# 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)

### April 2007

"Jaron's World," by Jaron Lanier. Discover, April 2007, page 28.
"Körper in vier dimensionen (Bodies in four dimensions)", by George Szpiro. Neue Zürcher Zeitung, 29 April 2007.

 "Symmetrical arrangement of five hemi-icosahedra,forming a partial hendecachoron." Computer model courtesy of Carlo Sequin, UC Berkeley, styled by Jaron Lanier. Lanier begins by describing his childhood fascination with geometric shapes, especially those "in which every angle, every facet, and every edge is identical. There are only five such shapes in the three-dimensional world"---the cube, the tetrahedron (the regular three-sided pyramid), the octahedron (8 triangular sides), icosahedron (20 triangles) and dodecahedron (12 pentagons)." Inspired by a recent biography of geometer Donald Coxeter (King of Infinite Space: Donald Coxeter, The Man Who Saved Geometry, by Siobhan Roberts), Lanier began to explore the concept of an 11-sided, perfectly regular polytope that would exist in a higher dimension. He goes on to explain 4-dimensional shapes and symmetry and the idea of an 11-sided Platonic shape with a prime number of sides. (This shape is named "hendecatope" in the Discover article, but after further consideration the authors have since chosen to use the term "hendecachoron," a literal translation of "11-cell" into Greek.) The accompanying illustration---the first published picture of the 11-cell---also accompanies the article. It is a projection of the regular four-dimensional hendecachoron, and "colored beams represent the edges of triangles; some triangles are left out for simplicity." --- Annette Emerson

"What You Know About Math," by Pam Lundborg. The Post-Standard (Syracuse), 30 April 2007.

Move over, T.I. There are two new rappers in town---or at least in Manlius, New York. Ethan Gilbert and Aaron Flack, seniors on the Fayetteville-Manlius High School Math League team, have changed the lyrics to the rap song What You Know (About That) to lampoon themselves as math geeks. Their song, What You Know About Math, has become a hit on the Internet website YouTube.com, according to Pam Lundborg, staff writer for The Post-Standard. The video was a broadcast class journalism project of fellow senior Kathleen Fletcher. Fletcher appears in the film, along with calculus teacher Charles Stedman and sophomore Christopher Quinn, notable at the school for having memorized 231 digits of pi. To see the video, go to http://www.youtube.com/watch?v=Ooa8nHKPZ5k.

--- Claudia Clark

"Professor sees magic, mystery in mathematics," by Rick DelVecchio. San Francisco Chronicle, 27 April 2007.

The San Francisco Chronicle gives significant play to mathematician Marcus du Sautoy's "performance" later the same day at UC Berkeley. Du Sautoy is clearly enthusiastic about the the pursuit of mathematics: "Mathematicians have much in common with artists. We're all looking for patterns that say something universal. Math, no less than art, is about beauty and symmetry." His talk---also the topic of his 2003 book The Music of the Primes---is about prime numbers and the quest to uncover the mystery behind them (prime numbers are those that can be divided only by themselves and 1). The article gives some background on the research on patterns in the distribution of primes, touching on work of historical figures such as Bernhard Riemann and David Hilbert---as well as such contemporary mathematicians as Peter Sarnak and Zeev Rudnick---and quoting David Eisenbud (Director, Mathematical Sciences Research Institute) and Brian Conrey (Director, American Institute of Mathematics) on the topic. The article concludes, "Du Sautoy says more people around the world are catching the thrill of math. He points to movies and TV shows and puzzles like Sudoku." The reporter tells us that du Sautoy will soon travel to Syria, China, and India to film a BBC series on the history of math---this is fitting, as du Sautoy is certainly one of the great "ambassadors" of mathematics.

--- Annette Emerson

"Fast Routing in Road Networks with Transit Nodes," by Holger Bast, Stefan Funke, Peter Sanders, Dominik Schultes. Science, 27 April 2007.
"Lost in transportation," by Davide Castelvecchi. Science News, 5 May 2007.

