# 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)

### February 2007

"Medieval Muslims made stunning math breakthrough", Reuters, 22 February 2007.
"Islamic tiles reveal sophisticated maths", Nature.com, 22 February 2007.
"Islamic Artisans Constructed Exotic Nonrepeating Pattern 500 Years Before Mathematicians", Scientific American online, 22 February 2007.
"Science imitates art?", by by Karen Weintraub and James Abundis. Boston Globe, 23 February 2007.
"Islamic 'quasicrystals' predate Penrose tiles", PhysicsWeb.org, 22 February 2007.
"Medieval Mosques Illuminated by Math", National Public Radio: All Things Considered, 22 February 2007.
"Advanced geometry of Islamic art", News.bbc.co.uk (London), 23 February 2007.
"Amazing maths of the mosaic makers", The Times (London), 23 February 2007.
"Islamic tilers may have led scientific field", The Daily Telegraph (London), 23 February 2007.
"New light on ancient patterns", Chicago Tribune, 23 February 2007.
"The art of repetition", National Post (Canada), 23 February 2007.
"Muslim Tile Patterns Show Math Prowess", The Washington Post, 23 February 2007.
"Medieval Muslims made stunning maths breakthrough", The Times of India, 24 February 2007.
"Ancient Islamic Penrose Tiles", Sciencenews.org, 24 February 2007.
"Medieval Islamic artists made amazing maths breakthrough", Gulf News (United Arab Emirates), 24 February 2007.
"Patterns of Islamic genius crystal clear centuries ago", Sydney Morning Herald (Australia), 26 February 2007.
"In Medieval Architecture, Signs of Advanced Math", by John Noble Wilford. New York Times, 27 February 2007.
"Islamic tilers got it long before Penrose." In Brief, New Scientist, 3 March 2007, page 18.
"Mathematik und Kunst beim Plattenlegen (The mathematics and art of tile-laying)", by George Szpiro. Neue Zürcher Zeitung, 18 March 2007.

In the 1970s, when Roger Penrose described what are now called Penrose tilings, they were thought to be entirely new. Peter Lu, a physics graduate student at Harvard University, was intrigued when he recognized what seemed to be Penrose tilings in decorations in an Islamic site in Uzbekistan. He then collaborated with Paul Steinhardt of Princeton University, a cosmologist and expert on quasicrystals, to produce a paper that appeared in the 23 February 2007 issue of Science magazine. The paper analyzes tilings from Afghanistan, Iran, Iraq, and Turkey to showing that hundreds of years ago the Islamic tilers knew about Penrose tilings. The research generated a worldwide flood of media coverage, as the selected citations above indicate. See the March 2007 issue of Tony's Take, on the AMS Math in the Media web site, for further details. Links to additional media articles are available on Peter Lu's page.

--- Allyn Jackson

"New Baseball Statistic, With a Nod to an Old Standard," by Alan Schwarz. New York Times, 25 February 2007, page Sports 6.

 Cleveland Indians Baseball, Dan Mendlik 2006. Baseball fans use many statistics to measure players' performance. Some of the traditional measures for batting, such as batting average, aren't as descriptive as fans would like and so have been replaced by new measures such as on-base slugging percentage (OPS), which is the sum of a batter's on-base percentage (OBP) and his slugging percentage (SLG---the number of total bases reached by hits, divided by the number of at-bats). The problem with just adding those two numbers is that on-base percentage is much more important than slugging percentage when it comes to run production. Also, it is hard for nmost fans to gauge a player's OPS. For example, is an OPS of .850 good? Enter gross production average (GPA), devised by Victor Wang when he was 16. It is (1.8 OBP + SLG)/4. This statistic gives extra weight to OBP and yields an understandable range: Most hitters' GPA falls between .200 and .360, similar to batting average. Last year's Major League Baseball GPA leaders were Albert Pujols of the St. Louis Cardinals and Travis Hafner of the Cleveland Indians, who each had a GPA of .362. Schwarz points out that the traditional performance measures ruled in a time before Excel. --- Mike Breen

"Navigation als Kunst und Wissenschaft (Navigation as art and science)", by George Szpiro. Neue Zürcher Zeitung, 25 February 2007.

This article is the February installment of Szpiro's monthly column about mathematics. It explores the question, How round is the earth?, and discusses the navigational error that can arise if one does not correctly take into account the curvature of the earth.

--- Allyn Jackson

"Rhymes with good reason," the Sunday Puzzle with Will Shortz. Weekend Edition Sunday, National Public Radio, 25 February 2007.

