December 2007
"Marking the 300th year of mathematical giant," by Gerry Rising. The Buffalo News, 30 December 2007. Rising opens his article by characterizing Leonhard Euler as "kind of a mathematical Rodney Dangerfieldgetting too little respect." Yet it is only outside of mathematics that Euler gets too little respect. Rising lists some of Euler's accomplishments, paying particular attention to his formula for polyhedra and his solution to the Königsberg Bridge Problem, which led to graph theory and topology. The article was published at the end of the year marking the 300th anniversary of Euler's birth. (The January 2008 Feature Column, Urban Geometry, by Joe Malkevitch, has more on Euler and the Königsberg Bridge Problem.)  Mike Breen
"Elementary Math Grows Exponentially Tougher," by Maria Glod. Washington Post, 26 December 2007, page A1. Many elementary schools now include some very basic algebra ideas as early as first grade, yet many elementary school teachers aren't comfortable with algebra. Glod writes of how school systems, mathematicians, and business leaders are working together in many districts to improve the math skills of elementary school teachers. Virginia Commonwealth University math professor William E. Haver says, "Elementary math isn't elementary. There are a lot of deep ideas there." Kenneth I. Gross, a math and education professor at the University of Vermont, runs the Vermont Mathematics Initiative, which has improved the math skills of more than 150 teachers. He says that "All of mathematics depends on what kids do in the elementary grades. If you don't do it right, you're doing remedial work all the way up to college." In a related story, but one with an apparent contradictory theme, Dennis DeTurck, dean of arts and sciences at the University of Pennsylvania, is the author of a book that advocates not teaching fractions to elementary school children. DeTurck says, "Fractions have had their day, ... but in this digital age, they're as obsolete as Roman numerals are." DeTurck is also against teaching long division and multiplication of long numbers. Some quoted in the article agree, but not everyone supports DeTurck's position. George Andrews, AMS presidentelect and professor of mathematics at Pennsylvania State University, counters, "All of this is absurd... It is fine to talk about it, but this is not good pedagogy." Francis "Skip" Fennell, president of the National Council of Teachers of Mathematics, says, "I think it's an interesting discussion, but fractions are fundamental and I'm not kicking them out."  Mike Breen
"Math teacher sings way to fame, " by Michael D. Clark. The Enquirer, 20 December 2007.
"Research Highlights 2007," selected by the editors. Nature, 20/27 December 2007, page 1130. The editors of Nature nominated favorite research papers published elsewhere in 2007. Among the 20 were two in mathematics: "The 248th dimension" (about the E_{8} structure, see http://www.liegroups.org and the Math Digest summary), and "Mind over Möbius" (how Gert van der Heijden and Eugene Starostin calculated the "relaxed" shape of an elastic Mobius strip, originally published Nature Materials, doi: 10.1038/nmat1929, 2007; see the Math Digest summary).  Annette Emerson
"We Need to Invest in Math and Science Teachers," by Linda DarlingHammond. Chronicle of Higher Education, 21 December 2007, page B20. Two articles in the 21 December 2007 isssue of the Chronicle of Higher Education discuss the shortage of math and science teachers. DarlingHammond, an education professor at Stanford University, writes about the national shortage. She offers her recommendations for increasing the number of such teachers:
One specific program is UTeach at the University of Texas, which is the subject of the second article. ExxonMobil's National Math and Science Initiative has made grants of US$2.4 million to 12 universitites to copy UTeach. Students in the program do some practice teaching early in their college careers, and are mentored by "master teachers": experienced math and science school teachers. According to the article, 70 percent of UTeach's graduates are still teaching five years after graduation, compared to 50 percent nationwide. Critics say that there is little hard data to back up the positive anecdotal evidence for the program. Some of the new grant money is targeted for data collection.  Mike Breen
"Magic Carpets a Reality, Professor Says", by Roger Highfield. Daily Telegraph, 19 December 2007.
"Why Math is Important," by Chuck Shepherd. San Jose Mercury News, 18 December 2007. Shepherd's news item is so short that we quote it in its entirety: "The Army Corps of Engineers announced with great fanfare in June [2007] that its repairs and upgrades of levees in the Lakeview neighborhood of New Orleans, after Hurricane Katrina, would allow the system to hold back a storm's flood waters more than 5 feet beyond the Katrina level. However, in November [2007], the corps announced a mistake in calculation (an engineer had used a `minus' sign when a `plus' sign was called for). The expensive levee repairs would actually protect against flooding only 6 inches above the Katrina level."  Allyn Jackson
"A Mysterious Mind": Review of The Indian Clerk, by David Leavitt. Reviewed by Andrew Robinson. New Scientist, 15 December 2007, pages 4647. The book under review presents a partly fictionalized account of the life of Srinavasa Ramanujan, the brilliant selftaught Indian mathematician who was born in 1887 and died at the age of 32. The author of the book, novelist David Leavitt, has written about mathematics before, in his biography about Alan Turing, The Man Who Knew Too Much. Ramanujan had deep insights into mathematics, but he did not provide proofs in the traditional sense. Nevertheless what he knew was sufficiently impressive to British mathematician G. H. Hardy that Hardy brought Ramanujan to England and wrote several papers with him. Ramanujan's mysterious writings have captivated mathematicians to this day. The reviewer of Leavitt's book says there is a mismatch between what is known about Hardy and Leavitt's fictionalization of him. The result is a book that "does not convince overall, but is never less than engaging and intelligent."  Allyn Jackson
"The beauty of maths," by Lisa Jardine. BBC News, 14 December 2007. Reading the new novel The Indian Clerk prompted Jardine to recall her father telling her Ramanujan's story when she was young. At the time, she was particularly struck by the famous RamanujanHardy taxicab conversation that occured when Ramanujan was sick in the hospital. She writes that just as parents can pass on, for example, a fear of spiders to their children, they can also pass on their anxieties about math. Jardine feels that it is the responsibility of a good math teacher to encourage students to overcome such anxieties: "Perhaps, just as we try so hard to instil a love of great writers in successive generations, we should be looking for more stories like that of Ramanujan, to inspire all our young people with a lasting love for the beauty of numbers."  Mike Breen
"N.H. Math Professor Up For Grammy Award," WBZTV (NH), 11 December 2007.