 A team of researchers has devised an algorithm to determine optimal driving routes between destinations. According to Science News, the researchers claim the new algorithm improves on existing commercial systems and "can efficiently deliver the best directions with mathematical certainty---save for traffic jams". The new algorithm exploits a common-sense observation: "Each route into or out of a city typically passes through one of a handful of major intersections." The article in Science explains in a bit more depth the researchers' approach, called "transit node routing," and provides links to supporting online material. --- Annette Emerson

"Of beer and bubbles: the formula for a perfect pint," by Julie Steenhuysen, Reuters, 27 April 2007;
"Go figure: Use math to get the perfect head of beer," by William Atkins. iTWire, 28 April 2007;
"Finding and formulating the fizz factor," by Tom Avril. The Philadelphia Inquirer, 30 April 2007.

 David Srolovitz (Yeshiva University, NY) and Robert MacPherson (Institute for Advanced Study, Princeton, NJ) have developed a mathematical formula that predicts how the head on a beer and its bubbles change over time (and we do learn from Srolovitz that "smaller bubbles generally mean creamier foam"). As journalist Avril states, "such networks of bubbles, grains or cells tend to become `coarser' over time: some cells become larger, while others shrink and eventually disappear." In their article "Added dimensions to grain growth," published in Nature, 26 April 2007, the researchers write: "the formula should lead to predictive models for various industrial and commercial processes, from the treatment of metals to controlling the head of a glass of beer". (See the Math Digest summary of the Nature article.) --- Annette Emerson

"A sense of proportion," by Martin Kemp. Nature, 26 April 2007.

In the same way that modern mathematicians flaunt the artistic nature of their work via color pictures of fractals, animated videos of knots, and graphical representations of high-dimensional shapes, artists of the Renaissance sought to flaunt the mathematical nature of their work via geometry and proportion. Martin Kemp, an Oxford professor who studies visual connections between art and science, discusses a painting, on display in Rome this month, of Federico Zuccari, the founding father of the Roman Academy of Arts. One hundred years after Zuccari's death in 1695, Giovanni Maria Morandi painted him holding a piece of chalk inside a stylish metal holder that any math teacher would envy. With that chalk, it appears that he has just drawn a series of simple geometric figures, leading up to a proportional human. The series brings to mind depictions of evolution, except that apes and other predecessors have been replaced with points, lines, triangles, squares, and semicircles. Since the 1400s, artists have studied basic Euclidean geometry in order to enhance their understanding of proportion and perspective. But in the wake of the Scientific Revolution, Kemp claims, the display of geometric figures also elevated the painter's status by publicly exhibiting the painter's expertise and emphasizing its scientific nature.

--- Brie Finegold

"Added Dimensions to Grain Growth," by David Kinderlehrer. Nature, 26 April 2007.

Understanding crystalline growth is not only an exciting challenge for mathematicians, but also an important problem for materials engineers, who must determine whether objects are strong enough to support the intended load. Mathematician Robert MacPherson and materials scientist David Srolovitz recently collaborated to find an equation that would explain in three dimensions how the grains of a material grow. In the 1950s John von Neumann and William Mullins successfully tackled the two-dimensional problem. MacPherson and Srolovitz's solution breaks the problem into one-dimensional properties of the grain: linear size and the sum of the edge lengths. Their equation is an important step in understanding how the microstructure of an object changes over time due to topological and thermodynamic constraints---a question that applies to most engineered materials on earth.

--- Lisa DeKeukelaere

"Senate OKs bill to boost science and math skills," by Joel Havemann. Los Angeles Times, 26 April 2007.
"Senate OKs Funding for Math, Science." KOCO-TV (Oklahoma City), 26 April 2007.

