April 2010
"Biological Systems Theory," by Jeremy Gunawardena. Science, 30 April 2010, pages 581582. The resilience of biological structures experiencing changes in their environment has long been of interest to biologists, and mathematics may help identify which types of structures are most robust. Mathematician Martin Feinberg and biologist Guy Shinar recently proved a theorem that identifies structural attributes of a network which lead to absolute concentration robustness. If the concentration of a component in a network is not affected by changes in concentrations of other components, the network is said to display absolute concentration robustness. Understanding the robustness of a network helps explain how and when cells can continue to function properly despite variations in their environment. The researchers give a mathematical notion of robustness by representing reactions in a biochemical network by systems of differential equations whose solutions may include many positive steady states. They then say a network has absolute concentration robustness if there is some component whose concentration is the same in all possible positive steady states. While experiments have identified certain networks to be robust, this theorem helps explain why they are robust and identifies a large class of systems that have absolute concentration robustness. Dr. Gunawardena closes his commentary on Feinberg and Shinar's paper ("Structural Sources of Robustness in Biochemical Reaction Networks," pp. 138991 in the 12 March 2010 issue) by stating that mathematical tools are becoming more vital to biology as the focus shifts from identifying functions of components of a system to explaining properties arising from interactions between these components.  Brie Finegold "Electoral Dysfunction: Why Democracy is Always Unfair," by Ian Stewart. New Scientist, 28 April 2010. The author charges that ensuring the fairness of political elections is a task for mathematicians, who must ensure that each vote is worth the same when counted. He notes, however, that achieving perfect fairness is not possible because each method for allocating representation based on votes has at least one mathematical flaw. Deciding which flaws are most acceptable is, in contrast, a task for human judgment. The author examines the plurality method, in which the candidate with the most votes wins the position but all votes for the losing candidates are “wasted,” and candidates can win the election with less than 50% of the votes. Another method, in which voters rank preferences rather than choosing just one candidate, can result in a paradox in which all candidates appear as winners. Tying the seats a political party holds in government directly to the proportion of voters that chose that party appears to be more fair, but it is impossible to represent an exact proportion of a large population using a whole number for the amount of seats.  Lisa DeKeukelaere "Hooked for Life on Math," by Terence Tao. CNN.com, 25 April 2010. As one of millions of Americans being counted as part of the 2010 U.S. Census, Fields Medal winner Terence Tao shares insights into his personal discoveries and views on life. A native Australian, Tao moved to the U.S. to attend Princeton University in 1992 and married an American, becoming an American citizen himself last year. Tao, who was attracted to mathematical puzzles and logical thinking even as a child, recounts his realization as a university student of the power of mathematics in understanding the seeming paradoxes of the world. His brief autobiography reveals him to be first and foremost a captivated mathematician.  Lisa DeKeukelaere "Playful Shapes." Random Samples, Science, 23 April 2010, page 409. On June 25, the Exploratorium in San Francisco opened the Geometry Playground, a group of 20 exhibits, which exhibit director Thomas Rockwell says combines "handson with bodyin geometry." According to the Exploratorium, "this exhibition is one where geometry is based on action. Sometimes you'll use your hands, other times your entire body. And always your brain." Before the exhibit opens Rockwell and the museum's science education researcher are studying use of the playground to see how "navigation or climbing through structures involves spatial reasoning." The exhibit runs through Labor Day and then will travel to Minneapolis, San Diego, and other cities in the U.S. (Photo of a visitor to the "Stellated Rhombic Dodecahedron" by Amy Snyder© Exploratorium.)  