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Summaries of Media Coverage of Math
Edited by Mike Breen and Annette Emerson, AMS Public Awareness Officers
Jean-Paul Bourguignon, who was recently named as the next head of the European Research Council. Photo by Jean-François Dars.
This Month's Math Digest Summaries Posted here December 2013: New strategies in Prisoner's Dilemma, why scientists swear by math, and national test scores ...
See also: The AMS Blog on Math Blogs: Two mathematicians tour the mathematical blogosphere. Editors Brie Finegold and Evelyn Lamb, both PhD mathematicians, blog on blogs that have posts related to mathematics research, applied mathematics, mathematicians, math in the news, mathematics education, math and the arts and more. Recent posts: "How Quadratic Reciprocity Is Like Dealing Cards" and "Exploding Myths About the History of Science."
"Together and Alone, Closing the Prime Gap," by Erica Klarreich. Quanta Magazine, 19 November 2013.
If you thought you'd heard the last from the twin primes conjecture, boy were you wrong. Since Yitang "Tom" Zhang stunned the mathematical world with his May proof that there are infinitely many pairs of primes separated by no more than 70 million, a flurry of activity has been centered on that arbitrary but enormous number. On May 30, Scott Morrison of Australian University in Canberra dropped that distance to 56 million and change. The comments on his blog post chronicle the bound's precipitous drop over the next few days, engineered by Morrison, Terence Tao, and others. By the end of May 31st, Morrison had brought the bound down to 42 million and change; by June 2nd, Tao had introduced improvements bringing the bound down to 13 million and change. By June 4th, Tao had created the Polymath Project, an open, online collaboration to improve the bound, and by June 27th, the maximum infinitely recurring separation between primes was 4,680. "At times, the bound was going down every thirty minutes," says Tao. But it seems the prime gap conjecture was an idea whose time had come: on November 19th, University of Montreal postdoc James Maynard posted an independent proof showing that there are infinitely many pairs of primes no further than 600 apart. This fascinating article takes a close look at some of the working parts of Zhang's and Maynard's proofs, the techniques being used to improve them, and the interplay between open collaboration and independent research that has driven the advances. Zhang's proof involves three pieces, each of which has been refined by the Polymath Project. First, Zhang used a collection of results by Pierre Deligne to draw conclusions about the distribution of primes, and in turn derived specifications for a new class of sieves--which Klarreich describes as "a comb with some of its teeth snapped off." Second, he used results from the calculus of variations to determine how many teeth one of his sieves would need to "catch" infinitely many pairs of primes. Finally, he calculated how large a comb he would need to start with to end up with a sieve with enough teeth. Progress has been made on all three fronts, even eliminating Deligne's difficult machinery from the proof. But Maynard has taken a different approach, by looking at the sieves themselves and obtaining more precise information about them, to show that certain sieves are much more powerful than originally thought. The Polymath Project is already working on Maynard's result, hoping that his insights can be combined with theirs. Meanwhile, Zhang has a "secret weapon" in reserve, a technique he developed before publishing his proof, which may bring the bound down even further--so stay tuned.
--- Ben Polletta
"Advanced Mathematics With Legos in a Washing Machine," by Colin Lecher. Popular Science, 11 November 2013.
This whimsical story discusses an equally whimsical paper by Ingo Althöfer, a mathematician at the University of Jena in Germany. In the paper, he describes mathematically oriented games in which a bunch of Lego toy pieces are run through a washing machine (warm water, no detergent, no spin cycle). The washing machine tosses and mixes the Legos in a more or less random fashion. Lego pieces get stuck together, knocked apart, and stuck together again. What kinds of shapes emerge from this process? Read the PopSci article to find out, or go straight to the source, Althöfer's paper: "Random Structures from Lego Bricks and Analog Monte Carlo Procedures".
--- Allyn Jackson
"Whose Brain Is It Anyway?" News of the Week. Science, 8 November 2013, page 678.
In the hope of understanding genius, Rudolf Wagner gathered many brains in the 19th century, including that of Carl Friedrich Gauss. Recently it was discovered that the brain labeled as Gauss's was actually that of Dr. Conrad Heinrich Fuchs. Renate Schweizer, who discovered the mistake, thinks that the brain had been mislabeled since the 1860s. She adds that anatomically Gauss's actual brain is not exceptional. [For more on this story, see Tony's Take]
--- Mike Breen
"U.S. Math, Reading Achievement Edges Up, But Gaps Remain," by Catherine Gewertz. Education Week, 7 November 2013.