The House and Senate recently passed bills to increase funding for math and science, both in research and in education. The Senate voted 88-8 in favor of the America Competes Act, which would increase math and science funding by US$60 billion over four years and would double National Science Foundation funding over the next five years. The House voted 389-22 for a bill that includes an authorization of more than US$600 million to provide annual scholarships of US$10,000 to students who commit to teach math and science to elementary or secondary school students. Once the bills pass both houses, they are expected to be signed by the President. --- Mike Breen Return to Top "Mathematicians set Chinese test." BBC News, 26 April 2007. The Royal Society of Chemistry (UK) offered a prize of 500 pounds for the solution to a geometry problem taken from a national test in China given to "pre-entry" students. The Society also published a much easier problem involving the Pythagorean Theorem---which it claims is part of a placement test at a respected English university---as evidence of the difference in the two countries' educational systems. The Society's chief executive Richard Pike said, "UK chemistry departments are often world-renowned for their creativity; however, mathematics tests set in England by many universities for undergraduate chemistry students in their first term to diagnose remedial requirements are disconcertingly simple." An English math professor dismissed the Society's criticism as "nonsense." --- Mike Breen Return to Top "Founder of East Setauket management company uses math-based formulas to select investments," by Keiko Morris. Newsday, 25 April 2007. By making US$1.7 billion last year, mathematician James H. Simons, founder of Renaissance Technologies, was the highest-paid hedge fund manager for the second year in a row. The article notes that the company's success "is based on use of math skills and computerized statistical models to select investments." Simons, the son of a shoe factory owner, earned his bachelor's degree at the Massachusetts Institute of Technology and his Ph.D. at the University of California, Berkeley. In 1976 he won the AMS Oswald Veblen Prize in Geometry. Recently he's created the Math for America program to help future New York City teachers learn more math and gave US$25 million to the math and physics programs at Stony Brook University. --- Mike Breen Return to Top "Britannica Blog," by Ian Stewart. Britannica.com, 24 April and 2 May 2007. Ian Stewart, veteran science writer and professor of mathematics at the University of Warwick, blogs about the motivation for writing his two most recent books: Why Beauty is Truth and Letters To a Young Mathematician. He wryly recalls the comment by his wife that the latter might better be titled Letters From an Old Mathematician, adding that the novel idea was not his but his publisher's. The first scientific installment in the "Art of Mentoring" series, Stewart's book is a string of letters written to a fictional young woman named Meg, encouraging and advising her in her mathematical endeavors from high school through college. Stewart hopes the book will debunk the stereotypical view of university-level mathematics and inspire future mathematicians. Despite the book's unusual format and content, the author remarks that it was easy to write, partly because it was strongly based on his own experiences. The idea for his most recent work, whose title hails from Keats's poem "Ode to a Grecian Urn," was hatched nearly thirty years ago when he first lectured about Galois theory. An ill-fated algebraist, Galois developed an interest in finding a general solution for fifth-degree polynomial equations (similar to the commonly known solution for a quadratic equation). But in proving the impossibility of such a general solution, Galois invented a much richer tool for exploring symmetry, a tool studied in many undergraduate math courses today. Stewart explains how he charts the history of symmetry in mathematics, focusing on personalities like Galois as well as their work. As to the title, Stewart notes that the practical science of today rests on research whose pursuit was driven "by the internal structure of mathematics itself, divorced from any considerations of the real world." Thus his book discusses the relationship between a beautiful theory and a true one. --- Brie Finegold Return to Top "Book Loft": Interview with author Walter Isaacson. GreaterBoston with Emily Rooney, WGBH (Boston PBS-TV), 23 April 2007. Rooney celebrates science every night throughout the week of April 23. Her guest on the last day of the week was Walter Isaacson, author of Einstein: His Life and Universe. Isaacson debunks the myth that Einstein flunked math (he jokes that a Google search for "Einstein flunked math" returns thousands of results). Einstein in fact did well in math and had an extraordinary capacity to visualize mathematical concepts. Isaacson reports that Einstein was slow to talk as a young child and suggests this may have enhanced his ability to visualize (he came up with his own proof of the Pythagorean theorem and visualized Maxwell's equations, for instance). Rooney asks if Einstein was really so much more brilliant than others, and Isaacson asserts that Einstein did not have more mental capacity than people like Lorenz, Planck, and Poincaré, but his rebellious nature and imagination allowed him to come up with groundbreaking ideas. The interview is posted as a podcast in the "Book Loft" section of the GreaterBoston program website. --- Annette Emerson Return to Top "Math fest hosted at Google charms kids who count," by Barbara Feder Ostrov. San Jose Mercury News, 23 April 2007.  Students at the Julia Robinson Mathematics Festival. (Photo courtesy of David Eisenbud, Mathematical Sciences Research Institute.) Hundreds of students ages 11 to 18 worked math challenges during the first Julia Robinson Mathematics Festival at Google's headquarters in Mountain View, California. The challenges involved fields of mathematics that students don't normally see in school, such as game theory and topology. Jaya Narasimhan, an eighth grader from San Jose, said of the festival, "It's pretty fun. I like math because you can prove everything you do." The online article included two of the questions given to the students at the festival. --- Mike Breen Return to Top "Warwick couple cleans the deck in poker," by Paul Kenyon. Providence Journal, 19 April 2007.  Charlotte Chabot after winning the tournament. (Photo courtesy of Minimax Consulting.) Charlotte Chabot and her husband Pierre (who live in Warwick, RI) are trained in mathematics and statistics and they've put that training to good use---at the poker table. At a recent tournament, Charlotte took first place in the women's Texas Hold 'Em tournament, while Pierre netted over US$15,000 in the casino's main event. Kenyon writes about Charlotte's poker strategy and notes that she and her husband approach poker as a mathematical challenge. Says Charlotte, "You have to apply mathematics and make the optimal moves." --- Mike Breen