The challenge from February 18, 2007, was "to develop nine different mathematical expressions that equal eight. You must use the digits 2, 7 and one other. And that other digit must be a one in the first expression, two in the next expression and so on, up to nine. You can use a digit once and only once in each expression. You may use the four arithmetic symbols: plus, minus, times and divided by, as well as exponents and decimal points. You may use parentheses as you need them." Listen to the segment and see one answer.

--- Annette Emerson

"The angel that flew to the moon," by Ed Belbruno. New Scientist, 24 February 2007, page 51.

 Ed Belbruno received his doctorate at the legendary Courant Institute of Mathematical Sciences at New York University, under the direction of Jürgen Moser. His field is celestial mechanics, or, as he puts it, "the way things move in space", and he is especially interested in unstable, chaotic motion. He worked at NASA's Jet Propulsion Laboratory in Pasadena, California, designing spacecraft trajectories. He started to apply ideas of chaos theory to trajectory design and managed to save a Japanese spacecraft that was headed to the moon but had gotten stuck in a low orbit with little fuel. He tells his story in hid book Fly Me to the Moon: An Insider's Guide to the New Science of Space Travel, which appeared in March 2007. --- Allyn Jackson

"Coming Soon: 'The Number 24'," by Carl Bialik. The Wall Street Journal, 23 February 2007.

Columnist Carl Bialik's humorous attempt to write a few scenes for a possible sequel to the recent Jim Carrey thriller The Number 23 demonstrates that a lot of numbers, including the number 24, are everywhere---what you see just depends on what you're looking for. Screenwriter Fernley Phillips chose the number 23, coincidentally the number of times Caesar was stabbed and a sum associated with the date 9/11/2001 (9 + 11 + 2 + 0 + 0 + 1), as his movie subject at least in part due to his belief in its "powerful, possibly sinister properties," according to Bialik. A little research on Bialik's part, however, reveals a host of quirky facts about 23's successor, raising the question of what really sets 23 apart.

--- Lisa DeKeukelaere

"Better Geometry Through Chemistry," by Randall Kamien. Science, 23 February 2007.

A team of Israeli chemists can now program a thin sheet of gel to self-assemble according to your favorite Riemannian metric. Only surfaces that can be embedded in R3 are allowed, specifically those that minimize elastic energy of the surface by admitting the least stretching. In addition these transformations are reversible, much like a flower's daytime bloom closes at night. Temperature triggers the gel's metamorphosis, activating a change in volume of a molecule spread throughout the gel in a radially symmetric gradient. A disc of material bends and buckles according to the gradient, birthing shapes such as spheres and wavy hyperbolic surfaces. Shapes other than discs can also be used. For example, cylinders become trumpet-like. According to a physicist not involved in the study, these made-to-order surfaces might make it "possible to assemble structures known for their useful photonic properties."

--- Brie Finegold

"Other Lives": Review of Pythagoras: His Life, Teaching and Influence, by Christoph Riedweg, and Pythagoras and the Pythagoreans: A Brief History, by Charles Kahn. Reviewed by M.F. Burnyeat. London Review of Books, 22 February 2007.

 In the second sentence of this erudite and enlightening review, Burnyeat writes: "I can with confidence say to readers of this essay: most of what you believe, or think you know, about Pythagoras is fiction, much of it deliberately contrived." The review presents a good deal of evidence showing that Pythagoras, far from deserving his reputation as the world's first mathematician, was in fact the leader of a mystical cabal that believed in transmigration of the soul and set forth minute rules of conduct that, for example, required one always to put on the right shoe first but to wash the left foot first. "[Pythagoras] belongs to the history of politically intrusive religious movements, not to the history of philosophy or science," Burnyeat concludes. "Even less does he deserve his traditional place in the history of mathematics." --- Allyn Jackson

"Bringing Cartoons to Life," by John J. Tyson. Nature, 22 February 2007, page 823.

In this article, professor of mathematics John Tyson discusses the use of mathematical models to understand cells as dynamic systems. He proposes that, instead of using diagrams of molecular interactions along with descriptions of "how the link between molecules and behaviour ought to be made, a better way to build bridges from molecular biology to cell physiology is to recognize that a network of interacting genes and proteins is a dynamic system evolving in space and time according to fundamental laws of reaction, diffusion and transport. These laws govern how a regulatory network, confronted by any set of stimuli, determines the appropriate response of a cell. This information processing system can be described in precise mathematical terms, and the resulting equations can be analysed and simulated to provide reliable, testable accounts of the molecular control of cell behaviour."

