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March 2010
Some Mathematics Blogs: The Numbers Guy, Tanya Khovanova's Math Blog, Emory eScience Commons, n-category cafe. This month, Carl Bialik, "The Numbers Guy," has focused his blog for The Wall Street Journal on measuring popularity, damages, and sales. The measuring of these qualities is speculative by nature, and what leads so many people to speculate about them is their relationship to money. Apple has not released its sales figures so bloggers are using order numbers to try and guesstimate their sales of the iPad. The aftermath of the earthquakes in Haiti and Chile has not played out long enough for insurers to know what the damages are, but they need some sort of ball-park figure to use in their businesses. Celebrities' likeability is not quantifiable in any absolute sense, but advertisers seeking celebrity endorsements want to have some idea of whether they will get a good financial return. Bialik outlines various strategies used to make predictions and educated guesses, leaving the reader to look for the mechanism driving the numbers. Overall, Bialik's blog addresses measurement--how to quantify qualities that may or may not seem inherently quantifiable. In an attempt to predict future winners of the Abel Prize, Tanya Khovanova, a visiting scholar at MIT with a PhD in mathematics, recently wrote in her blog about "The Greatest Mathematician Alive." In an effort to establish a gross measure of "greatness," and after acknowledging her own bias towards Russian mathematicians, she looks at the number of Google hits for various mathematicians' names. John Conway, who received over 200,000 hits, is featured in another blog entry concerning his "recipe for success" in mathematics. Khovanova had received Conway's advice on picking mathematics problems which concluded with "Enjoy your life." Indeed, most of her other entries focus on enjoyable math puzzles. While the blogs profiled above are by-and-large about mathematics and numbers, it's always interesting to see mathematics pop up in a blog that is more general. Emory University's science blog featured Skip Garibaldi this month, a mathematician and rock-climber whose peer-reviewed paper debunks the ideas in an attention-grabbing 2007 preprint, "An Exceptionally Simple Theory of Everything," by physicist and avid surfer Garrett Lisi. Lisi's theory centered around the exceptional (and simple) Lie Group E8, four of whose subgroups correspond to four fundamental forces of nature. Although Lisi believed that E8 somehow unified all of the fundamental forces, Garibaldi and his co-author prove that there is no "theory of everything" inside of E8. There are in-depth discussions of the mathematics used in this paper in another blog called the "n-category cafe" which is co-hosted by John Baez, a mathematician/physicist. And the linking from one blog to the next is to be continued ... . --- Brie Finegold
"Book Mixing Math And Crochet Wins British Prize," by Mary Louise Kelly. NPR Morning Edition, 29 March 2010.
"Odds Are, It's Wrong," by Tom Siegfried. Science News, 27 March 2010, pages 26-29. Siegfried, editor-in-chief of Science News, writes that "The 'scientific method' of testing hypotheses by statistical analysis stands on a flimsy foundation" because statistical tests are often misunderstood and misinterpreted. One problem is the practice of combining many studies into one analysis without allowing for differences in the individual studies. The idea of statistical significance is also examined. A common error is to confuse the chance of obtaining a result given that a hypothesis is true with the chance of a hypothesis being true given that the result has been obtained. Also a treatment may be statistically significant but not practically important (because, for example, of only a slight increase in the number of people cured). Siegfried is not calling for an end to the use of statistics, but for more care in its use. The online article includes examples to illustrate the author's points. --- Mike Breen "Maths behind Internet encryption wins top award," by Zeeya Merali. Nature, 24 March 2010.
The Abel Prize, established in 2002, is a prize awarded by the King of Norway to outstanding mathematicians, and has quickly earned the nickname of "Nobel prize of mathematics" (it also carries a cash award of US$1 million). This year, it was awarded to John Tate, a number theorist who has recently retired from the University of Texas at Austin. Mathematician Helge Holden, from the Norwegian University of Science and Technology in Trondheim, states that this award truly recognizes a lifetime of achievement, going all the way back to Tate?s doctoral thesis. Tate?s work in the field of number theory revolutionized one of the oldest areas in mathematics, concerned mainly with finding properties of whole numbers. Number theory is extremely useful nowadays, since it is necessary for Internet encryption algorithms and for constructing error-correcting codes (which allow us to listen to CDs in our car and send text messages). His work on elliptic curves was also an essential tool for Wiles's proof of Fermat?s Last Theorem, a renowned mathematical problem that took 350 years to solve. Read the formal announcement of the prize. [Photo by Charlie Fonville/University of Texas at Austin.] --- Adriana Salerno
"Bias Called Persistent Hurdle for Women in Sciences," by Tamar Lewin. The New York Times, 21 March 2010. This article discusses a recent report of the American Association of University Women, which found that in mathematics and other traditionally male-dominated fields, women have made many gains but still face obstacles. According to the report, innate differences between males and females probably do not account for sex differences in mathematical performance. One piece of evidence is that 30 years ago, boys outnumbered girls 13 to 1 among mathematically precocious youth; today that proportion has dropped to 3 to 1. The report also discusses research showing that both sexes are affected by suggestions about sex differences in ability. Studies have been conducted in which one group taking a math test is told men do better in math than women, and another group is not given this suggestion. The women in the first group got lower scores than the men, while the men and women in the second group scored around the same. The article also mentions that Harvard University recently tenured its first woman math professor. She is Sophie Morel, who works in number theory. --- Allyn Jackson
"Will reclusive mathematician accept $1 million prize?", by Jacob Aron. New Scientist, 19 March 2010. These articles are among the many brief news stories reporting that the Clay Mathematics Institute has awarded a US$1-million prize to Grigory Perelman, who resolved the Poincaré Conjecture. In 2006 Perelman was awarded the top honor in mathematics, the Fields Medal, for work that included the resolution of the conjecture, and he turned the medal down. These articles report that the Clay Mathematics Institute did not know whether Perelman would accept its prize. The ABC News piece quoted Perelman as saying that he had not yet decided whether he would accept. --- Allyn Jackson
"Intel Science Talent Search spotlights America's whiz kids," by Lisa Grossman. Science News, 17 March 2010.