The recently released results of the 2013 National Assessment of Educational Progress indicate that since 2011, the average math score of American fourth graders has improved by three points, and the average math score of eighth graders has improved by one point, on a 500-point scale. Although the scores show general improvement, only 42 percent of fourth graders and 36 percent of eighth graders are achieving "proficiency level" in math, a "less than rosy picture" according to the author. Tennessee and the District of Columbia, which recorded the largest score increases in the country, both credit their progress to implementation of the Common Core State Standards for curriculum and enhanced teacher evaluation programs. Across genders and ethnicities, math results indicated Hispanic students improved 2 points and female students improved 1 point, but gaps persisted between Hispanic or black students and white students, as well as between male students and female students.
--- Lisa DeKeukeleare
"Why do scientists swear by Mathematics?", by Mayank Vahia. Daily News and Analysis, 2 November 2013.
Dr. Mayank Vahia writes an interesting article for the Indian broadsheet newspaper, Daily News and Analysis (DNA) about how everyone can learn to appreciate mathematics. Dr. Vahia's piece is based on answering a very fundamental question: Why do scientists swear by mathematics? The answer boils down to "Because it is really useful," but Dr. Vahia takes the reader on a fun and exciting journey from prehistoric times up to the present day. Dr. Vahia starts by explaining how mathematics originally came to humans as a counting system, probably to keep track of the number of their livestock. Since humans have 10 fingers, most early cultures had special symbols for units of 5 or 10 similar to the Roman numerals. Though such numerical systems come naturally, they are not suited for adding or subtracting. Mathematics took a major step forward when a number system similar to the one we use today was introduced. The new number system allowed for introduction of concepts such as multiplication and division, also the invention of a number representing no value, the number zero. Armed with division and multiplication, the field of algebra soon followed creating the foundation for scientists of the 16th and 17th centuries such as Newton who were able to describe nature's patterns using simple algebraic equations.
Dr. Vahia's piece does a great job describing mathematic's evolution through the ages and its close relationship to science. A highly recommended read.
--- Baldur Hedinsson
"Sharing Math's Appeal With First-Generation Students," by Susan D'Agostino. The Chronicle of Higher Education, 1 November 2013, pages B28-B30.
In this article, Southern New Hampshire University (SNHU) mathematics professor Susan D'Agostino describes why her college--which offers many career-oriented degrees--decided to develop a mathematics major, and how they went about recruiting and retaining students. As is typical at other regional institutions, a large proportion (one-third) of the students attending SNHU are the first in their family to attend college. By offering a mathematics degree, the university is serving first-generation students who "represent an untapped pool with potential to increase the quantity and quality of highly educated workers in areas of national need." In order to attract students, "the launch of [the] program included an awareness campaign alerting students to a range of career and graduate-school options in math." These have included a well-attended panel of professionals, all of whom were undergraduate math majors, as well as visits to entry-level math courses by math faculty who explain "why courses with unfamiliar names like 'differential equations' or 'regression analysis' are interesting and worthwhile." At the same time, the program offers students "a highly social Math Club, potential paid employment as math tutors, well-attended faculty office hours, and career counselors who are eager to place majors upon graduation." D'Agostino is proud to report that SNHU currently has 27 math majors and 50 math minors.
--- Claudia Clark
"French Mathematician Tapped to Head Key Funding Agency," by Martin Enserink. Science, 1 November 2013, page 545.
Science's News and Analysis section has a piece about the newly appointed head of the European Research Council (ERC), mathematician Jean-Pierre Bourguignon (left). The ERC is a young agency and has become popular among European scientists for its prestige and relatively easy procedures. The Frenchman Bourguignon has headed the Institute of Advanced Scientific Studies (IHÉS), a private institute in the southern suburb of Paris, for the last 19 years but will at the age of 66 succeed Austrian sociologist Helga Nowotny at the ERC on January 1. Bourguignon is credited with giving IHÉS a solid financial footing through worldwide fundraising. Bourguignon is also known for his enthusiastic educational efforts, which include a 2012 video that went viral called A Beautiful Formula, in which Bourguignon spends eight minutes illustrating the beauty of Euler's identity. "He is extremely dynamic, efficient and reliable," says Daniel Barlet, a mathematician at the University of Lorraine. Photo by Jean-François Dars.
