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)

July 2007

"How Many Ways Can You Spell V1@gra,?" by Brian Hayes. American Scientist, July-August 2007, pages 298-302.

Cataloguing over one million ways to "spell" Viagra, science writer Brian Hayes really seeks to discover whether the answer to his title question will affect the likelihood that unwanted ads appear in our inboxes. Explaining the results of systematically searching through three years of his past emails for messages containing the word Viagra, Hayes discusses some possible techniques used by spammers. He also points out that unlike the spam-combatting software designers, these nagging advertisers do not publish their message-blitzing methods in journals.

Hayes draws an analogy between the human immune system and systems for filtering out junk mail. Like an immune system, the filter "learns" from user reactions by upping the "spamminess" factor of key words in user-marked emails so that the probability that a future email is spam can be more accurately measured. The method by which the "spamminess" factors are combined is Bayesian. The biological framework includes the possibility of an autoimmune disease whereby spam emails that contain bits of quotidian language cause normal phrases inside desirable emails to be marked as "spammy." If enough spam emails contained language that resembled regular emails, then this might lead to important messages being counted as spam. In any case, as spamming techniques become more sophisticated, anti-spamming strategies emerge from mathematics and computational learning theory. Newer mathematical methods for filtering are briefly mentioned, but with no comment on their effectiveness or whether they have been implemented.

--- Brie Finegold

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"The Shape We're In": Review of The Poincaré Conjecture by Donal O'Shea. Reviewed by John Morgan. American Scientist, July-August 2007, pages 352-354.

The shape we're in may have been resolved by Grigory Perelman, who has proved the Poincaré Conjecture. In this review, Morgan gives the history of the conjecture, including a brief description of Perelman's proof. Morgan writes that "No matter what their mathematical background, readers will find much to further stimulate their interest and will learn about both the history of mathematics and its most recent spectacular advances. The book should also be required reading for mathematicians, who will derive great pleasure from seeing their subject so well presented."

--- Mike Breen

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"Harmonious Relations": Review of Music: A Mathematical Offering by David J. Benson. Reviewed by Peter Pesic. American Scientist, July-August 2007, pages 364-5.

Pesic writes that Benson has assembled a fascinating variety of topics that makes his book a uniquely rich source, whether for classroom use, reference, or self-study. Benson begins his book with the basics of vibrating strings and a discussion of harmonic analysis. He later gives the mathematics of orchestral instruments, scale construction, and digital music formats. Finally, Benson writes about symmetry in music. Pesic concludes his review with "Anyone who knows some college-level mathematics and is curious about how it can illuminate music will be richly rewarded by reading Benson's outstanding book."

--- Mike Breen

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"Wenn Wähler Noten geben dürften (If voters could give grades)", by George Szpiro. Neue Zürcher Zeitung, 29 July 2007.

This is the July 2007 installment of George Szpiro's monthly column on mathematics, and it concerns the mathematics of election procedures. If voters in France had been able to express their opinion rather than just putting a vote into the ballot box, Nicolas Sarkozy might not have won the presidential elections. Szpiro discusses an election procedure that avoids some well known election paradoxes.

--- Allyn Jackson

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"Verschiedene Arten von Unendlichkeit (Different Kinds of Infinity)": Review of Eins, zwei, drei ... unendlich, by Rudolf Kippenhahn. Reviewed by George Szpiro. Neue Zürcher Zeitung, 29 July 2007.

The author of the book under review is a mathematician and astrophysicist. Written as a conversation with the author's nephew, the book discusses various notions of infinity, touching on such topics as countability and uncountability, convergence and divergence, proof by induction, high-dimensional space, and non-Euclidean geometry. Topics from modern physics, such as particle-wave duality and the infinity of the cosmos, also come into play.

--- Allyn Jackson

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"Mathematicians Propose New Model for Cancer Growth," by Adriana Salerno. Voice of America, 31 July 2007.