Two of the top four prizes, and three of the top ten, in the 2010 Intel Science Talent Search went to math projects. Akhil Mathew, an 18-year old student from Madison, NJ, won third place and a $50,000 scholarship for his research in Deligne categories. Akhil combined algebraic geometry, representation theory, and category theory in his project. Lynelle Lin Ye, also 18, of Palo Alto, CA won fourth place and a $40,000 scholarship for her analysis of the two-person combinatorial game Chomp. The other math project in the top ten was one on sphere packing by Katherine Rebecca Rudolph of Naperville, IL. First place and a $100,000 scholarship went to Erika DeBenedictis of Albuquerque, NM for designing an autonomous navigation system for spacecraft, using the "Interplanetary Superhighway." The awards ceremony took place in Washington, DC. --- Mike Breen
"On Pi Day, one number 'reeks of mystery,'" by Elizabeth Landau. CNN, 10 March 2010. These articles deal with some events on Pi Day (3-14) as well as individual accomplishments associated with Pi. The Chronicle article begins with Joe Anderson, a 17-year-old student at the Texas Academy of Mathematics and Science, who planned to get up at 1:59 on the morning of Pi Day to recite the first 1000 digits of Pi. MIT posted online the names of those who were admitted to the school at 1:59 p.m. on the 14th. The CNN piece relates some of Pi's properties---for example, the number 360 occurs in digits 358 through 360 of Pi's decimal expansion---and ongoing research involving Pi, such as whether the digits are truly random. --- Mike Breen
"Are you as smart as a kindergartner? Read the proposed new national math, English standards," by Donna Gordon Blankinship. Los Angeles Times, 10 March 2010. The National Governors Association and the Council of Chief State School Officers have led an effort to create "Common Core State Standards" in math and English. A draft of the document was released in early March, and the final document is expected in May. Blankinship writes that the standards are "expected to lead to standardization of textbooks and testing and make learning easier for students who move from state to state." Forty-eight states (all but Alaska and Texas) and the District of Columbia have endorsed the effort. Blankinship quotes William McCallum, chair of the math standards committee and head of the math department at the University of Arizona, who says, "These are rigorous standards. These standards are as high as the highest standards that any state has." Yet in the Education Week article the executive director of the Pioneer Institute in Boston, Jim Stergios, is said to be "worried that Massachusetts' own standards will be 'dumbed down' if the state adopts the common standards." The Science piece is that issue's editorial, written by three of the members of the Common Core State Standards for Mathematics working group. --- Mike Breen
"Algebra in Wonderland," by Melanie Bayley. The New York Times, 7 March 2010, page 11.
"Tostitos Ad." Sports Illustrated, 8 March 2010.
"The Mutual Inspiration of Art and Mathematics," by Julie Rehmeyer. Science News, 6 March 2010.
"Fashion and Advanced Mathematics Meet at Miyake," by Jenny Barchfield. ABC News, 5 March 2010.