Tyson illustrates his idea with the example of programmed cell death and the use of kinetic equations to model the network of biochemical reactions involved. Noting areas of molecular cell biology where this "dynamical perspective" has proven its merits---e.g., the molecular basis of circadian rhythms---he predicts that this perspective will "revolutionize how we think about the molecular basis of cell physiology."

--- Claudia Clark

"Picture imperfect," by Nicola Jones. news@nature.com, 19 February 2007.

 "Digital detective" Hany Farid (Dartmouth College) tells the interviewer that his "primary research area is developing computational and mathematical techniques to detect tampering in digital media." He gets so many requests that he now charges for his time; he also has a grant from the FBI. He describes how his software is used to analyze digital photographs to see whether a person in the photo was actually photographed in a different place, wheher an image has been re-sized or rotated, whether part of a photograph has been copied and pasted---and even whether scientific research has been faked. Although the interview focuses on his work involving digital tampering, his Image Science Group does research in a variety of areas including image analysis, computer vision, human vision, and medical imaging. --- Annette Emerson

"Hot Type," by Susan Brown and Richard Monastersky. The Chronicle of Higher Education, 9 February 2007, page A18.

The former editors of the journal Topology, who resigned en masse last year, have started a new journal, The Journal of Topology, which will be published by the London Mathematical Society. The resignations were over the pricing policies of Topology's publisher, Elsevier. The new journal will cost US$570 for four issues; Topology cost US$1665 for six issues. As to the future of Topology, the short article quotes Don Davis of Lehigh University: "I'm anticipating the Elsevier journal will cease to exist."

--- Mike Breen

"Math prodigy corrects Discovery Place," by Peter Smolowitz. Charlotte Observer, 8 February 2007.

Parker Garrison, an eight-year-old student at Charlotte Christian School, found a mistake in an exhibit at a local museum---a mistake that no one had mentioned even though the exhibit had already been to eight cities in four years. The exhibit, "Jelly Belly Presents Candy Unwrapped," asked visitors to calculate how many jelly beans would fill half a pyramid. The formula given in the exhibit used the dimensions of the half-pyramid to find its volume, but then divided by two (which then gave half the required volume). After Parker got home and did the calculations three times, each time getting the correct answer, his parents called the museum. A new display is on the way.

--- Mike Breen

"Closing the Math Gap," by Katie Couric. CBS Evening News, 7 February 2007.

