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Edited by Allyn Jackson, AMS
Contributors: Mike Breen (AMS), Claudia Clark (writer and editor), Lisa DeKeukelaere (2004 AMS Media Fellow), Annette Emerson (AMS), Brie Finegold (University of California, Santa Barbara), Adriana Salerno (University of Texas, Austin)
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"Outcalculating the Competition," by Heather Wax. Scientific American, October 2008, pages 96-99.
Wax writes about Martin A. Nowak and his work in evolutionary dynamics, a term he coined to describe the field of modeling how populations change over time. In 2003, Nowak became the first person at Harvard University to receive a joint appointment in mathematics and biology. Now he is trying to model the origin of life, attempting to capture "the transition from no life to life." Nowak was trained as a biochemist but believes that mathematics is the "true language of science," which will help uncover secrets of the past. He encodes monomers---the first building blocks of life---as binary strings in a chemical system and allows the strings to combine randomly, hoping that they will develop the ability to replicate. Nowak thinks that his models will help guide experiments: "Mathematics is the proper language of evolution. I don't know what the 'ultimate understanding' of biology will look like, but one thing is clear: It's all about getting the equations right."
--- Mike Breen
"Electrons as Math Whizzes," by David Castelvecchi. Science News, 27 September 2008.
Two European scientists are attempting to use the energy levels of electrons---a concept in quantum physics---to prove the Riemann Hypothesis, a famous unsolved mathematical problem. The scientists hope to show that an electron constrained to movement in two dimensions and subjected to electrical and magnetic fields will have energy levels that correspond to the points at which a special function, Riemann's zeta, has a zero value. In addition to earning the scientists international fame, proving the hypothesis would have an important impact on the study of prime numbers and the frequency of their appearance along the number line. Some are skeptical that this recent work, which so far is only an approximation of a connection between energy levels and zero values, will lead to a solution, but the connection between mathematics and quantum physics is nonetheless interesting.
--- Lisa DeKeukelaere
"The Mathematician And The Pig," by Lionel Tiger. Forbes, 24 September 2008.
This opinion piece by weekly columnist Tiger, who is a professor of anthropology at Rutgers University, says that mathematics "defeated" the nation's investment institutions and financiers. He writes that complex financial models "are able to conceal that a bonehead mortgage banker in a suburb of Sacramento sold an alluring house to a property-lusting courtier who couldn't even afford the first date." Tiger says that early humans
had to live in the here, the now, and the next moment. Abstract theories about the character of the universe may have been entertaining diversions around the campfire, but far more vital were competent assessments about the realism of others and management of the flow of emotion and enthusiasm that a hunter-gatherer had to live by. Should a member of a group announce that he just developed a structured investment vehicle which was computationally certified by a computer to contain a plump pig, he would have an immediate challenge from his peers---to show them the pig.
He concludes that those using the models did not understand them, so "..in the gratifying swirl of lavishly rewarded human optimism, no one remembered to glance at the pig to be sure it was still there--or ever was in the first place."
--- Mike Breen
"Students in advanced math classes are doing worse, according to private researchers [sic] report," by Libby Quaid. Chicago Tribune, 21 September 2008.
A study by the Brookings Institution says that more kids than ever are enrolled in algebra in eighth grade, but aren't necessarily learning more math (the amount of encouragement derived from the title of this article may equal the amount of surprise generated in math teachers by that conclusion). Today almost one-third of eighth graders take algebra. The study's author, Tom Loveless, says that many eighth-grade algebra students "don't know very much math at all and yet they're taking courses in advanced math." The report also looked at low-achieving math students, defined as those who scored in the bottom 10 per cent according to the National Assessment of Educational Progress, and found that their enrollment in eighth grade algebra has more than doubled since 1990 and that their teachers are mathematically unprepared. William H. Schmidt, a professor of statistics and education at Michigan State University, replies, "So what's the alternative---to let them continue in eighth grade to take low-level or basic math?... My big worry is people will use this [the study's conclusions] to say, 'Aha, see, it ain't working, let's put these kids back where they belong.'" He does agree that students do need better preparation.
--- Mike Breen
"Prime directive: Ottawa math whiz lands a big one," by Tom Spears. Ottawa Citizen, 16 September 2008.
"Twelve-year search uncovers two massive prime numbers," by Scott LaFee. The San Diego Union-Tribune, 18 September 2008.
"Wissenschafter realisieren zwei neue Primzahl-Rekorde (Scientists reach two new prime records)", by George Szpiro. Neue Zürcher Zeitung, 17 September 2008.
"UCLA mathematicians disover a 13-million digit prime number," by Thomas H. Maugh. Los Angeles Times, 27 September 2008.