"Students 'Stand and Deliver' for Teacher," by John Blackstone. CBS Evening News, 4 March 2010. The articles from the beginning of March are about former students of Jaime Escalante, the mathematics teacher whose story is portrayed in the movie Stand and Deliver, who returned to their native Garfield High School in Los Angeles to show support and raise money for their beloved teacher, who was in the final stages of bladder cancer. The NBC and People items, from the end the month, are about his subsequent death on March 30 and his legacy. Escalante earned fame for teaching low-performing students from immigrant parents, “barrio kids,” to strive for and pass the AP calculus exam as a gateway to college and a brighter future. The former students credit Escalante not only with leading them to achievement as individuals, but also improving the way others view students from neighborhoods like theirs. Escalante’s medical costs depleted his savings, and the students raised money so that he—who taught them so much about dedication and determination—could live comfortably in his final weeks. --- Lisa DeKeukelaere
“Building a Better Teacher,” by Elizabeth Green. The New York Times Magazine, 2 March 2010. In recent years, there has been a surge in support for projects aimed at improving teaching quality in the country. From Bill Gates to the Obama administration, millions of dollars are being invested in this cause. It’s too bad that nobody really knows what characterizes good teaching, as Bill Gates himself has said. In this article (the magazine's feature article), Green explores the history of this problem and the most promising research in the area. There has been No Child Left Behind, which proposes standardized testing as the solution. Some people have suggested giving cash incentives to teachers whose students learn the most (from the standardized testing point of view). Some people even believe that teachers just have innate abilities, and we should hire the “good” ones and get rid of the “bad” ones. Green focuses a large part of her article on exploring the research of Doug Lemov, a former teacher, principal, and a charter-school founder who works as a consultant hired by troubled schools. Lemov believes that the best way to improve the quality of education students are receiving is to improve the quality of the teachers who are already teaching. So he set out to discover what qualities are common to all good teachers. After five years of videotaping and observing the best in the country, Lemov came up with what is now known in the education underground as “Lemov’s Taxonomy” (there is a book version coming out entitled Teach Like a Champion: The 49 Techniques That Put Students on the Path to College). Technique No. 23: Positive Framing, involves offering a “vision of a positive outcome,” instead of chiding students for misbehaving. In Warm/Strict, technique No. 45, a correction comes with a smile and an explanation for its cause. And the list goes on (obviously). Green points out that Lemov himself is a huge introvert, but in front of a classroom he transforms into a commanding presence. Whereas Lemov’s taxonomy is independent of content (it should work for English teachers as well as mathematics teachers), other people have focused more on the teaching of specific subjects, like mathematics. Deborah Loewenberg Ball, now a dean at the University of Michigan, realized that teaching math not only required knowing the math, but knowing how everyone else in the classroom might understand (or misunderstand) it. Ball named this Mathematical Knowledge for Teaching, or M.K.T. “Teaching depends on what other people think,” she told Green, “not what you think.” Interestingly enough, neither Ball nor Lemov are aware of each other’s work. Even though they disagree on the subject-free versus subject-based approach, they agree on one important issue: that teachers are not born but made. Lemov believes that he has found an incentive for teachers that is just as powerful as cash: the chance to get better. --- Adriana Salerno
"Striving to map the shape-shifting net," by John Markoff. The New York Times, 2 March 2010, page D1. This article discusses the growth of the internet and efforts to model its structure. The internet has not grown in a planned fashion, as Markoff points out. Rather, he says it is "an organic, interconnected communications web with no single control point." There are many different stimuli driving this growth, including content-delivery networks, the proliferation of wireless devices, and the explosion of streaming video. Being able to model the shape of the internet is a critical goal for advertisers and for law enforcement, as well as for social science researchers trying to understand how people connect on the internet. One of the most successful initial models of the internet was proposed by Albert-Laszlo Barabasi and his collaborators and is called the scale-free model. Their work suggested that connections among nodes are not random but that a small number of nodes have many more connections than others. One implication of the scale-free model is that the internet is vulnerable to attack if some of the highly connected nodes are compromised. This model was later criticized by other researchers, who argued that it was too simplistic and abstract and did not take into account engineering decisions that affect the shape of the internet. These criticisms are discussed in an article, Mathematics and the Internet: A Source of Enormous Confusion and Great Potential", by Walter Willinger, David Alderson, and John C. Doyle, which appeared in the May 2009 issue of the Notices of the AMS. The model Willinger et al have proposed implies that the internet is not as vulnerable to attack as previously thought. David Alderson told The New York Times that the scale-free models do not describe the real internet. "What they are measuring is not the physcial network, it's some virtual abstraction that's on top of it." --- Allyn Jackson
"Numbers War," by Linda Baker. Scientific American, March 2010, pages 20-21. The nationwide debate over the best approach for mathematics instruction has flared since last October, when the National Council of Teachers of Mathematics (NCTM) released its most recent set of standards. The new guidelines focus on reasoning skills and applications, an approach originally labeled “reform math” for its departure from the traditional rote memorization of rules and algorithms. Reform math first appeared in 1989 as part of NCTM standards released that year, and the new rules alter the delicate balance proponents of each side have found since then. A mathematician argues that encouraging students to use reasoning has little utility if the reasoning is flawed, and a math teacher points out that a focus on application-based instruction eliminates elegant problems and courses that require reasoning. Both sides agree, however, that the dismal math performance of U.S. high school students compared to the rest of the world indicates the current system needs improvement. --- Lisa DeKeukelaere
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