# 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)

### May 2007

Mathematics on Talk of the Nation, All Things Considered, and Morning Edition. National Public Radio, May-July 2007.

Various mathematical topics---math and music, technology, health and science, people, and books---are discussed on National Public Radio. The abstracts and audios for the segments, aired in May through July, can be accessed by searching for "mathematics" on http://www.npr.org. Segments include "New Tornado Rating System Scales Back Winds," (All Things Considered, 12 May 2007), "Computers May Help Identify Phony Art" (Talk of the Nation, 18 May 2007), "Fish Virus Spreads in Great Lakes" (Talk of the Nation, 25 May 2007), "Predicting Popularity: The Math Behind Hit Music" (Talk of the Nation, 25 May 2007), "Home-Schooled Student Wins Spelling Bee" (All Things Considered, 1 June 2007), "Economic Lessons from 'The Price is Right'" (Talk of the Nation, 14 June 2007), "Technology for Unmanned Planes Shown in Paris" (Morning Edition, 21 June 2007), "New Biography Focuses on Einstein's Creativity" (Talk of the Nation, 6 July 2007), and "The Magical Qualities of the Number 7" (Weekend Edition - Saturday, 7 July 2007).

--- Annette Emerson

"Fat Tails," by Brian Hayes. American Scientist, May-June 2007, pages 200-204.

Hayes presents what he calls the factoidal "function," one with no average. The factoidal evaluated at n, denoted n?, multiplies randomly chosen integers between 1 and n, inclusive. It terminates when 1 is the chosen integer. He likens it to "rolling an n-sided die and keeping a running product of all the numbers seen until a 1 appears." Its name is chosen because of its similarity to the factorial function, n!. As n increases, the proportion of n? values (in repeated trials) greater than n! converges to 1/e. For a fixed n, the median of n? results is finite, as is the geometric mean. But because of a few large values of n?, the arithmetic mean---the average---is undefined. The distribution of n? values for a fixed n does not die out exponentially; it is more like the distribution of incomes or of city populations---fat-tailed, obeying a power law. In addition to discussing n?'s properties, Hayes gives sources for similar functions.

--- Mike Breen

"The Most Dangerous Equation," by Howard Wainer. American Scientist, May-June 2007, pages 249-256.

 Abraham DeMoivre. The equation e = mc2 could be called dangerous because it led to the development of the atom bomb. Wainer, however, is interested in an equation that unleashes its danger when people know nothing about it. The equation he writes about is the one giving the standard deviation of the sample mean. This equation, which Wainer attributes to Abraham de Moivre, says that the standard deviation of the sample mean equals the population standard deviation divided by the square root of the sample size. Thus, averages of small samples should have more variation when compared to large sample averages. Wainer cites five examples in which ignorance of this equation led to improper conclusions. In one instance, money was spent to splinter large schools into smaller ones because student achievement was thought to be higher in smaller schools. And in fact, smaller schools are disproportionately represented at the top (based on test scores) in a study Wainer did of Pennsylvania schools. But smaller schools are also disproportionately represented in the bottom group of schools. Average test scores at smaller schools have more variance than those at larger schools, and so smaller schools are over-represented at both extremes. When the larger schools were broken up, the resulting smaller schools had fewer teachers and so couldn't offer certified teachers in as many subjects as larger schools could. The splintering of larger schools was stopped. Wainer hopes that this article will help inform people so that similar mistakes aren't made. --- Mike Breen

"Three-square": Review of The Pythagorean Theorem, by Eli Maor. Reviewed by Ben Longstaff. New Scientist, 26 May 2007, page 56.

Taught to school kids the world over, the Pythagorean theorem states a fundamental relationship among the lengths of the sides of a right triangle. This short review calls the book "an excellent biography of the theorem" that "makes for hours of glorious mathematical distraction."