"Impossible things for breakfast," by Robert Matthews. New Scientist, 14 April 2007, pages 30-33.

This article discusses work by two physicists, Andreas Doering and Chris Isham of Imperial College London, that appears to provide a way around the logical condundrums that arise in quantum theory. According to the Copenhagen interpretation of quantum mechanics, an electron exists in a range of different states until the moment the electron is observed, at which time all the possible states collapse down into one. What this implies, Matthews writes, is that "it is impossible to know the truth of any statement about, say, an electron until it has been observed." Efforts to get around this problem run up against a 1967 theorem by mathematicians Simon Kochen and Ernst Specker, which says that every statement in quantum theory depends on many assumptions, or runs counter to the rules of standard logic. What Doering and Isham did was to jettison standard logic and look instead for a new mathematical logic that would better fit quantum theory. They were led to a mathematical construct called a topos, which was first set forth by the mathematician Alexandre Grothendieck and which offers a way of constructing new forms of logic. "The logic associated with quantum topoi encompasses true, false and many shades of gray in between," Matthews writes. These ideas are pretty radical, and whether this new use of topos theory will become part of standard physics remains to be seen.

--- Allyn Jackson

"9 states to give common math test," by Nancy Zuckerbrod. Miami Herald, 10 April 2007.
"States to Give Common Math Test, Based on Shared Standards," by Leslie Olsen. WISH-TV, 10 April 2007.

In a move described by some as a step towards national educational standards in mathematics, nine states (Arkansas, Indiana, Kentucky, Maryland, Massachusetts, New Jersey, Ohio, Pennsylvania, and Rhode Island) have agreed to share a test and standards for Algebra II. Achieve, Inc., a non-profit in Washington, DC, is helping design the standards. Arkansas Commissioner of Education Ken James says that students are "going to need portable skills, and we should be able to agree on what those portable skills are going to be."

--- Mike Breen

"Ein Nestor der Mathematik: Zum 90. Geburtstag des Zürcher Mathematikers Beno Eckmann (Doyen of Mathematics: The 90th Birthday of Zurich Mathematician Beno Eckmann)," by George Szpiro. Neue Zürcher Zeitung, 10 April 2007.

This article discusses a two-day event celebrating the 90th birthday of the Swiss mathematician Beno Eckmann. A professor at the Swiss Federal Institute of Technology (ETH) in Zurich, Eckmann is a well known for his work in topology, geometry, algebra, and group theory, as well as for being the founder of the Forschungsinstitut in Mathematik (Institute for Mathematical Research) at the ETH.

--- Allyn Jackson

"The Countless Achievements of a Math Master," by David Brown. The Washington Post, 9 April 2007.
"A Math Great Gets His Due," an interview with Keith Devlin. Weekend Edition Saturday, National Public Radio, 14 April 2007.
"Eulers Leben und Werk (Euler's Life and Work)": Review of four books about Leonhard Euler. Reviewed by George Szpiro. Neue Zürcher Zeitung, 2 May 2007.

