"Primed for Success," by Dana MacKenzie. Smithsonian, Fall 2007, pages 74-75.
The fall issue of Smithsonian recognizes Terence Tao, a mathematician at the University of California, Los Angeles, as one of America's 37 top young innovators in the arts and sciences under the age of 36. Tao is best known for a theorem, which he proved in 2004 with Cambridge University's Ben Green, about patterns in the distribution of prime numbers. His colleagues hail him as one of the leading mathematicians of his generation and praise his ability to solve hard problems by breaking them down into smaller, solvable pieces and attacking them from novel directions by keeping an open mind. These qualities have helped Tao to solve problems not just in his specialty field, analysis, but also in number theory and image compression. At age 24, he became the youngest professor in UCLA history, and he was awarded the Fields Medal, often called the mathematical equivalent of the Nobel Prize, in 2006.
--- Lisa DeKeukelaere
"The square root of art", by Antoinette De Vito. University of South Florida Oracle, 30 October 2007.
"Getting Students Through Remedial Math Is a Constant Struggle, but This College Keeps Trying," by Debra E. Blum. Chronicle of Higher Education, 26 October 2007.
The Chronicle of Higher Education notes that "on average between 40 percent and 70 percent of new students entering two-year colleges around the country place into remedial math. What college officials and observers find so distressing is not so much the number of students who must take remedial math classes, but the number of students who fail them." Montgomery County Community College, outside Philadelphia, PA, is seeking to increase its graduation rate. To help achieve that goal, the college is running a pilot program in math. The new course, resulting from feedback at focus groups with students and staff, "condenses two semesters of class into one, and offers a medium-paced course that focuses on algebra but includes some review of arithmetic when needed." Tutors---students and former students---in this new program serve more like teaching assistants; they attend the classes and hold weekly help sessions designed to coordinate with the specific course. Walter Hunter, who teaches the new course, employs humor in the classroom, and says it's critical that students see "it's all right to take more than two years to graduate."
--- Annette Emerson
"Wandering albatross defies rational explanation," by Steve Connor. The Independent (U.K.), 25 October 2007.
"Some turtles win the old shell game," by Peter Calamai. Toronto Star, 24 October 2007.
Mathematician Gabor Domokos has discovered that only a handful of the world's 200 known species of sea and land turtles are "self-righting". The high-domed land turtles---tortoises---have a monostatic shape that enables the creatures to flip themselves upright after being on their backs. "No matter how you put a monostatic object down it will always rearrange itself to the same unique position," says Domokos, a math professor at Budapest University of Technology and Economics. He and graduate student Peter Varkonki discovered this after noticing that the "Gomboc" self-righting object they designed resembled some tortoises with high backs.
--- Annette Emerson
"Student snags maths prize", by Geoff Brumfiel. Nature, 24 October 2007.
These articles report on the "Wolfram 2,3 Turing Machine Prize", which carries a cash award of US$25,000 and which was won in October 2007 by Alexander Smith, a 20-year-old electrical engineering undergraduate at the University of Birmingham in England. The establishment of the prize was announced in May 2007 by Wolfram Research, the highly successful software company headed by physicist Stephen Wolfram. The prize was to be given for the solution to a problem about Turing machines, which are theoretical constructs that underlie the workings of all computers. The problem was to demonstrate that a certain Turing machine described in Wolfram's book A New Kind of Science, called the 2,3 Turing machine, is universal, meaning that it could simulate any other Turing machine. Judging from the comments of experts quoted in these articles, the solution to the problem is a laudatory achievement by Smith but is not particularly significant in computer science or mathematics. "I don't think anything is going to hinge on whether that Turing machine is universal or not," Martin Davis told Scientific American. Davis, a 20th century pioneer in logic and computer science, is retired from New York University and sat on the prize selection committee. In a posting on the Foundations of Mathematics list server shortly after the announcement that Smith had won the prize, Davis commented that as far as he knew, none of the members of the selection committee had seen Smith's 44-page proof.