--- Allyn Jackson

"'Reform Math' Leaves Some Perplexed," by Sharon Alfonsi. CBS Evening News, 26 May 2007.
"Battle Over Math in New Jersey Drives Off a New Schools Chief," by Winnie Hu. The New York Times, 14 June 2007.

The CBS report features people from both sides of the "Reform Math" movement. Amy Dillard, author of a reform textbook Everyday Math, explains that, "We're preparing kids now for jobs that we don't even know are going to exist, and we can't be teaching them the same mathematics that we did years and years ago, we really have to prepare them for the workforce that they'll be headed to." Carol Rounds, parent of a second grader, can't believe that her son's homework doesn't contain a single number. She's shown using subtraction flash cards with her son. Alfonsi concludes with, "Both sides are trying to give kids the tools they need for the future; the two sides just can't agree on the best way to solve the problem." In a related story, Martin Brooks, hired to take over as superintendent in Ridgewood, NJ after a nine-month search, backed out because of disputes about how math is taught in the district. The Times article (quoting the town's school board) said that "Martin Brooks, had been made to feel unwelcome by 'anonymous phone calls, e-mail messages, blogs and Web postings by some community members' that 'questioned his integrity, ethics and educational philosophy.'"

--- Mike Breen

"Why Mathematical Models Just Don’t Add Up," by Orrin H. Pilkey and Linda Pilkey-Jarvis. Chronicle of Higher Education, 25 May 2007, page B12.

Article authors Pilkey and Pilkey-Jarvis argue that quantitative mathematical models are inaccurate for predicting natural events—such as the transport of sand between beaches—because natural phenomena are driven by too many unpredictable factors to be precisely understood. Qualitative models, which rely on general principles instead of numbers to track trends, deliver more vague answers that are no more correct than their quantitative counterparts, according to the authors. They argue that all models must make assumptions about factors driving natural events in order to be workable, but the assumptions handicap the accuracy of the predictions. Their suggestion for evaluation of a model is titled the "embarrassment test": If the model’s creator would feel embarrassed describing to other scientists the assumptions the model makes, then the model should not be used. The authors are clearly frustrated by the government’s use of mathematical models in decision-making and they argue that worthy models are impossible to create, but they offer no alternatives.

--- Lisa DeKeukelaere

"Newsmakers---Movers." Science, 25 May 2007, page 1107.

Robert Bryant made the news in Science for being named the next director of the Mathematical Sciences Research Institute. He succeeded David Eisenbud on August 1. One of Bryant's goals as director is to "improve the exchange between the math and science communities."

--- Mike Breen

"Commencement 2007---Some Noteworthy Graduates," by Don Troop. Chronicle of Higher Education, 25 May 2007, page A6.

Included in these graduation-related stories in the Chronicle's Short Subjects was one about Betty McKnight Speairs, 82, who taught mathematics at Centenary College until 1987. She walked in every commencement ceremony at the college since 1947. Betty did not have her doctorate---until the 2007 commencement, when the college awarded her an honorary degree.

--- Mike Breen

"Swedish University, Alleging Culture Clash, Forces Out 2 Tenured Foreign Professors," by Aisha Labi. Chronicle of Higher Education, 25 May 2007, pages A49-50.

Oleg Viro and Burglind Jöricke were forced to resign their positions in the mathematics department at Uppsala University because of their clashes with other faculty members. Such clashes are not only against the norm in Sweden, but also they can be illegal. According to the article, in Sweden, "Compromising the quality of a workplace environment is seen as a breach of contract that can culminate in dismissal, although only after legal proceedings." The director of the Swedish Association of University Teachers says, "The question of tenure is basically one of academic freedom---the freedom to pursue your line of research and to choose this line of pursuit... and that academic freedom is not the freedom to behave rudely to others." In a letter to Sweden's education minister, mathematicians at Harvard, Princeton, Berkeley, and other institutions wrote, "the forced resignation of two professors, especially of this caliber, is unprecedented, not only in Sweden but also in the recent history of academia in democratic countries."

