Zittern des Fälschers (The trembling of the forger)," by Uta Deffke. Frankfurter Allgemeine Zeitung, 17 June 2007.

This article discusses the use of mathematics in identifying art forgeries. Mathematical techniques can uncover small irregularities in brush strokes that the human eye can miss. Wavelet theorist Ingrid Daubechies is mentioned in the article.

--- Allyn Jackson

"Keine angst vor Festenbindungen (No worries about tight laces)," Jochen Reinecke. Frankfurter Allgemeine Zeitung, 17 June 2007.

This article discusses the mathematical analysis of various ways of tying shoelaces. Among the references mentioned is The Shoelace Book by Burkhard Polster, published by the AMS. A review of this book appeared in the AMS Notices.

--- Allyn Jackson

"Gefahr für asymmetrische Kryptosysteme (Danger for asymmetric cryptosystems)", by George Szpiro. Neue Zürcher Zeitung, 13 June 2007.

This article discusses the factorization of a very large number (over 300 binary digits). Since the number lies close to a power of two, an efficient algorithm could be used.

--- Allyn Jackson

"Musical Illusions," by Julie J. Rehmeyer. Science News Math Trek, 9 June 2007.

Optical illusions are common but in this online article, the reader is presented with an auditory illusion: an audio clip that seems to play an ever-ascending sequence of notes. The author draws an analogy to Escher's famous work Ascending and Descending, which creates the illusion of stairs circling and ascending simultaneously. Psychology, mathematics, and art are linked via such illusions. Psychologist Diane Deutsch studies our understanding of pitch by creating and analyzing these illusions. From a mathematical perspective, pitch classes (the twelve notes of the Western scale) are equivalence classes. Two notes are in the same pitch class if the ratio of their dominant frequencies is an integer power of two. The power determines the number of octaves between notes. Ten frequencies, all in the same pitch class, come together to form a Shepard tone. But the middle frequencies are loudest, making the octave in which the tone lies ambiguous. As the tones are played in succession over and over again, we may hear them going up endlessly. Even skilled musicians can be duped by illusions whose designs use Shepard tones, which are named after psychologist Roger Shepard. The article ends with a discussion of Deutsch's hypothesis that that we all can distinguish between pitch classes to some degree. This hypothesis is supported by her experiments using Shepard's tones.

--- Brie Finegold

"Unbelievable truths": Review of Nonplussed: Mathematical proof of implausible ideas, by Julian Havil. Reviewed by Justin Mullins. New Scientist, 9 June 2007, page 53.

Mullins writes that "the mathematical world is filled with implausible ideas that turn out to be not just plausible, but provably, beautifully, eternally true." The book under review explores and discusses just such ideas. Many of them have a probabilistic twist: One example is the so-called "birthday paradox", which asks how many people one would need to group together to ensure a 50-50 probability that two of them will have the same birthday. The number is suprisingly small. Mullins says the book requires some mathematical background but that the author, who is a mathematics teacher at a boy's school in the UK, "offers a helping hand up many of the steepest climbs."

--- Allyn Jackson

"Sudoku helps hone logic", by Peter Calamai. Toronto Star, 7 June 2007.
"Die hohe Schule des Sudoku (The higher study of Sudoku)", by Holger Dambeck. Spiegel Online, 13 June 2007.
"Sudoku flexes math muscles", by Brandy Benedict. Milwaukee Journal-Sentinel, 25 June 2007.
"Sudoku für Fortgeschrittene (Sudoku for the Advanced)", by Wolfgang Blum. Süddeutsche Zeitung, 30 June/1 July 2007, page 22.