--- Allyn Jackson
"Math is more than numbers," by Kristina Peterson. San Jose Mercury News, 21 October 2007.
"Beginning math is boring, let's not pretend otherwise," admits Ketih Devlin, mathematician and executive director of Stanford University's Center for the Study of Language and Information. But as the article points out, he "has done his best over the years to prove that math can be used to analyze people and their reasoning, with results that are both accurate and interesting." US Devlin, author of 26 books and a regular guest as the "Math Guy" on National Public Radio, was recently awarded the Carl Sagan prize for "science popularization" and its US$5,000 reward for his widespread presence.
--- Annette Emerson
"The Ignobility of Wrinkles," by Julie J. Rehmeyer. Science News, week of 20 October 2007.
"Study on math, science should strike fear in our hearts", by Diane Stafford. Kansas City Star, 17 October 2007.
This opinion piece discusses a new report, issued by the Public Agenda research organization, about student and parent attitudes towards studying math and science. The report, Important, But Not for Me, describes results of a survey conducted in Kansas and Missouri. The survey found that seven in ten parents think that things are "fine as they are" when it comes to the education their children are getting in math and science. By contrast, "[b]usiness and science leaders could not disagree more," writes Stafford. Many parents and students seem to view study of math and science for a select few who plan to go on to be scientists or doctors. They do not seem to understand the range of careers available to those with training in math and science, much less do they realize that such training will be required more and more for all kinds of jobs in the future. The report found that only one-third of parents say it's a "serious problem" that their kids are not learning more math and science. One-quarter of parents wanted better math and science instruction, but they rated limiting class size and improving teacher salaries as higher priorities.
--- Allyn Jackson
"Americans' Theory for Maximizing Gains Wins Nobel", by Jim Zarroli and Melissa Block. National Public Radio, 15 October 2007.
In October 2007 the Royal Swedish Academy of Sciences announced that the Nobel Prize in Economics would be awarded to three economists, Leonid Hurwicz of the University of Minnesota Twin Cities (age 90), Eric Maskin of the Institute for Advanced Study in Princeton (age 56), and Roger Myerson of the University of Chicago (age 56). In the 1960s, Hurwicz began developing mathematical models to represent economic situations like auctions, in which the people involved hold private information about their preferences that they do not divulge to others. He also studied optimal methods for allocating public goods. Maskin and Myerson later expanded on Hurwicz's work and, together with other collaborators, developed what is now known as mechanism design theory, which offers ways to assess institutions and policies and see which ones are optimal. The theory has been used to assess proposed public policies, such as auctions for carbon emissions permits. Maskin and Myerson both hold PhDs in applied mathematics from Harvard University.
--- Allyn Jackson
"Cooperation counts for math professor," by Heather Wax. Boston Globe, 15 October 2007.
Sitting at the intersection of evolutionary biology and game theory, Martin Nowak studies cooperation through the lens of mathematics. His work has led him to believe that moral virtues are part of an evolutionary framework; he says "The most competitive scenario of natural selection... can actually lead to features like generosity and forgiveness." Aside from theology, Nowak has delved into cell biology, where he pictures cancer as simply a breakdown in cooperation. But his interdisciplinary bent does not end there. His most recently published work in Nature analyzes the evolution of language, comparing the rate of regularization of a word to the frequency of its usage. The paper, "Quantifying the evolutionary dynamics of language," states that "The half-life of an irregular verb scales as the square root of its usage frequency: a verb that is 100 times less frequent regularizes 10 times as fast." For example, as time goes on, more verbs acquire common past tense endings like "ed". It seems that just as we model earthquakes and animal migrations, we can mathematically model our own evolution.
See also: "Mit Mathematik der Sprache auf der Spur: Intensiver Gebrauch macht Wörter stabil (On the trail with mathematics: More intensive use makes words stable)", by George Szpiro, Neue Zürcher Zeitung, 17 October 2007.
--- Brie Finegold
"Kreuzzug gegen schlampige Mathematik (Crusade against slovenly mathematics)", by George Szpiro. Neue Zürcher Zeitung, 14 October 2007.
