# 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), Adriana Salerno (Bates College)

### November 2009

"Empathy provides X factor in GED tutoring program," by Sara Olkon. Chicago Tribune, 29 November 2009, page 8.

Some people wear their passion on their sleeves, but Adrianna Collis wears it on her ears and her upper arm. She is a math tutor and the coordinator for the education and vocation program at a youth center in Chicago who has helped 200 people get their GEDs. She loves math so much that she has pi earrings and has the first few rows of Pascal's triangle tattooed on her left arm. Collis is not bothered by not fitting the stereotype of a math teacher: "It's kind of fun fooling the world."

--- Mike Breen

"Invisibility Uncloaked," by Charles Petit. Science News, 21 November 2009, pages 18-23.

Petit writes of scientists' efforts to make objects invisible. Most of the article is about physics, but there is some mathematics discussed, especially geometry and conformal mapping. (See also articles on invisibility summarized in a previous Math Digest as well as the Mathematical Moment on cloaking [pdf].)

--- Mike Breen

Recent Math Masters Columns by Marty Ross and Burkard Polster:
"Even is even and odd is...,"
The Age, 16 November 2009;
"Lucky Friday the 13th,"
The Age, 9 November 2009;
"A Greek in an Italian restaurant," The Age, 2 November 2009.

 As pictured to the left, the 15 Puzzle has 15 numbered tiles in a 4x4 box, with one empty space in the bottom right corner. The object is to use the empty space to slide the tiles into numerical order. When the puzzle appeared around the year 1880 "it created as big a craze as Rubik's Cube a hundred years later. The most popular version was due to the famous puzzler Sam Loyd, who presented all the tiles in order, except with the 14 and the 15 swapped. Loyd offered a prize of AUS$1000--worth about$20,000 today--to the first person to solve his puzzle. The prize was never collected." The authors go on to explain why. In the Friday the 13th article, the authors explain that "The Gregorian calendar was introduced in 1582 and is based on a 400 year cycle. The cycle refers to the choosing of leap years, but it turns out that a 400-year period contains 146,097 days, which comes to exactly 20,871 weeks. This tells us that the days of the week have the same 400-year cycle. This means that to determine the frequency of Friday the 13th, we just have to check through the 4800 months in a 400-year period, and count the number of spooky Fridays." The authors show the calculations. The authors often find everyday examples to introduce or illustrate a mathematical concept. In the restaurant article the authors focus not on the menu, but on the unusual two-color floor tiling pattern. "What is remarkable is that hidden in the floor tiling is a PROOF of Pythagoras's Theorem." The illustrations in the article bring that conclusion to light. --- Annette Emerson

"America’s Top College Professor," by Naomi Schaefer Riley. Wall Street Journal, 13 November 2009.

 Edward Burger—a mathematics professor at Williams College and one of three finalists for Baylor University’s Cherry Teaching Award—knows that most mathematics students will never use calculus after college. As he puts it, “You don’t need to know how to build a bridge to go over one,” which is why his lectures emphasize mathematical thinking and he always considers what he wants his students to remember 10 years after his course. He measures student understanding by how well the student can produce a jargon-free explanation suitable for an adolescent, and his teaching philosophy has made him a wildly popular lecturer at Williams. Burger and his two fellow finalists note that good teaching is itself a slow learning process that requires preparation and practice. This article not only offers insights into the teaching styles of Burger and the other finalists, but also a look at the tendency of colleges to undervalue teaching in relation to publication as a measure of professorial quality. (Photo courtesy of Ed Burger.) --- Lisa DeKeukelaere

"Lincoln East top team at Math Day; LSW's Zhou top individual." Lincoln Journal Star, 12 November 2009.

 Each year the University of Nebraska-Lincoln's Department of Mathematics hosts a math day for Nebraska middle and high school students. On November 12, the department marked the 20th anniversary of Math Day and nearly 1400 students participated in the competition and in other events on campus. The AMS math game Who Wants to Be a Mathematician was one of the events that day. The winner in Who Wants to Be a Mathematician, Albert Zhou of Lincoln Southwest High School who won US$3000 from the AMS and a TI-Nspire graphing calculator from Texas Instruments, was also the big Math Day winner, earning an$8000 scholarship from the university. Many department faculty and students were involved in Math Day, which is organized by Gordon Woodard and Lori Mueller. (Pictured: Left, Albert Zhou and right, Jahan Clase, who won \$500 and a TI-Nspire.) --- Mike Breen

"Q&A: The algorist," by Daniel Cressey. Nature, 12 November 2009, page 166.