As part of its series "The American Spirit," the CBS Evening News ran a four-minute story on Math for America (MfA)---a program designed to increase the number of qualified math teachers in New York City. News anchor Couric talked with MfA founder and funder Jim Simons and with Melanie Smith, a teacher at the Manhattan Village Academy, who came through the program. Math for America pays for college graduates to get a master's degree in teaching and, once they are hired as teachers, pays them a bonus of up to US$20,000 a year. Simons, a mathematician who founded the hedge fund management company, Renaissance Technologies, says that it is the "intellectual power of America that gives us the potential to stay in front," but if something is not done nationwide to employ more qualified math teachers, the US will lose its position in the global economy. --- Mike Breen Return to Top "A sporting chance of beating the bookies," by Michael Reilly. New Scientist, 6 February 2007, pages 36-39. Stephen Oh, a former graduate student in population genetics, has a sports forecasting service that uses Monte Carlo methods to predict NFL winners. He now writes code that "simulates football teams instead of human genomes." Each player on a team is represented by up to 70 parameters. In a game each player's possible action is assigned a probability. A game is simulated through the branches of a tree diagram. Each game is simulated 10,000 times, running through the diagram, yielding different scores. Oh's prediction is the most likely score among the simulations. He says his service beats the point spread 56 per cent of the time. Hal Stern, a professor of statistics at the University of California, Irvine, says, "It seems almost insane to try and simulate the whole game. Then again maybe that's his edge." He adds, "I remain largely skeptical. If you could predict games, why would you sell the advice?" Reilly, a football non-expert, used Oh's advice one weekend, betting over US$200, and losing less than US$10. --- Mike Breen Return to Top "Here's the proof: Math + music mix for band's front man," by Jamie Gumbrecht. Lexington Herald-Leader, 4 February 2007. "The Apples in Stereo," John Schaefer. Soundcheck, WNYC, 15 February 2007.  The Apples in Stereo: (left to right) John Dufilho, Eric Allen, Robert Schneider, Bill Doss and John Hill. Logarithms and pop music? These are two things you don't usually see in the same sentence, but musician Robert Schneider composed tunes for his pop band's new CD---New Magnetic Wonder by The Apples in Stereo---using a musical scale in which the space between notes follows a logarithmic progression, rather than being evenly spaced like the do-re-mi we all learned in grade school. Alternative scales like his have been used before in Eastern music, but Schneider's sound has aroused curiosity from Western world music critics and fans. For years Schneider appreciated math, but applied it only marginally---through voltage equations to keep his electronic sound system functioning and his appreciation of stereo balance. His recent musical work, however, incorporates ideas he learned through classes at the University of Kentucky that he enrolled in as an adult. The WNYC piece is an interview with Schneider and includes some of the group's music as well as Schneider performing live. --- Lisa DeKeukelaere Return to Top "Painting by numbers": Review of The Fabulous Fibonacci Numbers, by Alfred Posamentier and Ingmar Lehmann. Reviewed by Justin Mullins. New Scientist, 3 February 2007, page 48. Compared to the book's mathematics, which the reviewer calls "delightful", its "desperate attempts" to connect the Fibonacci numbers with a dizzying array of artworks proves "unsatisfying". --- Allyn Jackson Return to Top "The Crayola Einstein," by Jordan Gentile. The Other Paper, 1 February 2007. This Columbus, Ohio news weekly profiles Christian Faur, a digital media technologist at Denison University who is also an artist. A physicist by training, he taught math for a time in Los Angeles before moving to Ohio, where he currently has an art show, Aggregate States. He creates works using crayons, "stacking them in such large numbers that they looked like pixels on a television screen." One of the works noted is "Euler," a portrait of the mathematician Leonhard Euler, which includes Euler's constant. --- Annette Emerson Return to Top "She's Got Their Number," by Chuck Salter. Fast Company, February 2007, page 100. This article profiles Brenda Dietrich, who has run the math sciences department at IBM's Thomas J. Watson Research Center since 2001: She's "the top manager at arguably the biggest and most important math department in corporate America." In addition to having co-authored 13 patents and twice being named one of IBM's top inventors, she knits during meetings, while on conference calls, and in her spare time. The department's work is increasingly moving from behind-the-scenes theoretical research to solving real-world problems, as IBM is shifting "from hardware to software and services." Nowadays "elaborate algorithms reveal a company's inefficiencies and opportunities... Entire companies---think Google---are being built are being built almost entirely around math. And others, like IBM, are integrating math into operations and decision making in ways never before seen." The article describes some of the math and how it is applied (e.g. how to fight forest fires more effectively by using an enormous model based on years of massive data that describes likely costs and results for any number of strategies). Another project described involves "how to assemble a project team from consultants dispersed around the world." Dietrich, who joined IBM in 1984 after earning her Ph.D. in operations research and industrial engineering at Cornell, is described as someone who was a young math whiz and still finds math beautiful, challenging, and useful in the real world. --- Annette Emerson Return to Top "Art: Of Doilies and Disease," by Stephen Ornes. Discover, February 2007, page 66.  Image courtesy of Bathsheba Sculpture LLC. Bathsheba Grossman, a mathematical sculptor from Santa Cruz, CA, creates steele-bronze works. One of them, this gyroid, is shown in the magazine. The intricate pattern, based on mathematical equations, is also found in living organisms. The other creations explained are stitched doilies by Laura Splan, based on images of pathogens. Ornes notes that the works "demand a double take--a second look that reveals the scholarly rigor behind the pretty surface." --- Annette Emerson Return to Top "What We Don't Know". Wired, February 2007.  The magazine issue includes a special section on 42 of the biggest questions, and two of them involve mathematics. In "Why don't we understand turbulence?" (page 121) Wil McCarthy starts off with the provocative "An airplane's sudden loss of lift, liquid fuel igniting inside a rocket engine, blood clotting in an artificial heart valve---turbulence can be deadly." After a brief explanation he concludes that "these mathematical tricks don't bring turbulence to heel, but they do get engineers close enough to make reasonably sure your plane touches down on time--and in one piece." Simon Singh covers "Can mathematicans prove the Riemann hypothesis?" (page 122). He explains prime numbers and the hypothesis, yet to be solved after 100 years, and reminds readers that this is one of the Clay Millennium Prize problems, noting that whoever proves (or disproves) the Riemann hypothesis will earn US$1 million. --- Annette Emerson