In late August, two Mersenne primes, 243,112,609-1 and 237,156,667-1, were discovered through the Great Internet Mersenne Prime Search (GIMPS), a distributed computing project connecting more than 100,000 computers worldwide. Both prime numbers are more than 10 million digits long, which earns a prize of US$100,000 from the Electronic Frontier Foundation for the first one discovered, the larger number. The cash prize will be shared by Edson Smith, of the UCLA Mathematics Computing Group, where the prime was discovered; and Scott Kurowski and George Woltman, who developed the software for GIMPS. The search will continue. There is now a US$150,000 prize for the discovery of the first 150-million digit prime. Jeff Gilchrist, a math Ph.D. student at Carleton University, was part of the verifying process for the larger prime. This is the sixth time that he has confirmed a record-setting prime number. His non-prime research area involves discovering hidden patterns in vital signs of patients in intensive care.
--- Mike Breen
"It's Likely That Times Are Changing," by Tom Siegfried. Science News, 13 September 2008, pages 26-28.
The change is a change in the way some physicists are thinking about how space and time fit together. They are rethinking the connection in hopes of making relativity mesh with quantum mechanics, which may help our understanding of so-called dark energy. Perhaps space and time are distinct, emerging separately from basic elements then merging into "the mirage that human inquiry is able to access." The mathematics in the article involves Hermann Minkowski. Einstein was a student---although not a very diligent one---in Minkowski's class. Later, Minkowski helped put Einstein's ideas on a sound mathematical footing. With regard to special relativity, Minkowski said, "Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality." The physicists in this article now aren't so sure.
--- Mike Breen
"Queuing conundrums." The Economist, 11 September 2008.
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Hyejin Youn and Hawoon Jeon (Korea Advanced Institute of Science and Technology) and Michael Gastner (Santa Fe Institute) have used sophisticated computer modelling, with real-time data from road sensors, satellites, and cell phones, to analyze the efficiency of traffic routes. Their research shows that in some cases the information does not help drivers get to their destinations faster. Their study (to be published in Physical Review Letters) "found that when individual drivers each try to choose the quickest route it can cause delays for others and even increase hold-ups in the entire road network... Eventually the traffic flow on the two routes settles into what game theory calls the Nash equilibrium, named after John Nash, the mathematician who described it. This is the point where no individual drive could arrive any fast by switching routes." The article highlights an example of a trip from Harvard Square to Boston Common in which 246 different links in the road network were possible, and summarizes how the traffic flows were calculated. Although the researchers acknowledge that more work needs to be done to understand the effects of the Nash equilibrium, they suggest that "planners should note that there is now evidence that even a well intentioned new road may make traffic jams worse." --- Annette Emerson
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"Oded Schramm, 46, Mathematician, Is Dead," by Kenneth Chang. The New York Times, 11 September 2008.
"Oded Schramm." The Telegraph, 19 September 2008.
Oded Schramm, a member of the Theory Group at Microsoft Research, who did groundbreaking work on phase transitions, died in a tragic hiking accident on 1 September 2008. Schramm received many awards in his career: the Clay Research Award, the Poincaré Prize, the Pólya Prize, and the Ostrowski Prize; and was elected to the Swedish Royal Academy of Sciences earlier this year. His work combining probability theory with Charles Loewner's equation in conformal goemetry, now called Schramm-Loewner evolution, was an impressive breakthrough. Jennifer Tour Chayes of Microsoft Research said that Schramm's work "was a revelation to both mathematicians and physicists... Any time you can relate two different fields obviously there is huge excitement about that. It just opens up all kinds of new horizons in mathematics." Schramm is survived by his wife, Avivit, and two children. Microsoft Research has posted a page in memory of Schramm.
--- Mike Breen
"The greatest theorem ever told: London calling with a new multimedia performance in Ann Arbor," by Norene Cashen. Detroit Metro Times, 10 September 2008.
Mathematicians have proved to be a genuine source of inspiration to writers, playwrights and filmmakers, as evidenced by the success of works such as Proof, A Beautiful Mind and NUMB3RS. British theater company Complicite has added to this list of mathematician-inspired art with their award-winning play A Disappearing Number. The play follows the brief life of brilliant mathematician Srinivasa Ramanujan and his relationship with English mathematician G.H. Hardy and draws parallels between this story and the fictional modern tale of Al Cooper, an American traveling businessman whose life changes when he falls in love with an English mathematician. The multimedia presentation includes a large rotating chalkboard in the middle of the stage, which serves not only as a visual aid for mathematics but also as a screen for video projection and sometimes even as another exit from the stage, with actors stepping in and out of it's frame. Cashen remarks that the play is "whirlwind of science, love, loss, genius and hallucination," in which equations and numbers are characters themselves. The United States premiere of the play ran in Ann Arbor's Power Center from September 10th to 14th.
