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March 2006
"Lost in Einstein's Shadow," by Tony Rothman. American Scientist, March-April 2006, pages 112-113.
"Knot Theory's Odd Origins," by Daniel S. Silver. American Scientist, March-April 2006, pages 158-165. This article focuses on work in the 1800s by William Thomson (Lord Kelvin) and Peter Guthrie Tait. At the time, although the existence of atoms was known, details about them were unknown. Thomson and Tait came to believe that chemical elements were "knotted tubes of ether" and chemical properties arose from the topological properties of knots. The article contains descriptions and illustrations of Tait's smoke ring experiments which were done to understand knots. Tait classified knots with up to seven crossings, but he and Thomson were unable to make a connection between the elements and knot theory. Despite their "failure," knot theory is a vibrant area of mathematics today. --- Mike Breen
"Schools Cut Back Subjects to Push Reading and Math," by Sam Dillon. New York Times, 26 March 2006, page 1.
"Ride the celestial subway," by Ian Stewart. New Scientist, 25 March 2006, pages 32-36. This article describes a new and more efficient way of engineering space travel by using the mathematical theory of dynamical systems. It turns out that the complex interplay of gravitational attraction between celestial bodies, such as the planets in our solar system, creates a network of "tubes" in which spacecraft can be propelled with very little or even no fuel. "The tubes can be seen only with mathematical eyes, because their walls are defined by the combined gravitational fields of all bodies in the solar system," Stewart writes. Junctions linking these tubes are called, in mathematical terms, Lagrange points, after the 19th century mathematician Joseph-Louis Lagrange. To use this "interplanetary superhighway", as the network of tubes has been called, you first calculate which tubes are needed to reach the destination. "You then route your spacecraft along the tube to a Lagrange point," Stewart explains, "and when it gets there you give it a quick burst on the motors to redirect to the next Lagrange point on the route...and so it goes." Through collaborations among mathematicians and space mission engineers, these methods have begun to be used in actual space missions. --- Allyn Jackson
"Windy City Return." Peer Review, The Chronicle of Higher Education, 24 March 2006, page A10. Robert J. Zimmer will become president of the University of Chicago on 1 July 2006. Zimmer is a mathematician who has published over 80 research papers and was on the University of Chicago faculty for many years. His most recent position was provost at Brown University. Zimmer succeeds Don Michael Randel who is leaving to become president of the Andrew W. Mellon Foundation. --- Mike Breen
"Congress Examines Science Teaching," by Jeffery Brainard. The Chronicle of Higher Education, 24 March 2006, page A28. At a U.S. House of Representatives subcommittee hearing on improving math and science education, college officials said that improving math and science education requires colleges to improve undergraduate instruction, especially that of future school teachers. The officials said that math and science departments should "provide financial rewards and support from colleagues to encourage faculty members to devote more effort to teaching over research." Daniel L. Goroff, vice president and dean of faculty at Harvey Mudd College, recommended expanding the budget for the National Science Foundation's division of undergraduate education, which is slated to be cut under President Bush's proposed 2007 budget. --- Mike Breen
"Book, How Do I Love Thee? Let Me Count the Words," by Noam Cohen. New York Times, 19 March 2006, Week in Review, page 3. Software at Amazon.com called Text Stats analyzes books by counting the number of big words in a book and how long its sentences are. Some literary scholars appreciate Text Stats, saying that it can answer questions about authorship and influence, while others see it as a gimmick. Software analysis of texts has been around for a while, but Amazon's software automates the process and puts the results on the Internet. The article includes word counts (presumably ignoring words like "the") for Stephen Hawking's A Brief History of Time ("universe" is the most used word with a count of 535) and Mickey Spillane's The Mike Hammer Collection, Vol. 1 ("get" tops the list with 714 appearances). --- Mike Breen
"Film to celebrate maths genius," by Soutik Biswas. BBC News, 16 March 2006.
"Mathematischer Beweis einer intuitiven Idee (Mathematical proof of an intuitive idea)", by George Szpiro. Neue Zürcher Zeitung, 15 March 2006. This article discusses recent work by the French mathematician Michel Talagrand concerning the ad hoc ideas about so-called "spin glasses" that were proposed the Italian physicist Girorgio Parisi 25 years ago. Talagrand has proven that these intuitive ideas are mathematically correct. --- Allyn Jackson
"National Pi Day," the subject of The Daily One Minute Trivia Challenge on 88Slide.com, 14 March 2006.
"Today's Lesson About the Brackets: Don't Always Follow the Crowds," by Bryan Clair and David Letscher. New York Times, 13 March 2006, Section D, page 5.