These stories, as well as many science-related web pages and blogs, discuss the article "Sudoku Squares and Chromatic Polynomials", by Agnes Herzberg and M. Ram Murty, which appeared in the June/July 2007 issue of the Notices of the AMS. Herzberg and Murty pose some mathematical questions about Sudoku and then use graph theory, in particular chromatic polynomials, to try to answer the questions. One of the questions some of the news articles discuss is whether a Sudoku can have more than one solution. The Notices article discusses the conditions under which this can happen. Some of the media coverage convey a tone of surprise at the notion that fun stuff like Sudoku could be connected to something serious like mathematics. Of course the authors of the Notices article aren't surprised at all. Murty, described in the Milwaukee Journal-Sentinel as a "number theorist by day", is quoted in the paper as saying, "I did this just for kicks."

--- Allyn Jackson

"Erinnerung an einen fast vergessenen Mathematiker (Reminiscence of an almost forgottten mathematician)": Review of Ernst Zermelo: An Approach to his Life and Work, by Heinz-Dieter Ebbinghaus. Reviewed by George Szpiro. Neue Zürcher Zeitung, 6 June 2007.

The book under review is a biography of the German logician Ernst Zermelo (1871-1953), whose formulation of the Axiom of Choice had a profound effect in mathematics.

--- Allyn Jackson

"Beweise sind in der Mathematik nicht das Wichtigste'" ("Proofs are not the most important thing in mathematics'"): Interview with Stephen Smale. Interviewed by George Szpiro. Neue Zürcher Zeitung, 6 June 2007.

Mathematics journalist George Szpiro interviewed Stephen Smale, on the occasion of Smale's receiving the 2007 Wolf Prize. Smale, who received a Fields Medal in 1966, talks about his wide-ranging work in mathematics and other areas. An English version of this interview appears in the September 2007 issue of Notices of the AMS.

--- Allyn Jackson

"Hip-Hop Math". WTVG-TV (Toledo), 5 June 2007.

Toledo, Ohio, math teacher Christine Smith has teamed with platinum record producer Alex Al E. Cat Nesmith to record Smith's students rapping out the multiplication tables. The team recorded one song last year and it was so successful (students' test scores rose 48 percent) that they recorded a complete CD to help students nationwide learn the multiplication tables. In 2008, the students plan a summer tour and a DVD. Although Nesmith's career is now in music, he is very familiar with the education system: his mother was a principal in Washington, DC.

--- Mike Breen

"New Spelling Bee Champ Prefers Math, Music,." KTVU News, 1 June 2007.
"Home-Schooled Student Wins Spelling Bee", by Robert Siegel. All Things Considered, National Public Radio, 1 June 2007.
"Spelling champ turns focus to math at UNL camp," by Zach Pluhacek. Lincoln Journal Star, 11 June 2007.

Prior to his big win in this year's Scripps National Spelling Bee, Evan O'Dorney was mentioned in the 31 March 2007 Science News Math Trek article entitled "Math Circles Inspire Students." Although the Berkley Math Circle may not have inspired him to spell well, the thirteen-year-old homeschooler notes that doing math and composing music are his favorite activities. He relates even juggling to mathematics through patterns. Although spelling has earned him US\$40,000 in cash and scholarships, Evan O'Dorney is also participating in math competitions. The video clip of this happy bespectacled young teen shows him at the board doing math and later recounting how "we went through the dictionary twice" in preparation for the Bee. Evan plans on taking a calculus course this fall at UC Berkley. The Lincoln Journal Star article is about Evan arriving at the 2007 Mathematical Olympiad Summer Program at the University of Nebraska-Lincoln, which took place 10-30 June. He was the youngest participant in the program.

--- Brie Finegold

"Math instruction a complex equation with many wrong answers," by Julie Mack. Kalamazoo Gazette, 3 June 2007.