Jean-Pierre Hébert is interviewed about his artwork, which he creates using mathematical algorithms. Hébert is a former engineer who is now the resident artist at the Kavli Institute for Theoretical Physics. He prefers to work with physical objects, such as sand, rather than work only with computers. Are algorithms important in art? "Over the past century most artists were algorists, even if they did not know it. Mondrian has an algorithm; cubism was a set of algorithms. Algorithms are just a tool, as is a computer, a brush or a pencil. The personality of the artist takes over and should transpire through the work. Algorithms are not an end in themselves."

--- Mike Breen

Recent articles on the state of mathematics education:
by Jessica Jordan. Gainesville Times, 8 November 2009;
"More Oregon studehts are getting math,"
by Betsy Hammond. The Oregonian, 7 November 2009;
"How to solve math problems,"
by Jeffrey S. Solochek. St. Petersburg Times, 7 November 2009.

The newspapers in Florida, Georgia and Oregon all report progress in their states regarding improving mathematics test scores and, importantly, generating interest of elementary through high school students. The Gainesville Times reports that "while using the state curriculum as a framework for math instruction, local schools are adding their own elements to support student achievement." This includes a successful program that puts students into three groups--remedial, standard and accelerated--to cater to the learning requirements and styles of those students. The article describes how a charter school, the Centennial Arts Academy, infuses math with the arts and how the Hall County schools are implementing Singapore Math, but notes budget cuts undermine teacher training. In Oregon, "math teachers have moved middle-schoolers far enough ahead in math that the typical eighth-grader now can do math at nearly the same level as many high school sophomores," and the article explains the reasons--new textbooks, workshop classes, and innovative methods. In Pasco County, Florida, the Bayonet Point Middle School has been charged with improving math proficiency. Among the new ideas launched--"something other than the well-worn drill and kill""--are peer tutors, smart boards and computerized projectors called Elmo to improve student interactivity, student math clubs, and math games.

--- Annette Emerson

"Quantum Computers Could Tackle Enormous Linear Equations," by Laura Sanders. Science News, 7 November 2009, page 11.
"Warp-Speed Algebra," by Davide Castelvecchi. Scientific American, January 2010, pages 22-24.

Researchers recently proposed a method much quicker than classical computers for solving very large linear equations: quantum computing, which operates using quantum forms such as the spins of nuclei and their properties. Very large linear equations are used to solve problems related to image processing, internet traffic control, and variety of other areas, and quantum computers offer a way to solve these equations in dramatically fewer steps and therefore less time. The advantage of quantum computers is their ability to store both 0 and 1 in a single bit of information, unlike classical computers in which a bit must be either 0 or 1, so an operation that would require many steps in a classical computer can be completed with just one in a quantum system. The idea of using quantum computing to solve linear equations is leading the researchers to seek out other new uses for quantum computing’s powerful abilities.

--- Lisa DeKeukelaere

“Russia’s Conquering Zeros,” by Masha Gessen. The Wall Street Journal, 6 November 2009.

In this article, writer Masha Gessen discusses the reasons that a Russian mathematician would solve the Poincaré Conjecture, one of the most difficult mathematical problems of our time. Several decades ago, mathematics was at odds with the Soviet regime: for example, Gessen observes that “math placed a premium on logic and consistency in a culture that thrived on rhetoric and fear; it required highly specialized knowledge to understand; and, worst of all, mathematics lay claim to singular and knowable truths—when the regime had staked its own legitimacy on its own singular truths.” However, mathematics had some factors in its favor, including its remarkable strength in Russia in the 1930s and, in 1941, the fact that it was needed to recalculate distances and speeds for the newly retrofitted civilian planes that would replace the recently destroyed Soviet air force. During the decades following World War II, Gessen notes, “the Soviets invested heavily in high-tech military research.” The number of people involved in this effort has been estimated to be as high as 12 million, a “couple million” of them employed at military-research institutes. By the 1970s, a mathematics establishment provided jobs, money, and other benefits—within a totalitarian system—to some of its privileged members. Mathematicians who were not welcome, including Jews and women, formed a mathematical counterculture, where, according to AMS publisher Sergei Gelfand, mathematicians did “math for math’s sake.” Their only reward was the respect of their peers. With the fall of the Soviet Union and the end of state investment in mathematics, mathematicians started coming to the United States. Here, Gessen writes, they would find a culture that “offers the kinds of opportunities for professional communication that a Soviet mathematician could hardly have dreamed of, but it doesn’t foster the sort of luxurious, timeless creative work that was typical of the Soviet counterculture.”

