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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)


September 2006

"New Report Urges Return to Basics In Teaching Math," by John Hechinger. The Wall Street Journal, 12 September 2006, page A1.
"NCTM Issues New Guidelines to Help Schools Home In on the Essentials of Math," by Sean Cavanagh. Education Week, 12 September 2006.
"Fuzzy teaching ideas never added up." Chicago Sun-Times, 13 September 2006.
"Fuzzy memory on fuzzy math," by Debra J. Saunders. San Francisco Chronicle, 14 September 2006, page B7.
"Math wars end in sight." Boston Herald, 17 September 2006.
"Math, Singapore style." International Herald Tribune, 18 September 2006.

The National Council of Teachers of Mathematics (NCTM) recently released its Curriculum Focal Points which are focused grade-by-grade guidelines for the mathematics that students in pre-kindergaten through eighth grade should know. Some states have close to 100 expectations for students in math in some grades. The NCTM hopes that its report will help state officials, teachers, and publishers set clearer goals for math education. In the Education Week article, R. James Milgram, a Stanford University math professor, says, "I would hope that this has a large impact, because I believe it gets it right....I hope that what this represents is an end to the math wars." This article gives examples in the areas of geometry, and number and operations, showing how students are expected to progress from grade to grade. To many people, the Focal Points appear to move closer to a more traditional approach to teaching mathematics. Hechinger also gives some of the guidelines, traces the history of previous recommendations from the NCTM, and describes programs such as Singapore Math and Investigations that are now being used in schools to teach math. He gives reactions to the report. For example, Ralph Raimi, a University of Rochester mathematics professor, calls the report "a remarkable reversal, and it's about time." The editorial in the Chicago Sun-Times says that "Recommendations are not reality, but considering the downward trajectory of young Americans in math and science, this basic recipe for turning that trend around couldn't be more welcome." In her article, Saunders expresses disappointment with current math teaching (calling it "fuzzy math") and is "thrilled to see the NCTM actually concentrating on math skills." Yet her spirits were somewhat dampened after speaking with Jim Rubillo, NCTM executive director. Rubillo says that the new guidelines are a "continuation" of NCTM's 1989 standards and that "The math wars are just an invention in the last few years of just a couple of people."

--- Mike Breen

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"Math Factor Radio," by Ivars Peterson. Science News Online, 30 September 2006.

While the weekly television series NUMB3RS may be increasing people's awareness of mathematics, it is not the only game in town. In this article, Ivars Peterson reports on two other sources of mathematical entertainment.

The first is The Math Factor, a weekly program of "newsy and entertaining math snippets" presented by mathematician Chaim Goodman-Strauss on University of Arkansas public radio station, KUAF. In a recent segment, Goodman-Strauss and program host Kyle Kellams discussed the Poincaré Conjecture with geometer Jeff Weeks. Other program topics have included "cardinality, encryption, paradoxes, puzzles, [and] rates of change," according to Goodman-Strauss. You can listen to podcasts of The Math Factor by searching for "math factor."

For a "different sort of edifying experience", Peterson suggests an Internet radio station that plays "all science and math songs, all the time!" The host is Greg Crowther of the University of Washington in Seattle. Check it out. Peterson notes that listeners must subscribe to the service, or can purchase individual tracks.

--- Claudia Clark

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"Black Mathematicians, Still a Rarity, See Light at the End of the Pipeline," by Carolyn Mooney. The Chronicle of Higher Education, 29 September 2006.

The article starts by identfying Emery N. Brown, Dennis Davenport, George F. Edmonds, and Elaine C. Smith as academic rarities when they earned their doctorates almost 20 years ago: "They were the only black Americans known to have earned a Ph.D. in mathematics during the 1987-88 academic year." Mooney reports that while the number and proportion of minority students and doctorates in math have grown steadily, black math scholars are "still relatively rare." Why? Brown, Davenport and Smith agree that "in mathematics, more so than in many disciplines, preparation must begin long before college. Miss a key course, and it's hard to catch up." Also, young black students need role models and mentors. The AMS's James Maxwell, co-author of the annual surveys on mathematics, "believes some of the steps that have drawn more women to mathematics---offering more research opportunities at an earlier stage, for example, and seeking out students beyond the obvious ones who win math awards---can also work for minorities." Davenport is concerned about the overall numbers of Americans earning math doctorates, calling it a national crisis. Brown, Davenport, and Smith reflect on their experiences and career paths, and each continues to be a role model.

--- Annette Emerson

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"A Web Site Tells Black Math Scholars 'Who We Are'," by Carolyn Mooney. The Chronicle of Higher Education, 29 September 2006.

Scott Williams

Scott Williams.

Scott W. Williams, a mathematics professor at the State University of New York at Buffalo, started a website in the 1990s to track black mathematicians worldwide: Mathematicians of the African Diaspora. The site is not simply a list or directory. It contains an essay, "You Can Get There Even From Alice, Texas," by Raymond L. Johnson, and information such as the first African-American to earn at math Ph.D. (Elbert Frank Cox, from Cornell University in 1925), and the first African-American woman to earn a math Ph.D. (Euphemia Lofton Haynes, from Catholic University of America in 1925). Williams reports that the website has become increasingly popular and appreciated, especially during Black History Month each February. He is giving an invited address, "Why 'Mathematicians of the African Dispora'?", at the Joint Mathematics Meetings in New Orleans in January 2007, just before the website celebrates its tenth anniversary in February 2007.