--- Mike Breen

"Awards for Eugene math whiz keep adding up," by Richard L. Hill. The Oregonian, 21 May 2007.
"Hot Competition," by Emily Sohn. Science News, 26 May 2007, page 326.

 Pictured, left to right, Vaintrob, AMS Menger Prize Committee chair Tatiana Shubin, and other Menger Prize winners Almas U. Abdulla and Lado Meskhishvili. One of the three top prizes---a US$50,000 scholarship---at the 2007 Intel International Science and Engineering Fair went to Dmitry Vaintrob's math project "The String Topology BV Algebra, Hochschild Cohomology and the Goldman Bracket on Surfaces." Vaintrob, who went to South Eugene High School, says, "I like the fact that [math is] abstract and beautiful and makes sense always." Vaintrob also won the first-place Menger Award from the AMS for his project. Earlier in the academic year he won the top award, US$100,000, in the Siemens Competition in Math, Science and Technology. Other Intel winners were Dayan Li of Eleanor Roosevelt High School (MD), and Philip Vidal Streich, who is home-schooled in Platteville, WI. --- Mike Brren

"Der Zufall führt manchmal auch ans Ziel (Randomness sometimes also leads to the goal)", by George Szpiro. Neue Zürcher Zeitung, 20 May 2006.

This article discusses the mathematical theory of percolation and in particular the work of Alain-Sol Sznitman, a mathematician at the Eidgenössisches Technische Hochschule in Zurich.

--- Allyn Jackson

"Time enough for countin'": Interview with Chris "Jesus" Ferguson. Interviewed by Michael Brooks. New Scientist, 19 May 2007, pages 52-53.