Mike Breen "Mets statistical analyst has seen growth and evolution of sabermetrics in MLB," by Jenny Vrentas. The StarLedger, 23 April 2010. Ben Baumer is a doctoral student in math at the CUNY Graduate Center who has been a statistical analyst for the New York Mets since 2004. He answers questions about how the team is doing and provides breakdowns of the various matchups between Mets' players and their opponents. Baumer is also exploring the application of statistics in new ways, such as measuring fielding ability. He says, "In the case of baseball players, we know there is some combination of skill and some combination of luck, and the trick is to try to discern how much of each we're getting." About half of Major League baseball teams now have a person who does statistical analysis. Vrentas writes that "Baumer is careful to point out that the numbers he runs bring an independent viewpoint to the game, but they don't imply causality (i.e., explaining the Mets' struggles over the past year)."  Mike Breen "Wise Up With The Apples in Stereo's Space and Time MathPop," by Scott Thill. Wired, 20 April 2010. Rob Schneider, the leader of The Apples in Stereo, loves math. In fact, Thill had to wait for Schneider to return from the Gathering for Gardner, a semiannual conference in honor of Martin Gardner, to do the interview. Schneider has created a 12note nonPythagorean scale based on logarithms, which he used on the band's new release Travellers in Space and Time. In the article, which links to a longer interview, Schneider says, "Playing with a scale tuned to logarithms reveals different mathematical relationships to the ear than are revealed in the usual chromatic scale,...[the beat frequencies and overtones] are often also notes in the scale, which just is a beautiful and very futuristic idea to me, to have this extra layer of meaning and information in the music to play with." [Image: Cover photo of Travellers in Space and Time, click for a larger image.]  Mike Breen "Make Math a Gateway, Not a Gatekeeper," by Anthony S. Bryk and Uri Treisman. Chronicle of Higher Education, 18 April 2010. The authors of this article focus on why so many students in community colleges struggle with traditional remedial math courses. "Remedial math has become an insurmountable barrier for many students, ending their aspirations for higher education," they write. "To earn a degree, certificate, or license, community college students usually must complete a collegelevel math course. However, the relationship between this particular course requirement and the specific quantitative competencies necessary for future success at work is often unclear to students." To address this problem, the Carnegie Foundation for the Advancement of Teaching is organizing a network of faculty members, researchers, community colleges, and professional groups to develop a new sequence of math courses for community college students that will bring the students up to the level of and through a course in statistics. The idea is that such a sequence would provide solid grounding in mathematics that is used in many professions. Bryk is president of the Carnegie Foundation for the Advancement of Teaching, and Treisman is a senior partner with Carnegie and founder and executive director of the Charles A. Dana Center at the University of Texas at Austin.  Allyn Jackson
Opinionator Columns by Steven Strogatz: Recently, in his series of blog entries "on math, from basic to baffling", Steve Strogatz writes "Naturecue the theme from The Twilight Zonesomehow knows calculus." He is referring to the fact that natural phenomena often seek the path of least resistance, minimizing energy expended i.e. seeking the point at which a derivative is equal to zero. Using plenty of pictures and analogies, Strogatz gets across this basic yet beautiful point. Following up on his explanation of derivative is the next blog entry "It Slices, It Dices" which focuses on the reconstructive powers of the integral. Although he mentions it by name, rather than trying to explain the Fundamental Theorem of Calculus, Strogatz decides to discuss its consequences and historically groundbreaking nature. He discusses how an unfamiliar shape like the bicylinder can better understood as decomposed into slices, as an accumulation of layers. Integral calculus requires us to take a, as Strogatz writes, "a VegOMatic view of the universe". (The "VegOMatic" is a product that slices your veggies in one fell swoop.) This view is one that facilitates the understanding of most physical laws, and so integral calculus gives a means of predicting physical behaviors. For readers who are more curious about calculus, Strogatz provides many references including a heuristic explanation for the fundamental theorem involving a staircase. Perhaps readers will integrate the slices of information that have appeared in his posts over the last few months to form an accumulated appreciation for mathematics.  