--- Annette Emerson

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"Statistical Flaw Trips Up Study of Bad Stats," by Jim Giles. Nature, 28 September 2006, page 379.

Two ecologists shook up the Nature editors in 2004 with a paper claiming that one in three articles in the journal contained statistical errors, but further examination has revealed that the ecologists may have erred themselves. The ecologists, Emili Garcia-Berthou and Carles Alcaraz, claimed that the prevalence of certain numbers in final decimal digits of reported statistics exposed errors in rounding. They used a continuous probability distribution to form their conclusion, but physicist Monwhea Jeng recently showed that a discrete distribution would have been the correct choice—and would have shown no evidence of rounding errors. The ecologists’ paper also claims that many Nature and British Medical Journal articles contain incorrectly computed p values, an assertion that remains unchallenged and has driven editors to seek methods for ensuring proper statistical calculations.

--- Lisa DeKeukelaere

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"A Closer Look at Sports Miracles," by Carl Bialik. The Numbers Guy, Wall Street Journal Online, 28 September 2006.

a home run

This September, in the bottom of a ninth inning, four Dodgers hit four consecutive home runs against two Padres pitchers. In August a father and son each hit a hole-in-one on the same 110-yard, par-3 hole at the Congress Lake Club golf course. What were the odds of these two occurrences? The Wall Street Journal's Numbers Guy Carl Bialik contacted Ian Stewart (Mathematics Institute of the University of Warwick, U.K.) to comment on whether the two golfers just had a stroke of luck. Stewart replied that "the math says it's going to happen every so often, there being so many golfers playing so many games. But, by the same token, the chance that it will happen to any pre-specified person is tiny---a bit like winning the lottery." Mathematician Ken Ross (professor emeritus, University of Oregon) weighs in with a "back of the envelope" calculation on the likelihood of the Dodgers hitting four straight home runs at some point in this year. The article includes more comments of both mathematicians and feedback on Bialik's past columns.

--- Annette Emerson

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"Die Rolle des Zufalls in der Mathematik (The role of randomness in mathematics)," by George Szpiro. Neue Zürcher Zeitung, 27 September 2006.

Out of the hundreds of research lectures at the International Congress of Mathematicians in Madrid in August 2006, at least one clear theme emerged: the role of randomness in mathematics. Szpiro describes some of the lectures in which this theme was present.

--- Allyn Jackson

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"Science gets image conscious," by Dan Vergano. USA Today, 25 September 2006.
"2006 Visualization Challenge," by Jeff Nesbit and Monica Bradford. Science, 22 September 2006.

Mathematician Richard Palais (University of California, Irvine) and graphic artist Luc Benard have been named winners in the 2006 Science and Engineering Visualization Challenge, sponsored by the National Science Foundation (NSF) and Science magazine. They are given top honors in the Illustration category "for computer graphic depictions of five mathematical surfaces rendered as a still life." The NSF site announces that the visualization contest, currently in its fourth year, "recognizes outstanding achievement in the use of visual media to promote understanding of research results and scientific phenomena. The judges' criteria for evaluating the entries included visual impact, innovation and accuracy, among others." The image of creations by Palais and Benard, "Still Life: Five Glass Surfaces on a Tabletop," can be seen in the 22 September 2006 issue of Science, and also on the NSF website. (More works by Palais and colleagues can be seen in the 3D-XplorMath album on the AMS's Mathematical Imagery site.)

--- Annette Emerson

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"How Random is the iPod's Shuffle?" by Carl Bialik. Wall Street Journal Online, 21 September 2006.

Carl Bialik, who has a degree in mathematics and physics from Yale University, writes a regular column as "The Numbers Guy" for The Wall Street Journal Online on "the way numbers are used and abused, in the news, business and politics." In this piece he discusses just what makes a string of numbers random, attempts at computer programming random numbers, and how this applies to the iPod shuffle feature. Other September columns by Bialik are "Grading Weather Forecasts" (September 14) and "'Drunkest' Rankings Need a Sobriety Test" (September 7). "The Numbers Guy" web page links to all of his past columns.

--- Annette Emerson

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"String theory: Hanging on a thread?" by Dan Vergano. USA Today, 19 September 2006.

In the sidebar to a longer article about string theory and its detractors, Vergano includes a sidebar titled "Knotty Old Issue." Here he quotes physicist Lee Smolin who likens string theory's tie to physics to knot theory's tie to (then untie from) physics. Mathematician John Ewing notes that "knot theory has many non-physics applications and is a thriving subject." At the end of the sidebar Vergano points readers to a graphic illustrating knot theory.

--- Annette Emerson

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"Mathematician Is Chosen for 'Genius' Grant," by Thomas H. Maugh II. Los Angeles Times, 19 September 2006;
"UCLA Mathematician Wins 'Genius' Grant." NBC4 TV in Los Angeles, CA, 19 September 2006.