--- Adriana Salerno
"Do numbers have personalities? You can count on it," by Damien Henderon. The Herald (U.K.), 6 September 2008.
"Baez to play three gigs in Glasgow," by staff reporter. Hi-Tech Scotland, 9 September 2008.
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Mathematician John Baez (University of California, Riverside) delivered a series of lectures, including the 2008 Rankin Lecture, at the University of Scotland. The Hi-Tech Scotland article notes that Baez is "a world leader in quantum gravity using higher-dimensional algebra" and author of 'This Week's Finds in Mathematical Physics,' a column of "simple and accessible explanations of advanced mathematical research papers." Baez's three lectures were on "My Favorite Numbers: 5, 8 and 24" respectively. He explains in the Herald, "I've noticed over the years that different numbers have their own personalities. If you're a mathematician doing a calculation and you get the answer 248, it means something completely different than if you get 247 --because the number 248 shows up in all sorts of amazing places, while 247 is just dull. So, I thought it would be fun to explain this idea with some examples." [Baez posted the lectures online.] --- Annette Emerson
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"Meeting Briefs: MathFest 2008," by Barry Cipra. Science, 5 September 2008, pages 1282-1283.
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Cipra writes about four presentations at the 2008 MathFest (31 July to 2 August) in Madison, WI. Erik Demaine (MIT) talked about a proof regarding the re-forming of polygons into equal-area polygons with a different number of sides, such as re-forming a square into an equilateral triangle. If the parts involved are "hinged," the re-forming is more difficult. Demaine, his father, and four students have devised a proof that shows that an arbitrary dissection of polygons can be transformed into a hinged dissection. In the proof, arbitrary hinges are added to an unhinged dissection, then pieces are subdivided, more hinges are added, until the polygon can be re-formed into the desired polygon. Demaine said the idea was "so crazy that we never thought of it." Other MathFest highlights written about are more effective ways of wrapping a sphere with an inflexible wrapper ("Sweet Inspiration"), a queen-and-pawns chess problem ("A Royal Squeeze"), and packing in a borderless space ("Taking the Edge Off"). --- Mike Breen
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"Mathematical Biology Center Launched, by John Whitfield. Nature, 4 September 2008, page 11.
A new center for collaboration between biologists and mathematicians is aiming to address growing concerns about outbreaks of animal-borne diseases at the national level. These concerns have led the US Department of Homeland Security to provide partial funding for the center, as diseases such as avian influenza and foot-and-mouth disease appear in headlines worldwide. The National Institute for Mathematical and Biological Synthesis hopes to expand mathematical biology beyond traditional use in the fields of ecology and evolution and apply it to development and immunology. One specific problem the Institute hopes to address is understanding the difference between natural outbreaks and deliberate release of a virus. Similar collaboration occurs, only on a smaller scale, in other parts of the world, such as Europe and Japan, and the Institute appears poised to have an important global impact.
--- Lisa DeKeukelaere
"Die Facetten der Mathematik (The facets of mathematics)": Review of Kaleidoskop der Mathematik (Mathematical Kaleidoscope), by E. Behrends, P. Gritzmann, and G. Ziegler. Reviewed by George Szpiro. Neue Zürcher Zeitung, 3 September 2008.
This book, published on the occasion of the "Year of Mathematics" being celebrated in Germany in 2008, is a collection of articles about the "queen of the sciences". The book is aimed at mathematically talented youngsters and the lay public. The review calls it a "stimulating ramble through mathematics".
--- Allyn Jackson
"How to keep secrets safe," by Anna Lysyanskaya. Scientific American, September 2008.
There are many things people do online nowadays, from keeping in touch with friends, paying the bills, buying and selling pretty much anything, to reading the news and even finding a date. All the personal information exchanged in some of these transactions is now vulnerable to all kinds of attacks. Someone might be interested in reading our personal correspondence, or they might want to pose as us, or even sell our personal information to annoying telemarketers. A somewhat shocking fact is that 87 percent of the U.S. population can be uniquely identified by just their zip code, date of birth, and gender.