Brie Finegold "Adding Humanitarian Value to Mathematics," by Elisabeth Pain. Science, 16 April 2010. In the face of emergency, humanitarian agencies rely on donated expertise in healthcare, law, and even mathematics. As an associate professor of Operation Research at the Complutense University of Madrid, Dr. Begoña Vitoriano first became interested in humanitarian projects through her involvement in the 90's in setting up a Masters programs in Statistics in El Salvador and Peru. Despite having faced several hardships in her own life, she says "I was shocked when I went there because being here, I really never could imagine how [precariously] other people are living in the world". Prior to traveling to and from South America, Vitoriano had been studying the setcovering problem, which asks, given a family of sets, whether there is a finite subfamily of a certain size whose union is the same as the original family. As her research became more focused on applications, she studied subjects ranging from the railway collisions to farm planning . In 2001, her student, Antonio Omana, won an award from Engineers Without Borders for a computer tool he designed to help decisionmakers respond to emergencies. Spurred by her colleagues, Vitoriano travelled to Mozambique in 2005 to volunteer for a rural development project with with Africa Directo. Her intention was to enhance education, but she realized that the distribution of basic needs like healthcare, food, water, and electricity were more pressing. Currently, she is part of a group of researchers who are designing computer tools that assess the severity of an emergency and then provide guidance on how to efficiently distribute resources to provide relief. Many military agencies pay top dollar to operations researchers who help create protocols for emergency situations and tools to mediate their losses on the battlefield. However, by the end of this year, Vitoriano's research group hopes to make the tools they are developing freely available (via the Web) to humanitarian agencies. [Photo: Begoña Vitoriano in Mozambique, 2007 (Courtesy, Begoña Vitoriano).]  Brie Finegold "Guaranteed randomness," by Valerio Scarani. Nature, 15 April 2010. This piece summarizes the findings of the paper "Random numbers certified by Bell's theorem," by S. Pironio et al (page 1021 in the same issue), in which the researchers "describe a method for obtaining numbers that are guaranteed to be random and private from an unknown process, provided that the numbers are certified as being derived from measurements on quantum systems." Scarani shows a Dilbert comic strip from the "Tour of Accounting" in which a random number generator repeats "Nine, Nine, Nine, Nine, Nine, Nine," and explains that that sequence is as random as 1,2,3,4,5,6 or 4,6,7,1,3,8. But the new method by Pironio et al that generates guaranteed, private randomness should have applications in the realm of internet security.  Annette Emerson
"Q&A: John Sims on Mathematical Art," Interview by Jascha Hoffman. Nature, 15 April 2010, page 983. In the Nature piece, conceptual artist/mathematician John Sims discusses his views on the power of producing and viewing mathematical art, in light of his current exhibit at the Bowery Poetry Club in New York City. Sims sees art and math as united in their search for truth, but different in their methods for pursuing it. Combining the two, according to Sims, provides a better platform for understanding the world than each discipline does when taken on its own, and helps stimulate deeper thinking, providing a balance in our often vacuous pop culture. His exhibit presents geometric art, by both mathematicians and professional artists, paired with a written response from a former U.S. poet laureate. Sims believes that mathematics is better taught as an accompaniment to art than as a strict science, and describes a current project at the Brooklyn Academy of Art and Environment in which mathematicians and scientists share a wall of M.C. Escherinspired tessellations and mathematical symbols as graffiti art. The Art in America article also notes the series of nine shows through August 2010 curated by Sims, Rhythm of Structure: Mathematics, Art and Poetic Reflection. The shows are divided into three groups of threegeometric, conceptual, sociologicaland this reviewer describes the current installation and recent performance developed for the location. See Rhythm of Structure on Facebook. [Photo of John Sims by Debbie DeAmorim.]  