Terence Tao, described in the article as the "Mozart of Math," was one of 25 winners of this year's MacArthur Foundation "Genius" grants. He'll receive US$500,000 over five years to use as he wishes. Tao also received the 2006 Fields Medal (see the citation). The media coverage featuring Tao and his MacArthur grant notes that he was a child prodigy in mathematics; took university-level courses in Australia at age 9; won awards at the International Math Olympiads at ages 10, 11 and 12; graduated with a bachelor's degree with honors from Flinders University at age 16; and received his doctorate from Princeton University at 21. He joined the faculty of the University of California at Los Angeles and became a full professor at age 24. Now at 31 years of age, Tao has written over 80 research papers, with over 30 collaborators, and his interests cover a wide range of mathematics. He says on his website that he also likes "Australia's easy-going, honest, and relaxed culture." Click here for the Digest item on Tao being named one of the "Brilliant 10" of the year by Popular Science magazine.

--- Annette Emerson

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"Newsmakers: Two Cultures," edited by Yudhijit Bhattacharjee. Science, 15 September 2006, page 1569.

math-inspired jazz

Modern jazz saxophonist Rudresh Mahanthappa says that his music is inspired by math. His new album, Codebook, scheduled for release by Pi Recordings on 26 September, "conveys elements of number theory and cryptography in musical form." He uses the Fibonacci sequence as the basis for the rhythm and melodies. Manjul Barghava, a mathematician and musician at Princeton University, is quoted on Mahanthappa's compositions: "He proves, by music musical notes, what mathematicians have always believed: that math is beautiful."

--- Annette Emerson

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"Go with the Flow." Netwatch, Science, 8 September 2006, page 1367.

John Bush, an applied mathematician at the Massachusetts Institute of Technology, has a collection of fluid dynamics images online. Among the striking images are those of the effects of a water strider. Also mentioned in this brief item is a gallery of winning entries from the American Physical Society's annual exhibition of photos and videos (a subcription is required to get to the most recent years).

--- Mike Breen

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"Controlling our errors", by Barry Mazur. Nature, 7 September 2006, pages 38-40.

This article describes recent breakthroughs in the solution of a 40-year-old problem in number theory. The problem originated in the work of two mathematicians, John Tate and Mikio Sato, and came to be called the Sato-Tate Conjecture. The two arrived at the conjecture independently and from different directions; their work was honored with the 2003 Wolf Prize. The abstract of the article states: "The Sato-Tate conjecture holds that the error term occurring in many important problems in number theory conforms to a specific probability distribution. That conjecture has now been proved for a large group of cases." Results released earlier this year, described concisely but technically in this article, are important steps towards proving the conjecture in full generality.

--- Lisa DeKeukelaere

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"What'd you say? Math sorts out noise," by Scott Canon. The Kansas City Star, 4 September 2006.

hearing conversations at a party

Can you remember the last time you tried to have a conversation in a noisy place? You probably relied in part on visual cues, such as hand gestures and lip movement. Even so, you may have missed some of your companion's words. Now imagine trying to follow that same conversation without being able to see the person. You are experiencing the "blind source separation problem," according to writer Scott Canon in his article in the Kansas City Star. Machines, lacking human experience and intuition, have even more difficulty pulling out a single voice---both words and vocal characteristics---in a noisy environment, a critical issue in speech recognition technology.

At Siemens Corporation in Germany, scientist Radu Balans and his colleagues were attempting to solve this problem, as stated by Canon, in the following way: "If you sample enough of a sound, can you re-create a part of that sound and break it into different parts without [using] information about the pitch?" Enter algebraic geometry, and University of Missouri professors Peter Casazza and Dan Edidin. First they tried to prove that solving the problem was impossible. Failing that, they found a solution by applying a special class of frames, known as Parceval frames, to the signal processing. Now, more work is needed to create efficient algorithms to do this.

For more information on Edidin and Casazza's work, go to the website of the University of Missouri-Columbia Department of Mathematics' newsletter Critical Point, select the Fall 2005 issue, and read "Signal Reconstruction without Noisy Phase" on page 12.

--- Claudia Clark

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"Die Mathematik gibt dem Arzt den Durchblick (Mathematics gives the doctor a glimpse)," by George Szpiro. Neue Zürcher Zeitung, 3 September 2006.

Szpiro reports on research presented in an article that appeared recently in the Bulletin of the AMS about mathematical techniques in medical imaging.

--- Allyn Jackson

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"Full proof? Let's trust it to the black box", Times Higher Education Supplement, 1 September 2006

Mathematician Brian Davies discusses some recent mathematics proofs that required huge calculations by computer and concludes that in the future. "Pure mathematicians still have to devise the strategies that computers follow, but the footwork is increasingly being left to the machines," he writes. "As a result, we can no longer survey the entire proofs of an increasing number of important theorems as we once could, and we have to accept our computers' word that they have carried out our instructions and obtained the result that we suspected." See Davies' article "Whither Mathematics?" in the December 2005 issue of the Notices of the AMS.

--- Allyn Jackson

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