 Leonhard Euler Brown's article offers a layman's tribute to Leonhard Euler on the 300th anniversary of the great mathematician's birth. He published more than 800 papers before his death at the age of 76, formulated three of the top five "most beautiful mathematical equations" according to readers of Mathematical Intelligencer magazine, and will soon appear on a Swiss postage stamp. And yet he remains relatively obscure outside of mathematical circles. Brown discusses Euler's major contributions to the fields of calculus and mathematical analysis and through biographical details demonstrates that Euler lived a relatively normal life. NPR's Scott Simon asks Keith Devlin to celebrate Leonhard Euler's 300th birthday (15 April). Devlin explains why Euler is one of the top mathematicians of all time, having invented many of the standard notations including pi. Simon asks if Euler can be put in the same category as Da Vinci, and Devlin says that the mathematician's work certainly exhibited "elegance, beauty, insight and depth." Furthermore, Euler oversaw finance, mapmaking, calendars, botanical gardens, and more. The audio of the interview is posted on NPR's website. --- Lisa DeKeukelaere and Annette Emerson

"Have prodigy, will travel", by Paul Collins. New Scientist, 7 April 2007, pages 50-51.

This article tells the intriguing and poignant story of Zerah Colburn, who was born in Vermont in 1804. He was a prodigy who could perform huge and complicated mathematics computations in his head. As an 8-year-old, Zerah was able to see that 10-digit number was divisible by 641. "Unknown to him, this was a shocking feat," the article says. "He had successfully disproved a Fermat number---a class of numbers that the legendary 17th-century mathematician Pierre de Fermat had conjectured were all prime. This same exception had only previously been found by the equally legendary Leonhard Euler." Instead of helping his son get an education, Zerah's father dragged him around Europe collecting money while Zerah performed calculating feats. After 13 years in Europe, Zerah returned to America and "drifted into obscurity", but he did write a memoir in which he tried to explain some of his calculation methods. He died of tuberculosis in 1839. A Vermont history web site has more information about Zerah Colburn.

--- Allyn Jackson

"The Memory Hacker," by Stephen Handelman. Popular Science, April 2007, page 66.

 Ted Berger and his research team at the University of Southern California are developing artificial memory strands that may benefit people who suffer from Alzheimer's, damage to the hippocampus, and other causes of memory problems. The memory chips would replace injured cells---a tampering that some ethicists think could alter healthy memories and perhaps alter an individual's sense of self as well. Meanwhile, Berger continues and is making headway. He "set out to reduce higher cognitive functions to a simple set of mathematical equations based on how neurons responded to stimuli---equations that could then be coded into some form of prosthetic device.... The challenge of mathematically mimicking brain function---and the internal language it uses to communicate concepts like emotion and memory---is complicated by the fact that brain cells converse in a sort of secret electrical code." The researchers---"an all-star roster" of neuroscientists, mathematicians, computer engineers, and bioengineers---are finding ways to measure those patterns and program the results for a computer that can communcate with live brain tissue. --- Annette Emerson

"Eraser" and "Swing" ExxonMobil ads. The Science of a Drive, April 2007.

"Math and science are everywhere": This is the topic of three ExxonMobil commercials that premiered during the 2007 Masters golf tournament in April. One of the commercials features golfer Phil Mickelson playing golf while a voice-over describes work he and ExxonMobil are doing to support math and science education. In the other two commercials, one a shorter version of the other, a series of images (one of which is below) is tied to a voice-over describing the importance of math and science in meeting current technological challenges. In each case, content-related graphs and equations, including Navier-Stokes, Fourier Series, and Maxwell's equations, appear everywhere, superimposed on objects and actions, making the point that, indeed, math and science are everywhere.

On the ExxonMobil website, meanwhile, the math and physics underlying the drive is presented at an elementary level on a series of web pages entitled "The Science of a Drive." Different parts of the drive---the club swing, the impact of the club head on the ball, and the flight of the ball---are explored. The viewer can vary the perspective and the speed of the action in each module, as well as play a game finding the range of a drive by varying the club head speed and initial launch angle of the ball.

To view the ads, go to the ExxonMobil web site and select the commercials entitled "Eraser" and "Swing." (Images courtesy of ExxonMobil.)

--- Claudia Clark