September 2007
"Sorting Out the Genome," by Brian Hayes. American Scientist, SeptemberOctober 2007, pages 386391. One way to measure the evolutionary distance between species is by examing their genetic codes and counting the number of reversals in genetic strings between the two. For example, badcef is two reversals away from abcdef. Is there an algorithm to find the minimum number of reversals in much longer strings? The answer is yes, and it involves signed permutations, for which the problem is easier to solve than it is for unsigned permutations. In this article Hayes describes the development of the algorithm and its relevance to genetics. Near the end of the article, he writes that "The decadelong effort to solve the sortingbyreversals problem stands as a model of interdisciplinary collaboration. The question that inspired the work in the first place was of genuine importance to biology, but it also turned out to hold real interest for mathematicians and computer scientists, who might well have tackled the problem even if it didn't have an appealing application."  Mike Breen "The fine art of painting by the numbers," by Kyle MacMillan. Denver Post, 30 September 2007.
"Les demoiselles d'Avignon", by Arthur L. Miller. New Scientist, 29 September 2007, pages 5051. This article describes the mathematical influences that led to Picasso's conception of his 1907 painting Les Demoiselles d'Avignon, which marks the birth of cubism. Picasso was very interested in photography and alternative ways to project reality onto a twodimensional space. The mathematical influences came through an insurance actuary named Maurice Princet, who showed Picasso a book by Esprit Jouffret about complex polyhedra in four dimensions. Jouffret was also a friend of the great mathematician Henri Poincaré, and Princet gave Picasso and his circle of friends lectures about Poincaré's ideas. The face of the squatting figure in the painting is "a projection from the fourth dimension, in which front and profile views are seen simultaneously, her head swiveled 180 degrees," Miller writes. "The seeds of cubism had been planted."  Allyn Jackson
"Mathematician puts people back into the equation", by Peggy Curran. The Gazette (Montreal, Canada), 29 September 2007. William Byers, the author of How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox, celebrates the chaotic rather than systematic nature of mathematical thinking. A mathematics professor at Concordia University in Canada, Byers says "Zero is clearly a paradox." And although the article states that the book has garnered good reviews in math journals, a reviewer for the Mathematical Association of America, computer scientist David J. Stucki, writes that the book "fails to deliver on many levels." A more complimentary review by mathematician Gregory Chaitin appeared in New Scientist (see July Math Digest). Peggy Curran writes, "As someone who wouldn't know a dodecahedron if I met one on the street, I was in no position to quibble when Byers cited irregularities from the simplest 1+1=2 through the complexities of Euclidean Geometry."  Brie Finegold
"2007 Visualization Challenge." Science, 28 September 2007, pages 18571863.
"Local Politics, Web Money," by Amy Schatz. The Wall Street Journal, 28 September 2007, page A6.
"Bellas geheimes Seminar (Bella's secret seminar)", by George Szpiro. Die Zeit, 27 September 2007.
"Ups and downs of a senator scientist": Review of The Volterra Chronicles: The Life and Times of an Extraordinary Mathematician 18601940 by Judith R. Goodstein. Reviewed by Salvatore Coen. Nature, 27 September 2007, pages 406407.