Mathematicians and computer scientists who work in the field of cryptography are dedicated to finding more efficient ways to keep our information safe, and many specialized protocols have been developed to accomplish this. Encryption protocols ensure that neither the ISP (Internet service provider) nor any eavesdroppers can read messages one sends online. Authentication protocols create "signatures" so that the identity of the sender of a message is verifiable. Anonymous channels protocols (or onion routing protocols) make sure that messages are untraceable to the original sender. And zero-knowledge proof protocols are designed so that for example an online service can tell that someone is a member without knowing their identity. Free software that takes care of all these issues is already available, like the GNU Privacy Guard package (which encrypts messages and signs them), and The Onion Router (Tor) project. The protocols mentioned, as well as some of the history behind them, are described in detail in this article by Lysyanskaya, a cryptographer herself. A common problem with all these strategies is that there is no real certainty that the codes won't be broken, but it's enough to know that any algorithm that breaks these systems would also have to answer a really difficult problem in mathematics.
--- Adriana Salerno
"Putting the science in fiction", by Carolyn M. Brown. Black Enterprise, September 2008, page 53.
This short article focuses on Jonathan Farley, a visiting professor of mathematics at Caltech. Together with a biochemist friend, Farley founded a company called Hollywood Math and Science Film Consulting, which has done consulting for numerous movies and television shows, including the highly popular NUMB3RS. The company helps movie and television producers bring mathematical and scientific accuracy and authenticity to their works.
--- Allyn Jackson
"Preschool Influences on Mathematics Achievement," by Edward C. Melhuish, et al. Science, 29 August 2008, pages 1161-1162.
"Long Division: The Debate Over the Value of Preschool," by Gautam Naik. Wall Street Journal, 29 August 2008, page A11.
"Preschool tied to higher math skills," by Nicole Ostrow. The Boston Globe, 29 August 2008.
According to a new study, the mathematics test scores of a child at age ten are most influenced by the mother's education, the home learning environment, and the quality of the preschool and primary school attended. These factors outweigh socio-economic influences, prompting researchers to recommend universal preschool as having benefits outweighing the potential costs. Previous work by the authors of the new study indicated that providing one year of preschool influences mathematical achievement in later years as much as a US$19,000 increase in family income. This research was based in England, where the typical child attends 18 months of preschool part time. By interviewing parents of over 2500 preschoolers, researchers established a standard of measurement for the "home learning environment (HLE)" and found that the influence of the HLE on a child's mathematical achievement at age 10 was second only to the mother's education (which was twice as influential as the father's education). As the article states, "This indicates that what parents do is as important as who they are."
--- Brie Finegold
"Math Problem: Democratic Convention's Logistics," by Pendarvis Harshaw. Morning Edition, National Public Radio, 27 August 2008.
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The segment reports on a mathematics class at the University of Colorado Denver that used many variables and a huge amount of data to come up with a plan that contributed to an efficiently organized Democratic National Convention held in late August. Matt Nabidy, who is pursuing his Ph.D. in mathematics at UC Denver, describes how the class used data to figure out 1) how to organize 21,000 volunteers, 2) how to design a bicycle-sharing system for the convention delegates (with 1,000 bikes available), and 3) how to assign space for the various competing events over several days. The team modeled how many volunteers would be needed, where they would be needed, and what tasks they would need to handle at what times. The reporter concludes, "as politicians, delegates and friends of delegates pedal their way to the evening speeches, most of them won't even realize they are riding on a foundation built of math." [Professor Harvey J Greenberg taught the Math Clinic and has posted .] --- Annette Emerson
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"Book Excerpt: The Numerati by Stephen Baker," Stephen Baker. Business Week, 26 August 2008.
In a 2006 Business Week cover story entitled "Math Will Rock Your World," Stephen Baker wrote about how "with the rise of new networks...all of us were channeling the details of our lives into vast databases... Those with the tools and skills to make sense of them could begin to decipher our movements, desires, and shopping habits---and predict our behavior." Baker has now written a book on the subject, The Numerati, in which he "introduces us to the mathematical wizards who are digging through our data to decode us as patients, shoppers, voters, potential terrorists---even lovers." This article is an excerpt from a chapter called "The Worker."
In this excerpt, Baker introduces us to Samer Takriti, a mathematician at IBM, who is leading a team of Ph.D.'s tasked with mathematically modeling each of IBM's 50,000 tech consultants so that they can be utilized most efficiently. In Baker's words, Takriti's job is "to start optimizing his co-workers." Except for personnel files, Takriti's team has access to a large amount of information about each consultant, including resumés, online calendars, emails, and the use of cell phones and handheld computers. These provide information about each person's skills and experience, how they use their time, their movements, and their social networks. If Takriti is successful, a manager could sit down at a computer, and, by filling out a simple form, she could compile a team who has the skills and abilities to quickly accomplish a particular task within budget anywhere in the world. And that's just one way such a system could be used.