Lisa DeKeukelaere and Annette Emerson "The fragility of interdependency," by Alessandro Vespignani. Nature, 15 April 2010. Recent earthquakes, the volcano in Iceland, Internet vulnerabilities, and terrorist attacks that triggered a cascade of failures demonstrate "the need to consider mutually dependent network properties in designing resilient systems." Researchers of such complex networks (Sergey V. Buldyrev et al, "Catastrophic cascade of failures in interdependent networks," p 1025 of the same issue) use percolation theory. Their model shows that "the failure of nodes in one network can lead to a failure of nodes in a second network that in turn can cause the escalation of failures in the first network, ultimately leading to the disruption of the system." Vespignani notes that not all realworld system failures are defined by a connectivity problem, but that the research models can be used "by introducing higher levels of realism, and by simultaneously tackling engineering issues and globally emerging features in the analysis of infrastructure resilience."  Annette Emerson "Reunited Set of Math Problems Gives Clues to How Lincoln Learned," by John Reynolds. The State JournalRegister, 14 April 2010. It may surprise you to know that the oldest known documents of Abraham Lincoln are not from his presidency, his term in the U.S. Senate, or his law practice. Rather they are 10 pages from an arithmetic copybook created by Lincoln in the 1820s. Recently, the work of researchers with the Papers of Abraham Lincoln project has digitally reunited two of these partial pages, one found at the University of Chicago and the other at Brown University. On one side of this reconstructed page, Lincoln wrote several questions and answers about direct and indirect proportion; on the other side he wrote and solved a series of exercises. Lincoln copied this work from The Schoolmaster’s Assistant, Being a Compendium of Arithmetic, Both Practical and Theoretical in Five Parts, originally published in London in the 1740s. The editor of the Papers, Daniel Stowell, points out that these documents provide some interesting insights into Lincoln. “We know that later on, when he was a politician and an attorney, he would read the newspapers out loud to himself. He told people, ‘Well, that gives me two senses, I see it, but I also hear it.’ Here, he could have just read this book, but he is also copying it out. So it seems to me a pattern is developing of a way of learning.” Claudia Clark
Reviews of Duel at Dawn: Heroes, Martyrs, and the Rise of Modern Mathematics, by Amir Alexander: Brady reviews Amir Alexander's book Duel at Dawn: Heroes, Martyrs and the Rise of Modern Mathematics in Forbes. In the early 19th century, Brady writes, "mathematics began to evolve from a science based in the empirical realities of the Enlightenment to an art form informed by the ideals of Romanticism, concerned only with its own internal truths. Through the life stories of... Evariste Galois, Niels Henrik Abel and Janos Bolyai, Alexander reveals how their transgressive work changed mathematics and led to their lionization as Romantic heroes." At the same time, according to Brady, Alexander debunks the myths surrounding these men, providing "concise yet compelling biographical sketches," and portraying them "warts and all, with all their petty jealousies, personal foibles and professional rivalries exposed." Brady also finds Alexander's suggestion in his introductionthat readers may skip the sections that discuss equations and formulasunnecessary. In fact, he finds these chapters to be "among the most engrossing and informative parts of the narrative, thanks to Alexander's crisp, comprehensible prose," praising in particular Alexander?s analysis of Bolyai's discovery of nonEuclidean geometry. In Hoffman's review in Nature, he focuses on the shift stereotypical views of mathematicians during the Romantic era. "As the ideal of the mathematician shifted from worldly scholar to tortured soul, so did the pursuit of maths itself, from an Enlightenment effort to model the Universe to a Romantic quest for a hidden truth." Hoffman notes that the archetype endures, in mathematicians such as Gödel, Ramanujan, Nash, and most recently Perelman. "Yet Alexander speculates that, in this era of computerassisted proofs, the vision of the mathematical martyr might fade away to be replaced by a different stereotypethe powerhungry nerd." In any case, Hoffman says the book is valuable for its revelations about "gloriously complicated men."  Claudia Clark and Annette Emerson "Counting on Each Other," a review by Liesl Schillinger of The Solitude of Prime Numbers, by Giordano Paolo. New York Times Book Review, 11 April 2010. Italian author Paolo Giordano uses prime numbers, and the space between them, as a metaphor for human relationships in his book The Solitude of Prime Numbers, an Italian bestseller recently translated into English. Giordano's book explores the relationships between his two main characters, the emotionally detached and neurotic Mattia and Alice, and their suitors, who try to ascribe feeling where none is present. Giordano's presents Mattia and Alice as prime numbers; even when relatively close together, like the numbers 11 and 13, they will never truly touch. Mattia further likens the rarity of close prime number pairs as one advances along the number line to the human conditionor at least his own of preferring solitude over companionship. The reviewer notes that Giordano, a physicist by training, has crafted complex and deep characters through which to explore what she terms "the mechanics of need."  