Chris Ferguson gained the nickname "Jesus" for his beard and long hair. He is a professional poker player who uses game theory, which the article describes as "the branch of mathematics that predicts the optimal outcome of competitive situations". While spending 13 years completing a PhD in computer science at the University of California, Los Angeles, Ferguson played a lot of poker and developed game-theoretic approaches to perfect his strategy. He has won more than US$4 million and a champion title in the World Series of Poker. Asked for an example of how game theory helps in poker strategy, Ferguson replies that the theory can help one figure out how often to bluff. "It turns out the best hands to bet are your best and worst hands, but you need to bet them in the right ratio, betting your bad hands one-third of the time," he says. Ferguson believes that computers will one day excel at poker but that there is a "big human element" to the game that would be hard to teach computers. Although he has won a lot of money playing poker, Ferguson is not out to milk players whose strategies he has figured out. "There will always be people who keep on putting their money on the table, but I don't want to be the one who takes it," he says. "I don't think it's fair, and I don't enjoy it." But winning a poker tournament, where all the players have paid the casino before the competition starts, is a different story. --- Allyn Jackson Return to Top "A fine fight": Review of The Poincaré Conjecture, by Donal O'Shea. Reviewed by Ben Longstaff. New Scientist, 19 May 2007, page 58. This brief review says that the approach of the book is more narrative than technical but that the author "conveys the gist of topology's mind-bending contortions with great flair." --- Allyn Jackson Return to Top "Hedge fund guru: Improve U.S. math skill," by Madlen Read. Associated Press, The Houston Chronicle, 19 May 2007. James Simons, a billionaire hedge fund manager, years ago was the first student to receive a fellowship from the National Defense Education Act to study math. In 2004 he founded Math for America, and recently his foundation donated US$10 million to the Mathematical Sciences Research Institute. His interview with AP reporter Madlen Read about math education's importance in America's competitiveness in the job market ("he knows a thing or two about the laws of supply and demand") was also reported in the International Herald Tribune, Boston Globe, Business Week, ABCnews.com, Prescott Herald (AZ), and Wyoming News. There was also a local television broadcast about the donation to MSRI: "Berkeley: Mathematics Institute Adds US$10 Million to its Coffers," CBS5 (KPIX-TV), 4 May 2007. --- Annette Emerson Return to Top "Muslim World of Mathematics." The Muslim Weekly, 18-24 May, 2007. The article names several Arab and Persian scholars over the centuries who made many contributions to mathematics. Musa al-Khwarizmi (780-850 A.D.) is known as one of the greatest Islamic mathematicians. Other names---Al-Nasavi, Abu Zakariya Muhammad Al-Hissar, Nasir-ud-din Toosi, Omar Khayyam, Jabir Bin Afiah, and Abul Wafa---may be less familiar even though we use their mathematical contributions to this day. Among the achievements outlined in the article: writing fractions in the form used today, division of fractions, extraction of square and cubic roots, and the decimal system, as well as important works in geometry and trigonometry. The article concludes, "Such were the great mathematical giants which the Muslim world produced, who were not only the pioneers of mathematical science during mediaeval times, but are considered to be authorities on several mathematical problems even during the modern age. The development of mathematics owes a great deal to the genius of these Muslim luminaries." --- Annette Emerson Return to Top "The Prosecutor's Fallacy," by Mark Buchanan. The New York Times, 16 May 2007.  In 2003, Lucia de Berk---a 45-year old nurse---was convicted of murder and attempted murder, and she is now serving a life sentence in a Dutch prison. During her trial a statistical expert claimed that there was a 1 in 342 million chance that suspicious deaths at the hospital where de Berk worked were coincidental. This figure helped convict de Berk. Since the trial others have looked at the evidence and found that first, some of the deaths blamed on de Berk weren't labeled as suspicious until after she was identified as a suspect, and second, the rate of suspicious deaths at the hospital actually dropped during the period under investigation. Mathematician Richard Gill (University of Leiden) says that the probability of coincidence in this case is at least 1 in 50 and could be higher. In addition to the probability miscalculation, there is also the matter of the prosecutor's fallacy, in which at trial the chance that the defendant is innocent given the facts (which is what a judge or jury wants to know) is confused with the chance of the facts occurring given that the defendant is innocent (the chance of coincidence, the number quoted at trial). A judicial committee is investigating the legitimacy of de Berk's conviction and should have a decision soon. Buchanan also cites a case in England in which a mother was convicted of murdering her two sons based almost entirely on bad statistics and the prosecutor's fallacy. --- Mike Breen Return to Top "Is that painting real? Ask a mathematician," by Elizabeth Svoboda. Christian Science Monitor, 10 May 2007.  Vincent Van Gogh, self portrait. After the sale at auction of van Gogh's Still Life: Vase with Fifteen Sunflowers for US$39.9 million in 1987, some wondered if the painting was genuine or a fake. Now in 2007 computer scientist Richard Johnson (Cornell University) and a team are using "stylometry" to analyze the work. This method, which uses statistical formulas, is a tool to determine authenticity of letters, literary works, musical compositions as well as works of art. While Daniel Rockmore (Dartmouth College) and Jose Binongo (Emory University) have also used this and related methods, some remain skeptical that formulas and technology can authenticate attribution. Svoboda's article was picked up by USA Today and CBS News. --- Annette Emerson

"Designers did the math before starting their business," by Mary Beth Breckenridge. Akron Beacon Journal, 6 May 2007.

Two interior redesigners---Elizabeth Feeney and John Hively---are using the golden ratio, phi, in their redesigning and even named their business after the constant. The got advice about phi from Timothy Norfolk at the University of Akron. The article explains a little bit about the golden ratio, but is mostly about how Feeney and Hively use the ratio in their work, positioning furniture and pictures in accordance with the ratio. Before knowing about phi, Feeney tried many arrangements in her living room, but none worked. Now that she's used phi to position pieces in the room? "I haven't moved the furniture in months."

--- Mike Breen

"Sensor Sensibility," by Erica Klarreich. Science News, 5 May 2007.

Klarreich reports on the work of some mathematicians and engineers to provide information about the structure of future wireless sensor networks and the data they provide.