Most math teachers would probably agree with the dean of University of Michigan’s School of Education, Deborah Loewenberg Ball: being a math teacher is harder than some might think. Ball made the point at a recent conference for education writers by asking them to multiply 49 by 25—no problem for them. Then she asked them to describe the logic behind three wrong answers to the problem: at best, a few writers could identify the thinking behind 1 or 2 of the answers. Ball stressed that "such diagnostics are an essential part of a teacher’s job." Yet it is skills such as these, as well as knowledge of the subject, that some teachers of math lack. As Kalamazoo Public School superintendent Michael Rice notes, many math teachers in the upper elementary and middle school level are not math majors. And even though middle school teachers are now required by the No Child Left Behind law to be "highly qualified" to teach their subject, what teachers have in content knowledge they might lack in the ability to deliver that content. What are some solutions? Teachers could be provided with math "coaches" who can help them with the content and/or learn how to present it. On a longer-term basis, Mack suggests that we find ways to encourage more students to study math education and then send these teachers to the schools that need them the most.

--- Claudia Clark

"Take a Number: Kids show math insights without instruction," by Bruce Bower. Science News, 2 June 2007, pages 341-342.

"Silicon Smackdown," by Karen A. Frenkel. Scientific American, June 2007, pages 32-34.

 IBM's Deep Blue beat Garry Kasparov in chess, but computers haven't yet been able to beat strong players at the game of Go. One reason is the vast number of possible options to search through in Go. Frenkel writes that our edge may soon disappear. She describes an algorithm, based on Monte Carlo methods, that has been incorporated into a program called MoGo by mathematicians Sylvain Gelly (Université de Paris-Sud) and Yizao Wang (École Polytechnique). Their program has almost doubled the win rate of the previous best Go program and has beaten strong players on 9 x 9 boards, although it is still inferior to good players on the larger 19 x 19 boards. --- Mike Breen

"Breaking Network Logjams", by Michelle Effros, Ralf Koetter, and Muriel Medard. Scientific American, June 2007, pages 78-83.

Network coding, a new idea in the transmission of data through computer networks, offers promise for speeding up our internet connections by easing the bottleneck problems of our current router-based systems. If multiple people simultaneously attempt to send data that must pass through the same router to reach the end users, the speed of transmission will be constrained by the fact that a router can send only one signal at any given time. Network coding instead works by sending information about the data---not the data itself---through multiple channels in a way that allows for reconstruction of the original data. In a simplified model, network coding works by combining the two simultaneously sent data streams into a single message, sending this message to both end users through the router and at the same time separately sending each end user the initial data intended for the other through different channels. An end user can then effectively "subtract" from the router's message the data intended for the other user to obtain the message intended for her. Thus, network coding allows multiple messages to be simultaneously transmitted, easing the restrictions of a router.

--- Lisa DeKeukelaere

"Into the Fold," by Beth Jensen. Smithsonian, June 2007.

 "Fiddler Crab, opus 446," origami by Robert J. Lang. © Robert J. Lang Origami. "The art of paper folding is evolving artistically and technologically, thanks to a small but growing number of mathematicians and scientists around the world, including Lang," the article says. It presents a profile of Robert Lang and shows examples of his stunning and intricate origami models. His works, which now number nearly 500 and some of which use hundreds of folds, have been shown in galleries and at exhibitions worldwide. The author explains a technique that Lang and Japanese origami master Toshiyuki Meguro developed simultaneously in the 1990s, called "circle-river packing." It revolutionized folding. Lang developed computer programs---"TreeMaker" and "ReferenceFinder"---that enable users to draw online stick figures and determine the sequence of folds. Amazingly, Lang rarely uses his own programs except to "brainstorm" a design. The article includes a diagram of his crease pattern for a "Fiddler Crab" that looks bewildering, but Lang claims it looks mysterious only "if you don't know the background." Although he uses advanced mathematics, artistry obviously plays an equal role in creating his figures. Samples of Lang's origami and crease patterns are on his website. In the midst of the article Jensen also reminds the reader that the science and art of complex folding has many current and potential applications---collapsible air bags, solar panels, blood vessel stents, robotic arm manipulation, and large telescopes that need to be transported into space. --- Annette Emerson