--- Claudia Clark

"Somer Thompson's murder: A real-life 'Numb3rs' case?," by Ivy Bigbee. True Crime Examiner, 5 November 2009.

Dr. Kim Rossmo, who earned his PhD in mathematics while he was a police officer in Canada, inspired the pilot episode of Numb3rs. Now at Texas State University, Dr. Rossmo combines his interests in mathematics and forensics by creating new algorithms which pinpoint the location of a serial criminal's homes or areas of activity. Dr. Rossmo has designed new means of geographic profiling, which are being used by law enforcement to narrow their searches for evidence. By taking into account that criminals are just as likely to behave according to patterns as the average Joe, the algorithms pinpoint zones where the perpetrator of a previous crime is most likely living or is most likely disposing of evidence.

People do not commit crimes randomly, but have "comfort zones" as well as zones that are too close to home for pursuing their criminal activities. Little is said in the article about the algorithms themselves, what is new about them, or whether Dr. Rossmo is the first to use geographic profiling. As for Somer Thompson, Ms. Bigbee writes, "Should profilers suspect Somer's murder has similarities --'signatures' or modus operandi --to other area homicides, forensic data banks could be mined to produce a veritable map of the most likely suspects." Although there is no mention as to whether Dr. Rossmo's techniques are currently being used or not in Somer's case, these techniques have been extended to study the hunting patterns of sharks and the flight patterns of bees. Perhaps animals and humans have more in common than we care to think.

--- Brie Finegold

"The Numbers Guy: Coincidental Obscenity Deemed Extremely Dubious," by Carl Bialik. The Wall Street Journal, 5 November 2009.

How likely is it that you will accidentally spell out an obscenity with the first letters of each sentence in a short note? The chances are worse than one in 10 million. But in Governor Schwarzenegger's recent veto "the first letter of each of the seven lines spells out a profane rebuke that starts with 'F' and ends with 'you.'" Prof. Brendan McKay, a computer scientist at Australian National University in Canberra, warns "We shouldn't be too eager to claim a small 'probability' as a proof that something can't have happened accidentally." The Governor claims that this message was coincidental.

Computational linguists, who study patterns in language by using probability and statistics, agree that "secret messages" may coincidentally show up in long written works like the Bible, but such messages are unlikely to show up in shorter documents. For instance, the letter "K" is rare as a first letter of a sentence, but is part of one of the Governor's frequent phrases. Whatever the origin of the message, it has sparked an interest in connections between math and linguistics.

--- Brie Finegold

“Tomorrow’s Weather: Cloudy, with a chance of fractals,” by Robert Matthews. New Scientist, 4 November 2009.

 About 80 years ago, British mathematician Lewis Fry Richardson ventured to posit that the seemingly complex laws governing the atmosphere were actually quite simple. The known equations (worked out by Richardson himself) were extremely complex, and even today the world’s most powerful computers are pushed to their limits when predicting future weather and climate when using these equations. Richardson noticed that the atmosphere seems to exhibit a kind of self-similarity evocative of the one encountered in fractals. In other words, that the atmosphere seems to be a collection of cascade-like processes, with large structures breaking down to feed smaller ones. The controversial suggestion he made was that perhaps the atmosphere was modeled by a power law, like fractals. The idea of a single power law governing atmospheric processes proved to be overly simple, and so Richardson’s ideas were completely disregarded for many decades. This all changed when the notion of multifractal fields, where a system is described by a whole set of power laws, rather than just one, was introduced. Shaun Lovejoy, of McGill University, and Daniel Schertzer, of the University of Paris Est, France, joined forces to follow Richardson’s program in this new context, by searching for evidence of multifractal power laws in weather data. They started by looking at radar data, but the key to their study was in carefully studying satellite data. Earlier this year, they published their findings in Geophysical Research Letters, and their results are groundbreaking. The satellite data generated a beautiful collection of fractals and followed power laws on scales from tens of thousands of kilometers to about ten kilometers. Even though, as Lovejoy cautions “there are many issues to be resolved, and it may be some years before the techniques are implemented,” the results obtained by him and Schertzer seem to be ushering in a new era in our understanding of the atmosphere and the models that describe it. --- Adriana Salerno