"Improving math ed -- Bush right about that; But where are the teachers coming from?", by Jonathan David Farley. San Francisco Chronicle, 12 March 2006. Farley agrees with President George Bush's statement, in the 2006 State of the Union address, that the United States must improve mathematics education. But, Farley notes, there are not enough teachers with strong enough math backgrounds to address this challenge. He also points out the need for more inspirational teaching of mathematics and notes how the television program NUMB3RS is now being used by many mathematics teachers to spark students' interest. Farley also sees the use of mathematics in counterterrorism research as a way to engage students and presents a few specific examples of such research. "High school students could learn algebra, trigonometry, calculus and logic while also learning concrete applications involving homeland security," he writes. "No longer would students yawn and ask, `What is math good for?' Beauty could defeat both terror and boredom." --- Allyn Jackson
"All Square," by Ivars Peterson. Science News, 11 March 2006, pages 152-153. Manjul Bhargava (Princeton University) and Jonathan P. Hanke (Duke University) have proved a result in number theory whose history goes back a long way. In 1770, Lagrange showed that every positive integer could be written as the sum of at most four squares. In the early 1900s Ramanujan found 53 other sums involving multiples of squares, called quadratic forms (for example, w2 + 2x2 + 2y2 + 7z2) that can be used to represent every positive integer. One question is if there are other quadratic forms that represent all integers, and another is if there is a way to test if a given quadratic form does represent all positive integers. Bhargava has found other quadratic forms, adding to a list that mathematicians for more than 50 years had thought was complete. In 1993, John H. Conway (Princeton) and his student William Scheeberger found that a certain class of quadratic forms could be tested on numbers no larger than 15 and conjectured that a similar test could be found for a much broader class of quadratic forms. Bhargava and Hanke have now proved that conjecture (which involves a test on numbers no larger than 290). Bhargava presented the result at the International Conference on Number Theory and Mathematical Physics held at SASTRA University in India in December 2005. A sidebar in the article on Bhargava states that his mother, a math professor, encouraged his interest in mathematics and introduced him to the tabla, an Indian musical instrument. Bhargava compared patterns in the two: "The goal of every number theorist and every tabla player is to combine these patterns, carefully and creatively, so that they flow as a sequence of ideas, tell a story, and form a complete and beautiful piece." --- Mike Breen
"Untying a math mystery," by Margaret Wertheim. The Los Angeles Times, 6 March 2005.
"The Limits of Mathematics." by Ivars Peterson. Science News Online, 4 March 2006. In the early 20th century, mathematician David Hilbert dreamed of "codifying the methods of mathematical reasoning and putting them within a single framework." So writes Ivars Peterson in this issue of Science News Online. In such a system, there would be a definite procedure for deciding whether a proposition follows from certain axioms. A few decades later, mathematicians such as Kurt Gödel and Alan Turing proved that such a procedure is impossible. Their work, and the ongoing work of mathematician Gregory Chaitin, author of the book The Limits of Mathematics, is the subject of Peterson's article. Gödel recognized the incompleteness of a system as basic as elementary arithmetic, using just the whole numbers and the operations of multiplication and addition, Chaitin noted in his recent book, Meta Math. Peterson goes on to explain some of Chaitin's own work, including his proof that "no program can generate a number more complex than itself." (Chaitin defines a number's complexity as "the length of the shortest computer program (or set of instructions) that would spew out the number.") He notes that Chaitin has conversely shown that "it is impossible for a program to prove that a number more complex than the program is random." (For Chaitin, a sequence of numbers is random if it cannot be generated by an algorithm significantly shorter than itself.) For further information on Gregory Chaitin's work, see his article "The Limits of Reason" in the March 2006 issue of Scientific American. --- Claudia Clark "Number cruncher": Review of Letters to a Young Mathematician, by Ian Stewart. Reviewed by Justin Mullins. New Scientist, 4 March 2006, page 54. In this book, Ian Stewart writes letters to an imaginary niece who is studying to become a mathematician. Justin Mullins's review says that Stewart "shows us how mathematicians work, rest and play, and what kind of jokes they tell each other... As a mentor for a budding mathematician, he is remarkably good company." Another review of this book: --- Allyn Jackson "Researchers use math to explain dolphins' dance," by Judy Siegel-Iztkovich. The Jerusalem Post, 2 March 2006.
"Largest US math group calculates in Providence," by Tim Lehnert. The Providence Phoenix, 1 March 2006.
"The Elusive Goal of Machine Translation," by Gary Stix. Scientific American, March 2006. Since the 1950s, corporate and academic researchers have been attempting to develop fully automatic, high quality translation programs with relatively little success; some say it can never be accomplished, while others believe that new statistics-based programs are well on their way. The first generation of translation programs was rule-based: they used enormous lexicons and sets of guidelines developed by linguists on when to use which participle. The newer statistics-based programs compute the probability that a word is translated correctly using large libraries of text given in multiple languages. The boom of the world wide web has led to advancements in the statistical programs by increasing the amount of bilingual text available for the libraries and creating a demand for translation that drives further research, but disagreement persists on the accuracy of these programs and their potential for further improvement. --- Lisa DeKeukelaere
"2006 mathematics prize announced," BBC News, U.K., 23 March 2006.
"Math Professor Wins a Coveted Religion Award," by Dennis Overbye. New York Times, 16 March 2006.
"Math whiz, 17, hits big time with research," by Becky Bartindale, San Jose Mercury News, 7 March 2006. Winners of the Intel Science Talent Search were feted at a banquet in Washington, D.C. on March 14. Shannon Babb of American Fork High School in Utah won the competition and a US$100,000 scholarship for her study of pollution in a Utah river system. Three students who did math projects finished in the top ten. Yi Sun of the Harker School in San Jose, CA, won second place and a $75,000 scholarship for his study of the winding number of random walks. Nicholas Michael Wage of Appleton, WI. won fourth place and a $25,000 scholarship for his study of Paley graphs. Kimberly Megan Scott of Wellesley, MA, won tenth place and $20,000 scholarship for her study of Ehrenfeucht-Fraisse games. The Mercury News articles are about Yi Sun. One was published before the final results and gives some of his background. The other came out after the banquet and quotes the judges' impression of him: "Delightful, bright, energetic and clearly an all-star who has already shown excellent leadership in science and to whom we will look for future leadership." The Science Service website has more information about all the winners and their projects. --- Mike Breen
"Knit Theory," by David Samuels. Discover, March 2006, page 40.
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