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August 2010
"Brains behind the maths," by Kalyan Ray. Deccan Herald, 31 August 2010. “Math is everywhere,” said the famous tagline for the recently cancelled TV show Numb3rs. Still, it’s probably hard for most people to see how high level mathematical research really affects us in everyday life. In this article, Ray shows us a few examples inspired by the International Congress of Mathematicians held in Hyderabad this past August. Stanley Osher’s research in “level set methods,” for example, was used extensively to create the graphics for the movie Avatar [for more on math in 3D movies, see "Adding Depth" on the Mathematical Moments page]. The UCLA mathematician is more interested in the applications of his research to reallife problems, however, like in the military for detecting IEDs (Improvised Explosive Devices) from satellite images and in medical research for creating better scans of the body. His first famous application of mathematics to a realworld problem came following the Los Angeles riot in 1993, when image analysis revealed a rose tattoo on the arm of a suspect, and eventually led to his conviction. In the case of Yves Meyer, professor emeritus at the École Normale Supérieure de Cachan in France, and winner of the Gauss prize in the ICM, the applications of his work came later. Meyer’s work formed, a decade later, the basis for JPEG and satellite imaging. The winner of this year’s Rolf Nevalinna prize for outstanding contribution to the mathematical aspect of information sciences, Daniel Spielman, is behind the error correcting codes that make online credit card transactions secure. Spielman, a professor at Yale, says that new opportunities are opening up for applying mathematics in biology, drug development, economy, and political science.  Adriana Salerno "The Inconvenient Truth About Traffic Math: Progress Is Slow," by Carl Bialik. The Wall Street Journal, 28 August 2010. With a recent 60mile traffic jam in China as a backdrop, “Numbers Guy” Carl Bialik takes a look at the limitations of using mathematics to deter and detangle traffic snarls. One large problem is that over 50% of traffic jams are caused by special events, such as blizzards, that cannot be predicted. The frequency of irrational driving behavior also makes accurate modeling difficult. Research shows that adding roads—which seems like the most logical solution—actually does little to ease congestion because it draws out drivers who had travelled at alternate times or through alternate means. Mathematics has led to some advances, such as highway ramp metering, that save drivers small amounts of time, but researchers are hoping to use large amounts of data from GPS systems, which they hope will lead to greater advancements. Lisa DeKeukelaere
"Skilled at the Chessboard, Keyboard and Blackboard," by Dylan Loeb McClain. The New York Times, 28 August 2010. The first installment of the New York Times chess column talks about Harvard University mathematician Noam Elkies, who is a topclass mathematician as well as a gifted composer and a chess mastera rare "triple threat," as the column puts it. The brief sketch of Elkies's career mentions his graduating from high school at 15, finishing a bachelor's degree at the top of his class at Columbia University at 18, and receiving his PhD in mathematics from Harvard at 20. A decade later Harvard hired him as its youngestever professor. After noting that Elkies has written extensively about chess, the column discusses two chess games played by Elkies, one in 1984 and one in 1987. The second piece lists some other notable chess players who were or are mathematicians, with a link to the "Mathematicians and Chess" web page.  Allyn Jackson "NSF Turns Math Earmark on Its Ear to Fund New Institute," by Jeffrey Mervis. Science, 27 August 2010. An "earmark" is a clause in an appropriations bill instructing a federal agency to spend a certain amount of money on a specific project. Earmarks are rare in appropriations for the National Science Foundation, as the agency's peer review system is understood to be crucial to its mission. But in 2009, Senator Harry Reid of Nevada inserted an earmark that instructed the NSF "to establish a mathematical institute devoted to the identification and development of mathematical talent and to advance mathematical topics critical to the national interest." Reid's idea apparently was to build up the Davidson Academy, a school that served exceptionally talented middle and highschool students and is based on the campus of the University of Nevada, Reno. At the time the earmark was inserted, the NSF's Division of Mathematical Sciences (DMS) was already planning a new call for proposals for mathematical sciences institutes. Among the proposals that came in was one involving the Davidson Academy. Following the earmark's instructions to the letter would probably have meant funding that proposal. But the DMS turned it down and instead continued funding for four existing math institutes and funded a fifth new one, at Brown University (see 7 August Digest below). "NSF's decision appears to be okay with Reid," Mervis writes, quoting a Reid staffer who said that Reid was pleased the number of math institutes could be expanded.  Allyn Jackson