"Business by numbers." The Economist, 25 September 2007, pages 8587. The subject of this article is the importance of algorithms to business. Businesses use algorithms to improve processes, such as product delivery, and to analyze data, such as records of consumer purchases. An example of the first type is UPS's VOLCANO algorithm that UPS uses to schedule its airline fleet. UPS estimates that the algorithm has saved the company tens of millions of dollars since 2000. Examples of the second type are algorithms to detect consumer fraud and Internet search algorithms. Algorithms still depend on humans, though. The article cites a case of a UPS planning model that routed all packages through Iowa because of a data error that made it appear that sending packages to Iowa was free.  Mike Breen
"Microsoft Says Excel 2007 Produces Math Errors," by Paul McDougall. Information Week, 26 September 2007. The original version of Excel 2007 has trouble with calculations that result in numbers near 2^{16}. Molham Serry discovered that when he asked Excel 2007 to do 850 times 77.1, the program returned 100,000 instead of 65,535 (2^{16}  1). Microsoft manager David Gainer said that the problem, peculiar to Excel 2007 and not to earlier versions of Excel, is not in the calculation, but in the code that formats the displayed result. He noted that if a user does the previous calculation and then asks Excel to multiply that result by two, the final result displayed will be 131,070 (which is correct), not 200,000. The bug reportedly was fixed in the second week of October.  Mike Breen
"Report: Mixed Grades for No Child Left Behind," by Peg Tyre. Newsweek, 25 September 2007. The National Assessment of Educational Progress (NAEP) released its "report card" on the progress of U.S. fourth and eighthgrade students in math and reading. The percentage of fourth graders rated proficient or better went up three points to 39% and the percentage of eighth graders rated similarly went up two points to 32%. Some people, such as Secretary of Education Margaret Spellings, attributed the progress to No Child Left Behind (NCLB) programs, while others, such as the director of the Cato's Institute Center for Educational Freedom, said that the improvements are the result of measures taken before NCLB went into effect. The U.S. News and World Report article begins with a question from the test taken by fourth graders: The Ben Franklin Bridge was 75 years old in 2001. In what year was the bridge 50 years old? Thirtysix percent of the fourth graders chose the correct answer. The NAEP report on math scores is online.  Mike Breen
"In Theory, Diamondbacks Are Winning Way Too Often," by Dan Rosenheck. New York Times, 23 September 2007, Sports page 6. Baseball statisticians use a statistic they call the Pythagorean Theorem ([runs scored^{2} + runs allowed^{2}]/runs allowed^{2}) because of its similarity to the theorem about right triangles. Since 1901, 95 percent of teams' wonlost records in Major League Baseball have been within eight games of the formula's projection. At the time of the publication of the New York Times article, the number of wins by the Arizona Diamondbacks exceeded the number predicted by the theorem by the largest amount recorded since 1901. The Diamondbacks scored fewer runs than they allowed, yet won their division, mostly because of the team's record in games decided by one run: 3220. Baseball statisticians expect a team's record in such games to be much closer to 5050. Some of the Diamondbacks' success is attributed to luck, and some to the performance of its bullpen. Kyle Wright, author of the second article, was right: After sweeping the Chicago Cubs in the Divisional Series, the Diamondbacks themselves were swept by the Colorado Rockies in the National League Championship Series. The Diamondbacks' record in the playoffs was 34, scoring 24 runs and giving up 24. Their only onerun game was a loss.  Mike Breen
"Women, Girls, and Math," hosted by Ira Flatow. NPR Science Friday, 21 September 2007. This onehourlong NPR piece features conversations with former Wonder Years star and math major Danica McKellar, Harvey Mudd College President Maria Klawe, and two women involved with the US team that competed in the 2007 China Girls Math Olympiad. All four women spoke to the importance of teachers reaching out in the classroom to math students of both genders by providing realworld examples and encouraging students not to be frustrated by a certain type or level of mathematicsthere is no math gene, and practice makes perfect. McKellar, who is promoting her new book Math Doesn't Suck: How to Survive Middle School Math Without Losing Your Mind or Breaking a Nail, noted that most math students are drawn to the subject by one special teacher who provides a comfortable environment for doing math. In doing research for the book, she discovered that girls today are still inhibited by a sense of needing to "be nice" or "play dumb" in the classroom, which prevents them from asking questions and learning more.  Lisa DeKeukelaere