--- Baldur Hedinsson
"New Dilemmas for the Prisoner," by Brian Hayes. American Scientist, November-December 2013, pages 422-425.
Last year, two scientists uncovered interesting new strategies for Prisoner's Dilemma, the age-old game in which two prisoners must decide whether to confess or remain silent, with one prisoner's payoff (or amount of points earned) depending on the other prisoner's decision. The article focuses on strategies in which prisoners make successive decisions based only on the outcome of the previous round, and a prisoner's strategy can be represented by the set of probabilities that he will remain silent after each of the four possible combinations of previous decisions. Early research highlighted the "tit for tat" strategy, in which a prisoner initially remains silent, then in each subsequent round adopts his opponent's previous decision. In contrast, the new strategies, termed "mischievous" by the author, allow one prisoner to control the other's score based on special algebraic relationships between the probabilities in the prisoner's strategy set. By applying the new strategies in evolutionary experiments, other scientists revealed that in general, generosity is a more robust strategy than mischief.
--- Lisa DeKeukeleare
"Root of maths genius sought," by Erika Check Hayden. Nature, 29 October 2013, pages 602-603.
Jonathan Rothberg--a Conneticut native, biologist, entrepreneur, and philanthropist--has enlisted about 400 mathematicians and theoretical physicists from top-ranked universities in the U.S. in his quest for the genes underlying mathematical genius (no pun intended). Of course, these luminaries won't be looking for the genetic basis of STEM smarts on the blackboard or in the literature. Rothberg--who has founded and sold two gene sequencing companies for undisclosed scads of money--will be using his Ion Torrent technology to sequence participants' DNA in an effort he is calling Project Einstein. "I'm not at all concerned about the critics," says Rothberg, "this study ... is not a crazy thing to do." What critics, you ask? There are plenty, with a cornucopia of objections. For one thing, there is no guarantee that genetic determinants of high mathematical ability exist. Studies have found that up to two-thirds of twins' numerical literacy in primary school is shared, and so may be due to genetic factors. But the road from primary school to a successful career in mathematics is a long and tortuous one, and many would agree with Berkeley mathematician Michael Hutchings that, on this journey, "the notion of 'talent' may be overrated." Even if there are genetic influences on high mathematical ability, the complexity of human cognition suggests they are likely to be the sum of small effects from many genes, rather than large effects from a single gene, and teasing out these effects--in so-called genome-wide association studies--requires a huge number of genomes to attain statistical power. A recent GWAS (genome-wide association study) of 126,000 individuals (abstract available to all, full text available to Science subscribers), searching for genetic determinants of educational attainment, found only three mutations that together accounted for about three months' worth of schooling. Finally, if there are genetic determinants of mathematical genius, and they can be isolated, many question whether this information can and will be used for good. Still, there is something inevitable about the quest. A similar search through the genomes of 1,600 mathematically precocious children is being conducted in Beijing, and while some, like Fields medalist Curtis McMullen, have balked at Project Einstein's ethical dimensions and refused to participate, others have caught Rothberg's enthusiasm. "I like the idea of having my own genome sequenced,” says Berkeley mathematician David Aldous. "Maybe I’ll print a segment onto a T-shirt."
--- Ben Polletta
"The Myth of 'I'm Bad at Math'," by Miles Kimball and Noah Smith. The Atlantic, 28 October 2013.
In this article, economists Kimball and Smith challenge the idea that mathematical aptitude is based purely upon some inborn genetic ability rather than on "hard work, preparation, and self-confidence." They begin by describing what they have observed in their roles as educators, as well as a little of the research that has been done on the impact of students' beliefs about the nature of intelligence on their levels of success. Kimball and Smith then explain their focus on beliefs about mathematical intelligence: "math skills are increasingly important for getting good jobs these days," and "math is the area where America's 'fallacy of inborn ability' is the most entrenched ... If we can convince you that anyone can learn math, it should be a short step to convincing you that you can learn just about anything, if you work hard enough." One way to "help Americans excel at math" might be to adopt (some of) the features of the educational systems of East Asian countries, which "focus more on hard work than on inborn talent." They also suggest that we "treat people who work hard at learning as heroes and role models. We already venerate sports heroes who make up for lack of talent through persistence and grit: why should our educational culture be any different?"
--- Claudia Clark
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