"Ingrid Daubechies Heads International Mathematics Union," The Hindu 19 August 2010. According to applied mathematician Ingrid Daubechies, mathematics is like sports: although few people can play at the most competitive levels, everyone can enjoy playing with a few likeminded peers. A few days before the Fields medals and other prizes were awarded, Daubechies celebrated her birthday and became the first woman elected president of the International Mathematical Union (IMU). Best known for her work on wavelets, Daubechies has won many prizes and was (in 1993) the first woman to become a full professor of mathematics at Princeton University. When asked about why so few women are in the top levels of mathematics, she said, “the relative scarcity of women is a cultural phenomenon”. Similarly, she sees young peoples’ disinterest in math as being due to its “bad reputation,” which could be overcome by encouraging teachers who themselves enjoy mathematics. Daubechies will move from Princeton to Duke University in 2011 when she starts her term as IMU president.  Brie Finegold
"Fields Medal Recognizes Mathematical Achievement," Robert Siegel. All Things Considered, NPR, 19 August 2010. This is a sampling of the worldwide coverage of prizes given by the International Mathematical Union on August 19. The prizeswhich included the top honor in mathematics, the Fields Medalwere handed out at the opening ceremonies of the International Congress of Mathematicians in Hyderabad, India. The Fields Medals went to Elon Lindenstrauss, Ngô Bào Châu, Stanislav Smirnov, and Cédric Villani. While none of the medals were given for applied mathematics per se, the work of three of the four medalists (Lindenstrauss, Smirnov, and Villani) have strong ties to other disciplines and exhibit the increasingly interdisciplinary nature of mathematics research today. The Nevanlinna Prize for achievements in theoretical computer science was awarded to Daniel Spielman, and the Gauss Prize for outstanding work in applications of mathematics to Yves Meyer. The firstever Chern Medal, recognizing oustanding achievements in mathematics regardless of age, went to Louis Nirenberg. The Chern Medal carries a cash prize of US$250,000. What is more unusual is that the medalist can nominate one or more organizations to receive funding totaling US$250,000, for the support of research, education, or other outreach programs in the field of mathematics.  Allyn Jackson "How DNA evidence creates victims of chance," by Linda Geddes. New Scientist, 18 August 2010. DNA evidence seems foolproof but often the probability of a match between a suspect and a sample is a matter of dispute. In a trial cited in this article, a DNA analyst testified that the probability that a sample did not come from the defendant was about 1 in 95,000; the prosecution and the analyst's supervisor put the chance at 1 in 47; a later review estimated the chance to be 1 in 13 and a final review arrived at a probability of 1 in 3. The person was convicted, although he plans to appeal. Part of the reason for the discrepancies at this trial and others is because DNA samples are often degraded and contain DNA from more than one person. Alleles that match both the victim and the defendant are discounted in probability calculations by some labs but used by others. The National Institute of Standards and Technology sent identical DNA samples to 69 labs and got reports of probability estimates that differed by as much as 10^{10}. Labs currently use different statistics, which has prompted the Scientific Working Group on DNA Analysis to call for the use of one statistic: the likelihood ratio, which is the probability that the sample is from the suspect divided by the probability that the sample is not from the suspect.  Mike Breen "Step 1: Post Elusive Proof. Step 2: Watch Fireworks," by John Markoff. The New York Times, 16 August 2010. The P versus NP problem is considered to be among the most important and challenging open problems in computer science and mathematics. So when mathematician and computer engineer Vinay Deolalikar sent his 103page proof via email to several key researchers earlier this month with the announcement that he had proven that P does not equal NP, “Dr. Deolalikar set off shock waves because his work appeared to be a concerted and substantial challenge to a problem that had attracted intense scrutiny,” Markoff writes. After several days of work, the consensus among complexity theorists was that Deolikar did not prove that P does not equal NP. “What was highly significant, however, was the pace of discussion and analysis, carried out in real time on blogs and a wiki that had been quickly set up for the purpose of collectively analyzing the paper.” In the past, hashing out such a problem would take place via the pages of scientific journals, private email, and distribution lists, if not the actual presence of the participants. “Now, with the emergence of Webconnected software programs,” Markoff notes, “it is possible for such collaborative undertakings to harness the brainpower of the world’s best thinkers on a continuous basis.” In fact, New York University professor of interactive communications Clay Shirky claims these new tools are making a second scientific revolution possible: “a new set of norms is emerging about what it means to do mathematics, assuming coordinated participation.”  Claudia Clark