"Fast Computers and the Music of Math" by Caroline Evans. Song of the Day on National Public Radio, 20 September 2007. The song of the day on 20 September was "Sweden Hasn't Changed, You Have," by the band named Fast Computers. The band's first album, Heart Geometry, includes song titles "Math Predictions" and "Gravity/Love," which "betray the band's interest in the mathematical." Although the vocals "concentrate only fleetingly on math" reviewer Evans notes that "the group also uses math to trace intricate musical patterns and ornate designs." Hear the segment and the featured song on NPR.  Annette Emerson
"A Lust for Numbers": Review of The Indian Clerk, by David Leavitt. Reviewed by Nell Freudenberger. New York Times, 16 September 2007. David Leavitt's new novel has as its main characters two historical figures from twentieth century mathematics: the Briton G. H. Hardy, a Cambridge don and one of the leading number theorists of his time, and the young Srinivasa Ramanujan, brilliant, selftaught Indian mathematician. The novel explores the relationship between these two very different mathematiciansa relationship that, at least for Hardy, had romantic overtones. The reviewer writes: "[W]hat [Leavitt] makes of their relationship is much more subtle than a love affair. Initially frustrated by the young genius's tendency to pursue several ideas in an associative fashion, Hardy eventually realizes he has come in contact with a mind that expands his notion of their discipline." The review does not discuss mathematics much, beyond saying that Hardy was working on the Riemann Hypothesis. For citations of other reviews of this book, visit the Reviews page on the AMS web site.  Allyn Jackson
"Reality by numbers," by Max Tegmark. New Scientist, 15 September 2007, pages 3841. In this article, MIT physicist Max Tegmark makes a case for what he calls "the mathematical universe hypothesis". The idea is to strip away from our description of the universe all humandefined conceptsTegmark offers protons, stars, and molecules as examples of such conceptsin order to lay bare the mathematical structure they embody. Without such humandefined "baggage", Tegmark claims, "a sufficiently large supercomputer could calculate how the state of the universe evolves over time without interpreting it in human terms." The article contains some baffling passages. For example, Tegmark likens a physicist's outside overview of external reality to the viewpoint of a bird surveying the landscape from high above; the inside view of an observer living in that reality is like the viewpoint of a frog that is part of the landscape the bird is seeing. "[F]rom the bird's perspective, trajectories of objects moving in fourdimensional spacetime resemble a tangle of spaghetti," Tegmark writes. "Where the frog sees something moving with constant velocity, the bird sees a straight strand of uncooked spaghetti. Where the frog sees the moon orbit the Earth, the bird sees two intertwined spaghetti strands. To the frog, the world is described by Newton's laws of motion and gravitation. To the bird, the world is the geometry of the pasta." Tegmark says that the biggest objection to the mathematical universe hypothesis is that it is "counterintuitive and disturbing", a reaction that he dismisses "as a failure to appreciate Darwinian evolution."  Allyn Jackson
"Penetrating the mumbojumbo": Review of The Tiger that Isn't, by Michael Blastland and Andrew Dilnot. Reviewed by Mike Holderness. New Scientist, 15 September 2007, page 57. This book is an extension of the authors' BBC radio program More or Less, which aims to raise the level of mathematical literacy among the general public. One reason bogus numbers and statistics make their way so frequently into public discourse is that so many people do not understand even basic mathematics. The reviewer states that, according to surveys, one in three people "do not understand percentages at all" (and then he parenthetically quips: "Hang on: onethird of which population?"). Thus the authors of this book have taken on a daunting task. They "succeed engagingly," the review says, "even providing some very accesible critiques of quite advanced statistics."  Allyn Jackson
"Using Math to Track Terrorists," by Joe Palca. Science Friday (NPR), 14 September 2007. In the first half hour of the program, Rochester Institute of Technology mathematics professor Bernard Brooks and University of Arizona professor of management information systems Hsinchun Chen speak with Palca about the ways that mathematics and computer science are being used to track down terrorists. Brooks discussed how patterns of terrorist communications have been studied and modeled using graph theory. For example, given that one member of a terrorist cell has been identified on a network that can be monitored, Brooks stated that "we can use some of the algorithms useful for searching social networks to identify the clique of the terrorist cell" without necessarily even having to listen to the content. Chen noted how "tech mining" and "opinion mining" can be used along with language processing and mathematical models to identify "the most critical members and the most critical messages that you really need to pay more attention to" on existing forums.  Claudia Clark