"For some time now, laboratory scientists have known that cancer cells behave very differently from normal cells, constantly changing their genetic makeup," writes Adriana Salerno, reporting for Voice of America. (Salerno is this year's AMS-AAAS Mass Media Science and Engineering fellow.) Is this genetic instability advantageous for cancer cells or is it a side effect? Using optimal control theory, University of California mathematician Natalia Komarova has found that instability in the initial stages, followed by greater stability later on, pays off for tumors. Her findings have been published in the Royal Society's journal Interface.

University of Kentucky College of Medicine medical researcher Andrew Pierce finds these results reasonable: many living organisms such as bacteria operate in the same way. Neal Meropol of the Fox-Chase Cancer Center in Philadelphia values the work of researchers in other disciplines, such as Komarova, for the new ideas they provide. "We are certainly learning the hard way to some extent, through our failures, that a team approach to solving the cancer problem is required if we're going to achieve our holy grail of eliminating death from cancer in the future." (If the link in the reference does not work, go here and enter the search term "Komarova.")

--- Claudia Clark

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"Chasing Down Zeros at Math Camp," by Frank Kosa. Christian Science Monitor, 30 July 2007.

In 1994, two math-majors-turned-Silicon-Valley-computer-sellers, John Fry and Stephen Sorenson, decided to do something about the lack of collaboration in mathematics. They felt that it was a field in which, unlike other scientific disciplines, working together was like cheating, and they decided to turn Fry's electronics store into the American Institute of Mathematics, a virtual weeklong math camp for adult mathematicians to come together to tackle problems like the Riemann hypothesis. The author describes workshop participants at the Institute as surprisingly normal people with amazing mathematical talent who push around numbers and theorems to run their own "dating service for numeric ideas." Fry and Sorenson hoped the participants would make some solid matches if the right people worked at it long enough, and last March the Institute had a big success: the solution of the "exceptional Lie group E8." Their math campers have since moved on to Riemann, the solution to which involves zero---the quantity of mathematical knowledge the author claims you need to have in order to understand his article.

--- Lisa DeKeukelaere

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"Opponents Pay a Painful Price in Walking Bonds," by Dan Rosenheck. The New York Times, 29 July 2007.

Barry Bonds

©2007 S.F. Giants

Barry Bonds (pictured at left) recently became Major League Baseball's all-time home run leader. No pitcher wanted to give up any home runs to Bonds, let alone the record breaker, so he was often walked. Using a statistic called win expectancy (the probability that a team will win the game), Tom Tango, co-author of The Book: Playing the Percentages in Baseball, found that in most cases it is better strategically to pitch to Bonds than to walk him. For example, from 2001 to 2004, of the 136 non-intentional walks Bonds got, 77 helped the Giants' win expectancy. Rosenheck writes that "Barry Bonds may not be anyone's idea of a great teammate. But every time he takes a pitch, he is truly taking one for the team: passing up a chance at personal glory to edge the Giants closer to victory."

--- Mike Breen

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"Less proof, more truth": Review of How Mathematicians Think, by William Byers. Reviewed by Gregory Chaitin. New Scientist, 28 July 2007, page 49.

"Mathematics is a wonderful, mad subject, full of imagination, fantasy, and creativity that is not limited by the petty details of the physical world, but only by the strength of our inner light," writes Chaitin in this provocative and thought-provoking review. He agrees with the book's main premise, that "mathematics today is obsessed with rigor, and this actually suppresses creativity." The emphasis on rigor and technique has led to a "lawyer's vision of math, where the main goal is the nit-picking avoidance of mistakes". This is the real reason that students are often turned off to mathematics, which Chaitin asserts is "quietly dying". With powerful computers that are able to carry out calculations better than humans can, mathematicians "should be as unlike machines as possible."