"Math Buskers Juggle Numbers On English Streets," by Liane Hansen. NPR's Weekend Edition Sunday, 15 August 2010. For this story, Weekend Edition host Liane Hansen speaks with a mathematician at the Royal Institution of Great Britian, Sara Santos (pictured at left in the yellow tshirt), who has taken her love of mathematics to the streets. Santos entertains her fellow Londoners as a street performer, or busker. However, you won’t find her juggling chain saws or performing slight of hand: her shows are based on mathematics and include “mathematical mind reading” and “topological games, such as tying up people together or wearing your waistcoat, being handcuffed, and turning the waistcoat inside out.” According to Santos, “the reason why the shows work and why the shows are surprising and engaging is because the mathematics behind it makes it so.” Santos notes that she and her fellow math buskers don’t try to explain the math behind the performances. Instead “lots of people start shouting out answers or telling the volunteer how to play and that's when people are doing the math…they're actually learning the math. They're working it out themselves.” (Image courtesy of the Royal Institution in London, click for larger version.)  Claudia Clark "Silicon Valley girls capture medals in China math olympiad," by Eric Messinger. The Mercury News, 13 August 2010. American high school girls put in their best showing yet at this year’s annual China Girls Mathematical Olympiad, earning five gold and two silver individual medals and second place overall. Competitors at the twoday event, held in Shijiazhuang, China in midAugust, were scored based on their answers to eight math problems. The director of Berkley’s Mathematical Sciences Research Institute, which organized the trip, explains that the format was designed to evaluate creative problemsolving skills, rather than focusing on speed or specific advanced concepts. The American girls who competed were among the top finishers in the 2010 USA Mathematical Olympiad, and they enjoyed the opportunity to teach math to local students in Shijiazhuang before picking up their exam pencils at the competition. [Photo: Standing from left to right are Lynnelle Ye, Jae Eui Shin, Shiyu (Jing Jing) Li, Shijie Joy Zheng, Alissa Zhang (alternate), and Elizabeth Synge; Sitting from left to right are Alison Miller (Assistant Coach), Adisa Kruayatidee, Cynthia Day, Sheela Davades (alternate), Andi Wang, and Zuming Feng (Team Coach).]  Lisa DeKeukelaere
"Google Helps Find Simplest Solution to Rubik's Cube," by Priya Ganapati. Wired, 10 August 2010. Rubik’s Cube is arguably the best known and most popular puzzle of all time. And since its appearance, mathematicians have jumped at the chance to figure out the best algorithms to solve it, and naturally wondered how many moves a solution would take given any configuration. This upper bound for the number of moves earned the name of “God’s number,” since an allknowing entity would always know the best strategy for any starting configuration. “We now know for certain that the magic number is 20,” says Morley Davidson, a mathematician from Kent State University, who proved this together with John Dethridge, an engineer at Google, Herbert Kociemba, a math teacher, and Tomas Rokicki, a California progammer. The researchers first split the 43 billion billion possibilities into groups (cosets), then reduced those cases by using symmetry and spotting duplicates. In the end, they reduced the number of starting configurations to 56 million sets of 20 billion combinations. Google then stepped in to help with the supercomputing aspects (although they remain tightlipped about what exactly they did). In the end, the computers could solve all of these cases by using at most 20 moves (in fact, the majority of solutions take between 15 and 19 moves to solve). The researchers are now looking forward to tackling a fourlayered version and other mathematical problems related to the famous cube. Read a detailed account on the history of “God’s number.”  Adriana Salerno "Stanford and UC Berkeley create massively collaborative math," by Lisa M. Krieger. The Mercury News, 8 August 2010. While there is no “proof by popularity” in mathematics, mathematicians are taking a hint from websites that crowd source. Sites like Math Overflow provide a forum for brainstorming. “The idea is to have a place that is a repository of global knowledge,” explains Stanford University professor Ravi Vakil. Visitors to the site, including both eminent mathematicians and graduate students, ask and answer questions concerning mathematics and academia. But no mathematical pedigree is needed to enter the site. As Vakil says, visitors can "be anthropologists and watch our strange tribe.” Less than a year ago, Dr. Vakil decided to support the site through his research budget after being approached by four young Berkeley mathematicians who had come up with the idea. Since then, daily traffic has climbed to 30 new questions and 2,500 users. Blogs such as the nCategory Café, which focuses on mathematics, physics, and philosophy, also serve as hotbeds for international collaboration. For example, Timothy Gowers’ blog became the home to comments that led (in under two months) to a proof of the Density HalesJewett theorem. This is one of many recent popular articles dispelling the stereotype that mathematics is the domain of solitary practitioners working in their attics.  Brie Finegold "Brown gets $15.5 million to create center for mathematics and computational research." Providence Journal, 7 August 2010.