"Ein Neuling in der Walhalla (A newbie in the Valhalla)". Süddeutsche Zeitung, 13 September 2007, page 46. The Walhalla, located near Regensburg, Germany, is a collection of marble busts depicting outstanding Germans. This year a bust of Carl Friedrich Gauss (17771855) was the 128th addition to the collection. The short item in the Süddeutsche Zeitung is basically a caption for a photo of the bust of Gauss. The item describes Gauss as "one of the most important mathematicians of all time" but gives no hint of his achievements beyond saying that he "developed many formulas".  Allyn Jackson
"Kristalle für Köln (Crystals for Cologne)", by Ulf von Rauchhaupt. Frankfurter Allgemeine Zeitung, 9 September 2007, page 67. Taking the new stainedglass windows in the renowned cathedral in Cologne, Germany, as its starting point, this article discusses how mathematical notions of randomness can be used to create tiling patterns similar to those used in stainedglass windows.  Allyn Jackson
"May the Best Team Win," by Julie Rehmeyer. Science News Online, 8 September 2007. Luck is a much more important player on the baseball field than you might think, according to a physicist from Los Alamos National Laboratory who recently computed that the team with the best record wins only 56 percent of the time. He found that playing a season of continuous playoff style elimination rounds would increase the odds that the best team would win the World Series, but this system probably will never be implemented because fans like to see the underdog winan event bolstered by the importance of luck over skill on the field. In both baseball and football, the strongest team ends up with the best record only 30 percent of the time. This indicates not only that chance is a bigger factor in baseball than in football, which plays far fewer games per season, but also that this number30 percentmay be the ideal balance of luck and skill needed to please the fans.  Lisa DeKeukelaere
"Beautiful Minds," by Virginia Postrel. The Atlantic, September 2007, pages 140141. The public's stereotypes mad scientists and mathematicians are not easy ones to dispel. So how to explain the success of the television shows CSI and NUMB3RS, whose stars are a scientist and a mathematician, respectively? Neither show resorts to science fiction or conspiratorial coverups of alien sightings, so what makes the characters so compelling? Postrel thinks that the shows "align scientific curiosity with justice." The shows promise that the use of science and mathematics will lead to the truth, untainted by external pressures. She writes that the series' main characters' eccentricity does not alienate them from the viewer but instead "makes them more perceptive and, in many cases, more empathetic." The special quality of Charlie Eppes, the mathematician in Numb3rs, is that he sees patterns that others don't.  Mike Breen
"D'où viennent les maths? (Where does math come from?)", by Mathieu Grousson. Science et Vie, September 2007, pages 5067. This threepart article explores questions about the origin of mathematical ideas. The first part of the article discusses recent research showing that the human brain has an innate sense of numbers, and the second part looks at mathematical artifacts from ancient civilizations. The third part is titled "Math: Reality or pure mental construction?" and features interviews with two French mathematicians, J.P. Delahaye and J.P. Bourguignon. Delahaye comes down on the side of math having a separate reality: "When I do mathematics, I am convinced of having encountered a reality that is apart from me and that has not waited until I am there to take the form that I discover." Bourguignon, by contrast, argues that mathematics is a product of human minds. Asked if math has an independent existence, he replies: "No, I think that the cultural context determines the emergence of certain concepts." There are also interviews with historian of science A. Dahan and philosopher A. Barberousse.  Allyn Jackson
"Déjà Vu Disks," by Sourish Basu. Scientific American, September 2007, pages 3031. The déjà vu is the similarity between the current battle between new video technology content providers and codebreakers, which resembles the previous battle when DVDs first came out. In the earlier battle, decryption methods, rendered illegal by the Digital Millennium Copyright Act, were distributed via haiku, tattoo, and as a prime number (which Basu writes made it the first illegal number). One cryptographer said that "making digital files impossible to copy is about as easy as making water not wet." Now Bluray and HD DVD have much tougher encryption methods than original DVDs did. In fact, each player has a unique set of digital keys, and if a player is hacked, content providers can produce disks that won't play on that player but will play on others. Earlier this year codebreakers discovered and published a key online, so a revised key was created, which has also since been broken. One way to end the battle is a collective licensing scheme, like the one used by radio stations for music, but the entertainment industry has resisted this for video media.  Mike Breen

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