--- Allyn Jackson

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"The longest divisions," by Sarah Hemming. FT.com (Financial Times online), 28 July 2007.
"A beautiful mind," by Nikita Lalwani. New Statesman, 23 August 2007.
"Complicite's Tricks." The Economist, 30 August 2007

The encounter between Cambridge mathematician G.H. Hardy and Indian genius Srinivasa Ramanjuan in 1913 is the basis of a new play, A Disappearing Number, directed by Simon McBurney, performed by his company, Complicite. Hemming's article is primarily an interview with the play's director, and Lalwani's article uses the new play as an opportunity to explore the life and mathematical work of Ramanjuan. Hemming reports that A Disappearing Number "is a multi-layered piece that makes the beauty of mathematics its structure, as well as its subject." During the interview director McBurney explains--sometimes drawing pictures--some mathematical ideas and his theatrical conceptions of the topic. He is intrigued by mathematics describing the invisible, the concept of beauty in mathematics, patterns, the intellectual enjoyment of mathematics, and whether mathematical reality exists outside of human consciousness or is a product of it. Lalwani, author of the novel Gifted, about a mathematics prodigy of Indian descent, gives a detailed account of Ramanujan's background, his encounter with Hardy and English culture, and "his feeling that mathematics helped him in his attempts to understand the spiritual universe." The Economist piece gives some background on the Paris-founded theater company, and notes (from previous performances of this play at festivals in Vienna and Amsterdam) that McBurney "has been careful not to burden the audience with too much mathematical theory; rather, he portrays the loneliness of genius, the human need to be rooted--and the playfulness of maths." A Disappearing Number runs at the Barbican Centre in London from September 5 to October 6, 2007.

--- Annette Emerson

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"Group sees glimpses of divinity in math," by Rich Barlow. The Boston Globe, 28 July 2007.

Rich Barlow reports on a few of the speakers who presented talks at a recent Boston College gathering of the Clavius Group, an international fellowship of Catholic mathematicians founded in 1963. The Clavius Group is named for the 16th century Jesuit mathematician and astronomer Christopher Clavius, who was instrumental in developing the Gregorian calendar. One presenter, the Rev. Paul Schweitzer, discussed the influence of monotheism on modern mathematics. Barbara Reynolds, a Roman Catholic nun and mathematician who teaches at Cardinal Stritch University, a Franciscan school in Milwaukee, spoke of how her beliefs inform her teaching. She uses examples such as human trafficking, free trade, and the work of Florence Nightingale to help her teach mathematics. She has found that, in her years of teaching, "No matter who teaches, personal values do come through. What I've done is be explicit about the values I teach." In addition, Reynolds experiences "a deep sense of encountering the holy" while working on difficult math problems.

--- Claudia Clark

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"The Two High-School Pillars Supporting College Science," by Philip M. Sadler and Robert H. Tai. Science, 27 July 2007, pages 457-458.
"Want to be good at science? Take lots of math," by Randolph E. Schmid. Associated Press, 27 July 2007.
"First, Do the Math," by Rick Weiss. Washington Post, 30 July 2007, page A7.
"More math helps young scientists," by Davide Castelvecchi. Science News, 4 August 2007, page 78.

There has been discussion among science teachers about the order of courses for high school students. The traditional order of biology-chemistry-physics has been scrapped in many schools in favor of "Physics First." Sadler and Tai did a study of students at 77 colleges and universities to see if knowledge in one of the three subjects helped students in introductory science courses. They found that in each case, taking high school courses in a subject helped students in that subject but not in the other two. They also found that the number of years of math instruction in high school "was a significant predictor of performance across all college subjects, including introductory biology."

--- Mike Breen

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"Bush Awards Science, Technology Medals," by Christine Simmons. Associated Press, 27 July 2007.
"U-M math professor to be honored at White House," by Kristen Jordan. Detroit Free Press, 27 July 2007.

Medal winners Bass and Efron with Margaret Wright and Tony Chan
Left to right: Hyman Bass, Bradley Efron, Margaret Wright, and Tony Chan. Photo by Jerry Cuomo.

Hyman Bass, professor of mathematics and mathematics education at the University of Michigan, received a 2006 National Medal of Science from President Bush in a ceremony at the White House on 27 July. Also receiving a National Medal of Science, in this case the 2005 National Medal of Science, was Bradley Efron, a statistician at Stanford University. Their fields of study figured into the President's remarks at the ceremony: "In a single room, we have thinkers who have helped formulate and refine the Big Bang theory of the universe, the bootstrap resampling technique of statistics, the algebraic K-theory of mathematics. I'm going to play like I understand what all that means." The National Medal of Science honors pioneers in scientific research.