Lisa DeKeukelaere "Conquering by Copying," by Elizabeth Pennisi. Science, 9 April 2010, page 165. Imagine yourself transported back in time circa 10,000 years. How do you gather food and stay safe from predators in an everchanging environment? Do you spend your time innovating or copying others? Two graduate students surprised the behavioral science community by designing the winning algorithm in a social learning contest addressing the above questions. Even more surprising, the strategy, developed by Timothy Lillicrap a neuroscience student and Daniel Cownden a mathematics student, relies almost entirely on imitation and not innovation. More than four months of hard work and a combination of analytical and programming skills resulted in the winning formula. A computer program that carries out their strategy went head to head with over 100 other programs and outmatched every single one. The organizers and most other contestants thought innovation would play a more important role, but the tournament's results indicate that copying behaviors is key and plays a larger role in driving human progress than previously thought. [(Photo of Timothy Lillicrap (left) and Daniel Cownden (right), by Bronwyn McLean.]  Baldur Hedinsson "1 Solved. 6 Millennium Prize Math Problems Remain," Interview with Keith Devlin, by Renee Montagne. Morning Edition, National Public Radio, 7 April 2010. Grigori Perelman surprised the math world when he solved one of the most complicated problems in the discipline a few years ago: the Poincaré Conjecture. This problem belongs to a list of seven, each of which is considered to be so important and difficult that the mathematician who provides the first solution will get a prize of $1million. In this interview, Keith Devlin gives brief descriptions of the remaining six Millennium Prize Problems (Montagne asks him for a version "you can put in a tweet"). It is clear that the goal of the interview was to give a broad idea of what the problems involve: physics, computational mathematics, and prime numbers. Some of these problems, if proven to go a certain way, would have important consequences for the assumed security of communications over the Internet. The interview also gives some insight into Perelman, a man so reclusive and uninterested in fame and recognition that Devlin calls him "the mathematical equivalent of J.D. Salinger." It is still unclear if Perelman will attend the prize ceremony in Paris this June, or if he'll even collect the prize money. The Millennium Problems are described in detail in Keith Devlin's book of the same name or at the Clay Mathematics Institute website.  Adriana Salerno "Gathering for Gardner," by Robert P. Crease, Wall Street Journal, 2 April 2010. In this article, Robert Crease reports on the recently held "Gathering for Gardner," a fourday event held in Atlanta in honor of recreational mathematician and "public intellectual" Martin Gardner, now 95. As with previous gatherings, G4G9 (the ninth such gathering) was attended by those inspired by the man who wrote the "Mathematical Games" column for Scientific American for 25 years, as well as dozens of other books on topics that included calculus, relativity, puzzles, magic, and pseudoscience. Among this year's participants were Swedish magician Lennart Green, who performed card tricks, and mathematician John Conway, who discussed his current work. Hacking expert Pablos Holman wowed the crowd by using an inexpensive electronic devise to change one audience member's cellphone voicemail greeting, then displayed another audience member?s credit card information. And former Caltech cognitive neuroscientist Al Seckel ?used sensory illusions to demonstrate how humans 'map' incoming information to support preexisting organizational perceptual frameworks, even if the incoming information is contradictory or false.? In this way, the participants honored the man who "saw the world as resembling not a magazine, where the subject of each section bears little relation to that of the next, but a wellwritten novel, where ideas introduced in one chapter are apt to reappear?transformed, modulated and extended?in others." [Photo: At the G4G9 (2010 Gathering for Gardner). Photograph courtesy of Jimmy Stephens.]  Claudia Clark

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