"New Generation of Square Dancers Intrigued By Its Math Concepts," by Alexa Aguilar. Chicago Tribune, 10 December 2007.
"More time in class equals better math skills," by Greg Toppo. USA Today, 10 December 2007. The Brookings Institution examined eighthgrade math scores in 20 countries and found improved math skills in students in five of the seven countries that added instructional minutes to their math classes between 1999 and 2003. Students in 10 of the 13 countries that subtracted time in math class scored lower in the same time period. In the US, average math instructional time decreased from 49 minutes in 1995 to 45 minutes in 2003, yet US eight graders' scores on the Trends in Mathematics and Science Survey improved slightly. Toppo writes that researcher Tom Loveless called the counterintuitive improvement an "anomaly."  Mike Breen
"Knot Physics", by Clive Thompson. 2007 Year in Ideas, New York Times, 9 December 2007. This brief story appeared as part of the 2007 installment of the "Year in Ideas", a feature that the New York Times has presented for the past seven years. The story describes the work of physicist Doug Smith and his research assistant Dorian Raymer, who set out to understand why things like telephone cords end up in knots. After performing experiments in which lengths of string were whirled around in a box, they concluded that the amount of knotting that occurs depends primarily on the string's length and flexibility. Their work appeared in October 2007 in the Proceedings of the National Academy of Sciences.  Allyn Jackson
"15 = 3 x 5: Photons do their first quantum math," by David Castelvecchi. Science News, 8 December 2007. Two teams of physicists, one led by Jian Wei Pan (University of Science and Technology of China in Hefei) and another by Andrew White (University of Queensland, Brisbane, Australia), have independently manipulated the quantum states of photons and confirmed that 15 equals 3 times 5. As Castelvecchi points out, "multiplying whole numbers is easy, but the inverse operation generally isn't: Identifying when a number is the product of other whole numbers becomes exponentially more complex as the numbers get bigger, quickly overwhelming even the fastest computers." This complexity is the key to internet security. The recent research results suggest to White and colleagues "that photon techniques could lead to computers that can find factors of large numbers and potentially have other applications that are beyond the capacity of current computers, such as simulating the quantum behavior of large molecules." The research results of both teams will be published in Physical Review Letters.  Annette Emerson
"US Expert Panel Sees Algebra As Key to Improvements in Math," by Jeffrey Mervis. Science, 7 December 2007, pages 15341535. When the National Mathematics Advisory Panel convened in late November 2007, its report for the Department of Education recommended that programs revisit topics year after year and allow teachers flexibility to tailor practices and materials to the needs of their students. It also included an emphasis on algebra, with specific guidelines for the content of the course and prerequisites. Members of the panel hope the report will help to bridge the gap between math education standards across the 50 states. But achieving consensus on hotbutton issues was difficult, and significant portions of the report are still up for debate. At present, the report lacks recommendations on key issues such as whether the use of studentderived, alternative algorithms should be allowed in the classroom, or whether math specialists instead of regular classroom teachers should conduct math lessons at elementary schools.  Lisa DeKeukelaere
"When Will Virtual Surgery Make the Cut?," by Larry Greenemeier. Scientific American, 7 December 2007. Although simulations are possible for some things, surgical simulations are rare. According to Joseph Teran of the University of California, Los Angeles, Department of Mathematics, it would take nine months with current technology to create an accurate model of the human body. Teran thinks that within five years improvements in hardware and algorithms will allow doctors to scan patients and create threedimensional images that can be used for surgical practice before the real operation.  Mike Breen
"Math Geek Software Smackdown: Sage v. Mathematica," by Michael Calore. Wired, 7 December 2007. Sage is opensource mathematical software developed by William Stein (University of Washington) and others. Naturally since Sage is free its price is attractive, but another attraction is its complete transparency: The code is available to all, so that the exact methods used to determine a result can be examined. Stein and David Joyner (US Naval Academy) wrote an opinion piece about opensource software in the November 2007 issue of Notices of the AMS.  Mike Breen "All stirred up," by Dana Mackenzie. New Scientist, 1 December 2007, pages 5457. This article discusses new developments in the study of turbulence, in particular a phenomenon called a "Lagrangian coherent structure", which provides new insights into modeling the complex flow of fluids. "Turbulent flow governs many everyday processesthe way your milk and coffee mix and which direction smoke blows, for example," Mackenzie writes. "It can also cause serious problems, such as when an aircraft hits a rough patch of air. Until recently, however, no one had managed to create a predictable model of turbulence in the real world. Now coherent structures are allowing researchers to solve a raft of problems in oceanography, aviation, cardiology, and other areas."  Allyn Jackson

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