--- Mike Breen

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"Some assembly needed," by Ian Stewart. Nature, 26 July 2007.

origami by Taketoshi Nojima
Image courtesy of Taketoshi Nojima.

Stewart describes developments in mathematics to understand the science of folding objects flat. "Researchers' inspiration derives from two quite different sources: `biomimetrics,' the technological mimicry of biological processes and structures, and the ancient Japanese art of origami." Applications include folding maps and air bags, packing furniture for shipping, and folding solar panels and antennae on satellites. He poses origami's flat-folding problem: "Given a diagram of fold lines on a flat sheet of paper, can the paper be folded into a flat shape without introducing any further creases?" He notes that computer scientists Barry Hayes and Marshall Bern have proven that the problem is mathematically equivalent to the 3-SAT problem in logic. From there Stewart focuses on the work of origami creator Taketoshi Nojima, whose patterns resemble flows, cones, shells, and tessellations, and whose illustrated paper "Origami Modeling of Functional Structures Based on Organic Patterns" envisions applications to manufacturing, biology, and robotics.

--- Annette Emerson

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"Mathematik im Dienst der Praxis (Mathematics in practical service)", by George Szpiro. Neue Zürcher Zeitung, 25 July 2007.

This article reports on the 2007 International Congress of Industrial and Applied Mathematics, which took place in Zurich in July. The article discusses in particular the modeling of dynamical systems and the use of algebraic topology in robotics.

--- Allyn Jackson

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"Proof and beauty": Interview with Christopher Zeeman. Interviewed by Justin Mullins. New Scientist, 21 July 2007, page 48.

Christopher Zeeman is a British mathematician who did pioneering work in topology in the middle of the 20th century. In this brief interview, he discusses some of his views about Euclid, describes how he built a world-class mathematics department from scratch at the University of Warwick, and muses on the character of beauty in mathematics.

--- Allyn Jackson

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"Mathematical Lives of Plants," Julie J. Rehmeyer. Science News, 21 July 2007.

sunflower spirals

Updating her 5 May Math Trek article of the same title, Julie Rehmeyer discusses old and new mathematical models for understanding phyllotaxis, the mysterious spiral patterns made by plants. These models describe the placement of primordia, new cells that emerge at the center or tip of the plant. One physics-based model that produced spiral patterns emerged from observing magnetized droplets in 1992, and has since been found to be valid for plants in which primordia form consecutively. A hormone (analagous to the magnetic charge) causes new primordia to form as far from old ones as possible according to a spiral pattern related to the golden angle and the Fibonacci numbers. But a newer model coming from mathematics dethrones the golden angle as the architect of these patterns by predicting spiral patterns that differ subtly from the golden spiral. These patterns emerge especially when many primordia form simultaneously. Though oversimplified, the "coin game" may provide the "essence" of phyllotaxis since it produces a variety of spiral patterns. In this model, primordia forming at the tip of a growing plant are analogous to coins being placed on the surface of a vertical cylinder. The rules of the game require the coins to lie on the cylinder's wall at the lowest level possible without overlap, which leads over time to a rich family of spiral patterns. As biologists and mathematicians approach this puzzle from different angles, they may soon come to a widely applicable model.

--- Brie Finegold

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"From e to eternity", by Richard Elwes. New Scientist, 21 July 2007, pages 38-41.

This article discusses many aspects of the transcendental number e. Elwes writes that "almost all numbers are transcendental", and yet very few actual examples have been discovered, the two most famous being e and pi. A number is transcendental if it is not the solution of any polynomial equation with integer coefficients. Or, as Elwes describes it, given a transcendental number, "you can multiply it by itself as many times as you wish, combine these powers and divide and multiply by integers in whatever complicated fashion you want, but you will never arrive back in the familiar territory of the integers." The article discusses some intriguingly simple questions about transcendental numbers that remain unanswered to this day, such as: Is the sum of e and pi transcendental? He also discusses recent work in mathematical logic that holds promise of shedding new light on transcendental numbers. This work may have consequences in quantum geometry, which Elwes describes as "the theoretical framework that underpins many attempts to reconcile the disparate worlds of quantum mechanics and Einstein's general theory of relativity into a single quantum theory of gravity."

