"How Many Ways Can You Spell V1@gra,?" by Brian Hayes. American Scientist, JulyAugust 2007, pages 298302.
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 He also points out that unlike the spamcombatting software designers, these nagging advertisers do not publish their messageblitzing methods in journals.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 usermarked 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, antispamming 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
"The Shape We're In": Review of The Poincaré Conjecture by Donal O'Shea. Reviewed by John Morgan. American Scientist, JulyAugust 2007, pages 352354.
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
"Harmonious Relations": Review of Music: A Mathematical Offering by David J. Benson. Reviewed by Peter Pesic. American Scientist, JulyAugust 2007, pages 3645.
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 selfstudy. 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 collegelevel mathematics and is curious about how it can illuminate music will be richly rewarded by reading Benson's outstanding book."
 Mike Breen
"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
"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, highdimensional space, and nonEuclidean geometry. Topics from modern physics, such as particlewave duality and the infinity of the cosmos, also come into play.
 Allyn Jackson
"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 AMSAAAS 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 FoxChase 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
"Chasing Down Zeros at Math Camp," by Frank Kosa. Christian Science Monitor, 30 July 2007.
In 1994, two mathmajorsturnedSiliconValleycomputersellers, 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 E_{8}." Their math campers have since moved on to Riemann, the solution to which involves zerothe quantity of mathematical knowledge the author claims you need to have in order to understand his article.
 Lisa DeKeukelaere
"Opponents Pay a Painful Price in Walking Bonds," by Dan Rosenheck. The New York Times, 29 July 2007.
"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 thoughtprovoking 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 nitpicking 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
"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 multilayered piece that makes the beauty of mathematics its structure, as well as its subject." During the interview director McBurney explainssometimes drawing picturessome 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 Parisfounded 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 rootedand the playfulness of maths." A Disappearing Number runs at the Barbican Centre in London from September 5 to October 6, 2007.
 Annette Emerson
"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
"The Two HighSchool Pillars Supporting College Science," by Philip M. Sadler and Robert H. Tai. Science, 27 July 2007, pages 457458.
"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 biologychemistryphysics 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
"Bush Awards Science, Technology Medals," by Christine Simmons. Associated Press, 27 July 2007.
"UM math professor to be honored at White House," by Kristen Jordan. Detroit Free Press, 27 July 2007.
"Some assembly needed," by Ian Stewart. Nature, 26 July 2007.
 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 flatfolding 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 3SAT 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 
"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
"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 worldclass mathematics department from scratch at the University of Warwick, and muses on the character of beauty in mathematics.
 Allyn Jackson
"Mathematical Lives of Plants," Julie J. Rehmeyer. Science News, 21 July 2007.
"From e to eternity", by Richard Elwes. New Scientist, 21 July 2007, pages 3841.
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
"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
 "Möbius strip unraveled", by Louis Buckley. Nature, 15 July 2007. 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

"Visual mathematicsmath 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 artworksexhibited around the country and at conferences in Spain and Israelinclude "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
"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 3839.
"Swarm Theory: ants, bees, and birds teach us how to cope with a complex world," by Peter Miller. National Geographic, July 2007.
"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 ariseor 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 AfricanAmerican woman to do so.
 Annette Emerson
Math Digest Archives 
2016 
2015 
2014 
2013 
2012 
2011 
2010 
2009 
2008 
2007 
2006 
2005 
2004 
2003 
2002 
2001 
2000 
1999 
1998 
1997  1996  1995 Click here for a list of links to web pages of publications covered in the Digest. 