Douglas Keenan is a mathematician who has dedicated himself to, as the article puts it, "an outright crusade against unclean mathematical machinations". In this context "unclean" refers to the misuse of mathematical or statistical methods. Two examples described in the article concern the misuse of mathematics to support the case of global climate change.
--- Allyn Jackson
In this article, Julie Rehmeyer tells the story of a prayer book created about 700 years ago from a parchment copy of the works of the ancient Greek mathematician Archimedes. The manuscript is an example of a palimpsest---typically a parchment manuscript on which more than one text has been written. The book surfaced in the early 1900s, long enough for the barely legible original text to be studied under a microscope by Danish philologist Johan Ludwig Heiberg. However, it disappeared again until 1998, when an anonymous buyer purchased the book for US$2 million at a Christie's auction and funded a research project aimed at preserving the book and deciphering the original text.
The results of the research, headed by Stanford University historian of mathematics Reviel Netz and William Noel of the Walters Art Museum in Baltimore, have been fascinating. Multispectral and x-ray fluorescence imaging have made the original text and diagrams legible. As a result, the only known copies of two texts have been discovered. In one of these texts, known as The Method, Archimedes used both potential infinity and actual infinity to compute the areas of many curved regions (other than circles) and the volumes of curved objects. In Rehmeyer's words, "Netz argues that The Method reveals the originality and daring of Archimedes' thought and shows that he anticipated some of the bold steps that would later lead to the full development of calculus."
You can read more about Netz and Noel's research in their just-published book, The Archimedes Codex.
--- Claudia Clark
"A Society Makes a Logical---and Symbolic---Move to Cambridge U. Press," by Jennifer Howard. Chronicle of Higher Education, 5 October 2007, page A14.
Howard points out that lately scholarly societies have been abandoning university presses and allying with "well-heeled" publishing companies, but the Association for Symbolic Logic has made the opposite move, cutting ties with Springer (with whom it collaborated on the Journal of Philosophical Logic) and teaming up with Cambridge University Press. The two will begin publishing the Review of Symbolic Logic in June 2008. The new journal will expand its predecessor's scope, and will include the philosophy and methodology of mathematics, in addition to areas of logic. Says Penelope Maddy, president of the Association, "Assuming the Review does as well as we think it will do, this is a great boon to the organization."
--- Mike Breen
"Ben Green to receive 2007 SASTRA Ramanujan Prize." The Hindu, 4 October 2007.
"The powerhouse 'pirate' of the math classroom," by Billy Baker. The Boston Globe, 1 October 2007.
"Making the Grade," by Jeffrey Mervis. Discover, October 2007, pages 44-46, 92-93.
Science, technology, engineering, and mathematics (STEM) education reform is the focus of this article, which appeared in a special issue of Discover about the state of science in America. After noting some of the "signs of deficiencies" in STEM education, writer Jeffrey Mervis interviews a number of education reformers about their work and perspective on the subject. Some of these reformers, such as physicist and 2001 Nobel Prize winner Carl Wieman, are working on improving undergraduate science and math teaching. Wieman and others have incorporated educational tools into their classrooms, including "handheld electronic clickers" that allow students to answer questions in class, giving their teachers feedback that allows them to address problems immediately. Others, such as University of Vermont mathematician Ken Gross, are providing professional development for current teachers: Gross has developed a three-year graduate program to increase elementary school teachers' understanding of mathematics to improve their math teaching. Finally, Texas Instruments has tapped experts such as Deborah Ball, dean of the University of Michigan School of Education, to develop a professional development program for teachers in Texas Instrument's Richardson, Texas location.
There are some difficulties surrounding education reform. Not everyone is optimistic: George Washington University professor of education Sharon Lynch says that the decentralized nature of education in the United States makes the idea of "scaling up" any local improvements "ludicrous." At the same time, Mervis notes that reformers such as Wieman would agree that the challenge of finding the additional time and funding required to rigorously assess each innovation and identify its effect on student learning is "the only way to achieve the system of science education that the nation needs."
--- Claudia Clark
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