--- Allyn Jackson

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"Focus on math: Wizards put brains to the test," by Tiffany Erickson. Deseret Morning News, 17 July 2007.

The Park City Math Institute brings together undergraduates, graduate students, high school teachers, and college and university faculty for three weeks. This article gives an overview of the conference, especially how it relates to math education. This year the Institute had about 350 participants, including two Fields Medalists, from 17 countries. The director of the Institute, Robert Bryant, says, "The best way to be excited about something is to learn new things about it and that's one of the things that we emphasize here, to get people engaged and excited about learning new things about the subject so that they will be better teachers."

--- Mike Breen

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Moebius strip 1 Moebius strip 2
Two images of a Möbius strip from the Starostin-van der Heijden paper. Image courtesy of Eugene Starostin. Reprinted by permission from Macmillan Publishers Ltd: Nature Materials, volume 6, issue 8, copyright 2007.

"Möbius strip unraveled", by Louis Buckley. Nature, 15 July 2007.
"Moebius strip riddle solved at last." Agence France-Presse, 16 July 2007.
"A New Twist on the Möbius Strip", by Marissa Cevallos. ScienceNOW Daily News, 16 July 2007.
"Shaping Up a Möbius Strip", by Sourish Basu. Scientific American web site, 17 July 2007.
"Defining a very strange loop." New Scientist, 21 July 2007, page 6.
"Die Endlos-Schleife (The Endless Loop)", by Wolfgang Blum. Süddeutsche Zeitung, 24 July 2007, page 16.

These stories report on new mathematical results described in the article "The shape of a Möbius strip", by Eugene Starostin and Gert van der Heijden, which appeared in July 2007 in Nature Materials. A Möbius strip can easily be formed with a skinny strip of paper: Give the paper one twist, then glue the ends. What you get is a surface that, curiously, has only one side. Conveyor belts are often in the form of a Möbius strip: Since there is only one side, the belt gets worn out evenly. In mathematics, a Möbius strip is often considered as an idealized surface, so that questions about what the strip is made of, or what the proportion of length to width is, simply do not arise. But if you try to make a Möbius strip out of actual paper, you will find that the shape of the Möbius strip varies a lot depending on the proportion of the strip of paper you start with, the stiffness of the paper, and so on. Starostin and van der Heijden's article explores mathematically and computationally questions about the physical shape of Möbius strips and how that shape is affected by the material the strips are made out of and the proportions of the strips. In a commentary accompanying the article in Nature Materials, mathematician John Maddocks writes that this work could bring new insights into how energy distributes itself across unstretchable sheets and into the nature of materials that have the structure of a Möbius strip.

--- Allyn Jackson

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"Visual mathematics---math for art students," by Joan Morgan. Diverse, 13 July 2007.

This article profiles John Sims, professor and coordinator of mathematics at the Ringling School of Art and Design in Sarasota, Florida. He "doesn't buy into the left brain/right brain thing of art on one side and math on the other," the article says. So he aims to show that math can be creative and visual. He is both an artrist and a mathematician. His artworks---exhibited around the country and at conferences in Spain and Israel---include "Pythagoras' Theorem, Triangles, Triples, and Art" and "Time Sculpture: a 21st Century Clock." He develops the curriculum at the school, which includes courses on visual mathematics, creative geometry, mathematics and physics for animators, and art and ideas of mathematics. The article includes thoughts on mathematics and art from Sims, as well as comments from former students on his impact as a teacher.

--- Annette Emerson

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"In Hyperbolic Space, Size Matters"; "Pricey Proof Keeps Gaining Support"; "Bizarre Pool Shots Spiral to Infinity"; and "That's Not Some Knot Sum!", by Barry Cipra. Science, 6 July 2007, pages 38-39.

William Thurston and students
Bill Thurston and some of his students. Front: Bill Thurston; First Row (left to right): Craig Hodgson, Sergio Fenley, Robert Meyerhoff, Rich Schwartz, Benson Farb, Dick Canary, Yair Minsky; Second Row: Martin Bridgeman, Steve Kerckhoff, Jeff Weeks, Bill Goldman; Third Row: Biao Wang, Suhyong Choi, David Gabai, Genevieve Walsh; (Oded Schramm attended the meeting but is missing from the picture). Photographer: John Vincent.