“Alice Schafer, 94; math professor breached social barriers,” by Emma Stickgold. Boston Globe, 2 November 2009.

 On September 27, longtime mathematics professor Alice T. Schafer died at the age of 94. Schafer earned her B.A. in mathematics from the University of Richmond, where she was the first female student to take advanced mathematics courses and win the annual mathematics competition. She would go on to encourage other women to learn mathematics throughout her career. After earning her doctorate from the University of Chicago in 1942, Schafer taught at several colleges, eventually retiring in 1996. During the mid-1970s, when mathematics was becoming an increasingly important tool in a growing number of fields, Schafer developed a course at Wellesley College for students who were uninterested in, or fearful of, mathematics. Schafer was also one of the founders of the Association for Women in Mathematics, which, in 1990, named a prize in her honor to be presented each year to an undergraduate student who demonstrates excellence in mathematics. In 1998, Schafer received the Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service to Mathematics from the Mathematical Association of America. Part of the citation reads as follows: "As a mathematics educator, she championed the full participation of women in mathematics. She has been a strong role model for many women and has worked to establish support groups for women in mathematics, to eliminate barriers women face in their study of mathematics and participation in the mathematics community, and to provide opportunity and encouragement for women in mathematics." (Photo: Wellesley College Office for Public Affairs) --- Claudia Clark

"The Brain," by Carl Zimmer. Discover Magazine, November 2009.

Are our brains naturally wired for math? The answer seems to be yes, and that in fact our brains have been recognizing and understanding numbers for about 30 million years. Since the moment they are born, humans have an uncanny ability to understand numbers. But how does this innate sense develop as we grow older and learn new skills? Jessica Cantlon, a neuroscientist at the University of Rochester, and Elizabeth Brannon, of Duke University, investigated this question by designing an experiment that forced adults to rely on intuition alone. People would be shown two consecutive sets of dots on a computer screen, and then two sets side by side, and they scored points by selecting the set which represented the sum of the previous two. The scientists discovered that mathematical intuition consistently follows two rules. First, people scored better when the numbers were smaller, and second, they also scored better when the difference between the two numbers was large. These two rules have also been observed in babies and even monkeys, which suggests that our brains use the same mental algorithm throughout their lives, and have been for at least 30 million years. This begs the question: where in the brain is this happening? Neuroscientists have found that for both humans and monkeys the area that is most active while doing mathematical intuition problems is a strip of neurons near the top of the brain, surrounding a fold called the intraparietal sulcus.

Andreas Niedler, from the University of Tubingen, developed experiments which show that monkeys can even learn written numbers, a skill children develop only around age 5. Monkeys seem to have a very solid foundation for numbers, so why are they not able to perform high-level mathematics? Nieder and Cantlon have both speculated that our ability to understand symbols enables us to transform our intuition into a precise understanding. Even though our ancestors probably started out thinking about numbers the way monkeys and babies do, once they linked their natural instincts with an ability to understand symbols, everything changed.

"Crash Test Anti-Dummy," by Bjorn Carey. Popular Science, November 2009.

 André Paltzer, named one of PopSci's "Brilliant 10" most promising young researchers. Photograph by Ken Andreyo, Carnegie Mellon University. André Platzer, a computer scientist at Carnegie Mellon University, is named one of Popular Science magazine's "Brilliant 10" for 2009. His KeYmaera software helps computer-controlled safety systems avoid catastrophic events. His models can correct errors that could cause planes and trains to collide. --- Annette Emerson