The Providence Journal reports on a NSF grant awarded to Brown University to create a mathematics institute there. The grant is intended to bring entrepreneurs and academics together to solve realworld problems. The new Institute for Computational and Experimental Research in Mathematics at Brown will employ over a dozen researchers and include representatives of Google, IBM and Microsoft on its scientific advisory board. The institute has two main objectives: to design research programs that apply mathematics to solve reallife challenges and to improve instruction in kindergarten through grade 12 in view of new computational tools available to mathematicians. (Photo of institute director Jill Pipher by Mike Cohea/Brown University.) See also: "NSF Turns Math Earmark on Its Ear to fund New Institute," by Jeffrey Mervis, Science, 27 August 2010, page 1006.  Baldur Hedinsson "The pattern collector," by Julie Rehmeyer. Science News, 6 August 2010. These days, when a mathematician, computer scientist, physicist, or another researcher encounters a sequence of integers, there is only one place that they would think to look for more information: The Online Encyclopedia of Integer Sequences (OEIS). With only the first few terms of the sequence, one can search through the database for all sorts of details about it, and even its historical context. The website was created by Neil Sloane, now a researcher at AT&T Labs. Sloane started collecting integer sequences as a graduate student, when he would write them down on cards. In 1972, his collection of 2400 cards turned into a book, A Handbook of Integer Sequences. This book led to a sequel and eventually to the website. The online database has over 100,000 sequences, but often mathematicians and other researchers stumble upon sequences that are not on the website, in which case they will email Sloane and suggest an addition. Until recently, Sloane would read an average of 45 such emails a day, but this number has been steadily increasing. This is why the OEIS is going into a new stage of development: It will now be a wiki, with about 70 associate editors taking up Sloane’s duties. The wiki is still in its preliminary stages, but a version can be found at the above link. The developers of the wiki are still working on speeding up the ability of the wiki to search through sequences. Hopefully, Sloane’s dream, “that eventually the database will include every (interesting) number sequence that has ever been published,” will come true through this new format.  Adriana Salerno
“I Find the Subject Fascinating…,” Interview by Rosalind Ezhil K. The Hindu, 2 August 2010. World chess champion Viswanathan Anand took on 35 mathematicians and 5 others simultaneously at the International Congress of Mathematicians (ICM). His record was 39 wins and one draw, the draw coming against 14year old Srikar Varadaraj, who coauthored a paper that was presented at the conference. In the article from The Hindu, written before the ICM, Anand answers questions about links between math and chess and his own affinity for mathematics. According to Anand, mathematicians and chess players both benefit from studying and finding connections between multiple subject areas within their respective disciplines. He said that he expected some interesting games to develop during the ICM match and wishes he had studied more math in the past. Anand expresses enthusiasm for reading about various types of mathematical concepts and mathematicians on the Internet, but identifies himself as an amateur at math. He notes that an adult interested in math, like him, can find many resources that make learning math fun, but the constraints on school teachers—who have less context and a limited amount of time to convey new information—make it difficult to instill the value of mathematics in young students.  Lisa DeKeukelaere

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