For example, if a network uses few sensors, it may be practical to equip each sensor with a global positioning device to determine if the entire area under study is within range of at least one sensor. But for the much larger sensor networks anticipated by engineers, the cost would be prohibitive. Mathematicians Robert Ghrist and Vin de Silva have shown in the December 1, 2006, International Journal of Robotics Research how topology can be used to identify whether a network of sensors provides full coverage of an area: They determine the homology of a theoretical shape known as a Rips complex used to represent the sensor network.

What if sensors are used to count a specific object, such as the number of boats in a harbor: is it possible to get an accurate count if at least one of the boats can be counted by more than one sensor? Ghrist has worked with Yuliy Baryshnikov of Bell Labs on this problem. They have found that it is possible to get an accurate count by calculating a variation of the Euler characteristic.

You can read more about Ghrist's and de Silva's work in the January 2007 Notices of the American Mathematical Society ("Homological Sensor Networks").

--- Claudia Clark

"The Mathematical Lives of Plants," by Julie Rehmeyer. Science News Online, Week of 5 May 2007.

 The discovery that the spatial relationship between structures within a plant---such as the seeds of a sunflower or the bracts of a pinecone---conformed to the "golden angle" (related to the golden ratio) was a fascinating link between mathematics and biology, but the key question became what this discovery could tell us about how plants grow. Work on the question is ongoing, but a series of discoveries is building an explanation. German botanist Wilhelm Hofmeister in 1868 theorized that groups of undifferentiated cells at the tip of a plant would form in the spot farthest from the older groups of such cells, extending the stem outward and downward. Two British physicists found the connection between Hofmeister's work and the golden angle by observing the movement of magnetized droplets in a dish with magnetized edges---a new droplet would move away from its landing point in the direction of the golden angle with respect to the line connecting the landing point and the previous drop. --- Lisa DeKeukelaere

"Puzzle Me This," by Lauren Smith. Chronicle of Higher Education, 4 May 2007.

 Picture from the puzzle box, courtesy of David Redman Professors and students at Delta College (Michigan) used a 18,240-piece jigsaw puzzle in a middle school mathematics competition. First the Delta team assembled the puzzle, then they disassembled it into 285 64-piece squares, each disassembled into four 16-piece squares, which were disassembled into four 4-piece squares, which were disassembled into individual pieces. The loose pieces were put into small plastic bags (grouped with other 4-piece bags from the 16-piece squares and grouped with more bags from their original 64-piece squares) with instructions on how the middle school students should reassemble the puzzle. The original assembly took 15 people nine weeks, which includes two weeks when one of the puzzle pieces was missing. The middle school students at the competition took about three hours. David Redman, assistant professor of mathematics at Delta, said about the theme of the competition, "Math is not about numbers---it's about how things fit. It's about how to do things that look impossible quickly and efficiently." --- Mike Breen

"Shivering With the Sun." Random Samples, Science, 4 May 2007, page 669.

Statistician David Thomson (Queen's University, Canada) and colleagues have published an article in the May issue of Proceedings of the IEEE about signals both on earth and around it that are associated with vibrations from the sun. The team also reports upturns in dropped cell phone calls corresponding to solar-mode frequencies. A seismologist quoted in this short article thinks there is some truth in the findings, but doesn't think everything around the earth vibrates to a solar beat.

--- Mike Breen

"Report Urges More Coordination To Improve Science and Math," by Yudhijit Bhattacharjee. Science, 4 May 2007, pages 676-677.

The National Science Board, which oversees the National Science Foundation, has proposed a plan to create a body called the National Council on STEM Education (STEM stands for "science, technology, engineering, and mathematics"). The body, with members from state and federal government, education, and business, would help create a national core set of standards in the subjects. The plan to create the council came from a commission co-chaired by physics Nobelist Leon Lederman. Says Lederman, "We expect many to say: 'Oh, it's so difficult' [to reform education nationally]... We know it's difficult, but it's needed." One opponent of the plan cited in the article thinks that the council is just another level of bureaucracy.