From 7-11 June 2007, a conference entitled Geometry and the Imagination was held at Princeton University. The conference was held in honor of mathematician William Thurston. Writer Barry Cipra covered some of the conference highlights for the 6 July 2007 issue of Science.

After decades of effort by various mathematicians, David Gabai of Princeton University, Robert Meyerhoff of Boston College, and Peter Milley of the University of Melbourne in Australia presented a proof showing that the Weeks manifold is the smallest hyperbolic space. Cipra's article includes an interview with Jeffrey Weeks, who computed---but could not prove the minimality of---the tiny manifold in the 1970s when he was a graduate student of Thurston's. And what about the next smallest manifold? It could be one that Meyerhoff himself found when he was a graduate student of Thurston's, but that result is not proven.

In the 1950s, Bernhard Neumann proposed the idea of "outer billiards," in which an object outside some convex figure makes a path around that figure, following certain rules. Neumann asked whether the trajectory formed by that object could be unbounded. Cipra reports that Richard Schwartz of Brown University has now proved that the Penrose kite has an unbounded trajectory, the first polygon for which this result has been found. Cipra also reports on some recent work done by Marc Lackenby of Oxford University in the area of knot theory, and provides an update on topologists' work on Grigory Perelman's proof of the Geometrization Conjecture and the Poincaré Conjecture.

--- Claudia Clark

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"Swarm Theory: ants, bees, and birds teach us how to cope with a complex world," by Peter Miller. National Geographic, July 2007.

birds use local rules to flock

We may joke about the "herd mentality" but it seems that swarms exhibit intelligence far greater than any one of their members. Just as any airplane passenger has observed, our cars and trucks appear as little insects in a hive. So it may not come as a surprise that mathematical algorithms based on biologists' most recent observations of interactions between ants are helping airlines and truck fleets more efficiently deliver people and goods. Decision-makers might also learn from the cooperative actions of bees or the lightning-quick reactions of antelope avoiding their predators. By using relatively few rules, individuals in nature acting on only local information cooperate to produce a powerful global result. For example, birds flock by following a few local rules, such as copying the directions and movements of nearby neighbors while not bumping into them. Mechanical engineers hope to mimic this behavior, which lends itself easily to mathematical modeling, and create teams of robots that can efficiently accomplish tasks such as finding hidden objects. Miller observes the collective wisdom of the Internet as an example of our own "swarm intelligence" and anticipates the benefits of viewing phenomena as "self-organizing". Sometimes anthropomorphizing the insects to the extreme, the author exalts honey-bees' ability to "work through individual differences of opinion" and calls on us to model our actions off of the selfless actions of the bee, who does not see the big picture but whose small actions preserve the hive. Whether one agrees or not, this view certainly gives a mathematical ring to the adage "think global, act local".

--- Brie Finegold

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"A Little Privacy, Please," by Chip Walter. Scientific American, July 2007.

"Latanya Sweeney attracts alot of attention. It could be because of her deep affection for esoteric and cunning mathematics." So begins this profile of Sweeney, who runs the Data Privacy Laboratory at Carnegie Mellon University. She disagrees with the statement that privacy is dead. Although she acknowledges that the problems with protecting privacy grow with new technologies, she says that it is impossible to predict how the problems will arise---or be addressed. "Her group operates as a kind of digital detective agency staffed with a dedicated squad of programmers devising some seriously clever software." One program, "Identity Angel," links names, addresses, ages, and Social Security numbers from various databases on the Internet and alerts individuals susceptible to identify theft. The article outlines how another program "anonymizes" identities. Sweeney showed an early talent for mathematics and received scholarships that helped her attend the Massachusetts Institute of Technology. She left college to start her own software consulting business, but ten years later returned to Harvard University to complete her undergraduate degree, then earned her master's and doctorate in computer science at MIT, the first African-American woman to do so.

--- Annette Emerson

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