--- Mike Breen

"Envision This: Mathematicians Design Invisible Tunnel," by JR Minkel. Scientific American.com, 4 May 2007.

Last year, a 2 June 2006 article on Photonics.com reported that researchers from Duke University and Imperial College London had developed a blueprint for an invisibility cloak constructed from "metamaterials." These materials, which can be described by a precise mathematical function, would bend electromagnetic waves around a spherical area, making it "appear" as if the object behind the cloak were invisible, but only from far away.

Now, University of Liverpool mathematician Sébastien Guenneau, along with Frédéric Zolla and André Nicolet from the University of Marseille, have proven---using a computer model known as GETDP (General Environment for the Treatment of Discrete Problems)---that "objects can also be made to appear invisible from close range when light travels in waves rather than beams," according to the 2006 Photonics.com report. Such materials could be used by the military in the construction of equipment like fighter jets and submarines. However, cloaks for objects that don't have a "fixed structure and movement pattern," Gunneau notes, are more of a challenge: since their movement is flexible, the currently-designed cloak "would easily be seen when the person or animal made any sudden movement." However, he says, this "is a good example of what we are trying to move toward."

--- Claudia Clark

"Count down to 02:03:04 on 05/06/07," by Andrea Stone. USA Today, 1 May 2007;
"Sequences for Numbers Nerds," by Lenore Skenazy. The New York Sun, 4 May 2007.

You may not have witnessed it, but May saw the the time and date 02:03:04 05/06/07. The two articles discuss any significance this time and date may have. In the USA Today piece, Ed Burger (Williams College) said, "There are numerical patterns in nature all around us. Some are more significant and some are more beautiful than others. And this one is a silly one." Countries (and Digests) that write the day before the month had to wait until 5 June for their moment. In the New York Sun article, Noam Elkies (Harvard University) explains about other fun dates, such as Pi Day (3/14) and Mole Day (10/23).

--- Mike Breen

Math Blogs Revisited: Carnival of Mathematics, n-Category Café, Not Even Wrong, May 2007.

In its eighth edition, the Carnival of Mathematics is a forum for mathematics bloggers to link their favorite post to a host blog every two weeks. Bloggers take turns hosting and introduce the latest anthology of entries by weaving a little narrative. The virtual emcee for the latest edition is University of Utah Computer Scientist Suresh Venkatasubramanian, who studies computational geometry and started his Geomblog about three years ago. The posts bring together a diverse crowd: a female mathematician new to blogging; a lecturer in the Yale Mathematics Department; a software engineer for Google; several math educators from around the USA; graduate students in mathematics, computer science, and machine learning; and a math and magic enthusiast. Topics range from introductions to research-level mathematical concepts like "involutary quandle" to more accessible topics like the difficulty of internalizing the size of "big" numbers (i.e. How can we get a grasp on our odds of winning the lottery?).

The n-Category Café might provide a glimpse of the role of blogging in research. Maintained by mathematical physicist John Baez, philosopher David Corfield, and mathematician Urs Schreiber, this blog tosses around some of the newest thoughts of these researchers. An international array of mathematicians and scientists comment and add to the blog with regular guest posts linking the author's name to his/her arXiv papers. Perhaps this well-clicked blog will serve as a model for those interested in high-tech academic collaboration and inspiration.

Traveling even further towards physics, Not Even Wrong, a phrase referring to string theory, is written by Peter Woit, a Columbia University mathematician/phycist who argues that despite its trendiness, there are many faults with string theory. His book, Not Even Wrong, published in 2006, seems to have been inspired by his ruminations on the web, which are archived since 2004. The blog contains up-to-date information and commentary on mentions of string theory in the media as well as technical entries in the author's areas of interest which include quantum field theories and representation theory.

--- Brie Finegold