--- Claudia Clark
"Departments Scramble to Find Math Education Faculty," by Jeffrey Mervis. Science, 22 August 2008.
Those few people possessing both a doctorate in mathematics and hands-on experience with the U.S. public education system are flush with job offers in mathematics education. However, the modal starting salary of only US$45,000 toUS $50,000 provides little incentive to obtain such a range of experience. Over half, or "60% of 128 tenture-track academic job advertised last year in mathematics education went unfilled," and few doctoral degrees in math education are available to help increase the pool of talented applicants. The article cites "Jobs in Mathematics Education in Institutions of Higher Education in the United States,", by Robert E. Reys (Notices of the AMS, June/July 2008).
--- Brie Finegold
"Battling bureaucracy with maths," by Philip Ball. Nature news, 22 August 2008.
Anyone who's been fortunate enough to have had experience with committee work has probably noticed that committees with many members are often inefficient. In fact, in the 1950s a British historian, C. Northcote Parkinson, found a "coefficient of inefficiency" at about 20 members. Researchers in Austria have used mathematical models to justify that number. They found that consensus is possible with 10-member committees, but becomes less likely as the committee grows. At 19-21 members, the number of ways not to reach consensus grows significantly. The European Union has 25 member states, but would like to reduce the number of commissioners to 18, which this research indicates would probably be a good idea.
--- Mike Breen
"Seeing in Four Dimensions," by Julie Rehmeyer. Science News, 22 August 2008.
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Imagining four-dimensional objects is challenging. It can be done by looking at how three-dimensional objects can be viewed in a two-dimensional world, then extending the example to viewing four-dimensional objects in a three-dimensional world. Étienne Ghys of the École Normale Supérieure, in collaboration with graphic artist and engineer Jos Leys and mathematics graduate student Aurélien Alvarez, has created a series of videos to help the viewer imagine higher dimensions. Two familiar techniques are used: looking at "slices" of the five Platonic solids as they move through a plane or viewing the outline of the edges of these solids on a plane, then applying these techniques to the six regular four-dimensional objects. Ghys also applies a third technique called "stereographic projection," which Rehmeyer describes in this way: "Take a three-dimensional object, say a tetrahedron, and imagine pumping it up with air until it forms a perfect sphere with lines on the surface showing where the edges of the tetrahedron were. Now imagine putting the tetrahedron-sphere on a table, making it transparent, and putting a light bulb at the 'north pole.' The light would project patterns from the tetrahedron-sphere onto the surface of the table." See the videos, which include these stereographic projections as well as images of complex numbers and fractals. --- Claudia Clark
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"The code breaker": Interview with Jacques Stern. Interviewed by Laura Spinney. New Scientist, 16 August 2008, pages 42-43.
Jacques Stern is a mathematician who turned to cryptography research and now heads the Laboratory of Computer Science at the Ecole Normale Supérieure in Paris. In this question-and-answer interview, Stern describes two main advances in cryptography that protect today's commerce: the concept of a public key system, devised by Whitfield Diffie and Martin Hellman, and RSA, which is a public key system currently in use today. RSA was developed by Ronald Rivest, Adi Shamir, and Leonard Adelman. RSA is based on the difficulty of factoring numbers that are products of large prime numbers. Stern said in the interview that recently a new system that uses multivariate algebra instead of number theory was under consideration in Europe as an alternative to RSA. "Our group broke it wide open last year and it had to be abandoned," Stern remarked. "That was extremely rewarding, because we prevented future disasters."
--- Annette Emerson
"Cube routes", by Jason Palmer. New Scientist, 9 August 2008, pages 40-42.
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The Rubik's cube caught the world's attention in the 1970s. It also has fascinated mathematicians. This article talks about mathematicians' efforts to find the smallest number of moves needed to unscramble any Rubik's cube configuration---this number has been dubbed "God's number" by cube enthusiasts. The number of possible configurations is huge---43 billion billion, according to the article. Through an ingenious combination of group theory and computing power, mathematicians have been able to prove that God's number is 22 or less. Some Rubik's cube experts are convinced the bound is only 20, but a proof remains out of reach for now. --- Allyn Jackson |
"'Kiss My Math' Tries to Make Pre-Algebra Cool": Interview with Danica KcKellar. Talk of the Nation, National Public Radio, 8 August 2008.
Actress-mathematician Danica McKellar has written a new book, Kiss My Math: Showing Pre-Algebra Who's Boss. Although the book is aimed at girls aged 12-14, she finds that middle school boys also read it. Her previous book, Math Doesn't Suck (see media coverage), was written for younger students who, she found while doing extensive research, find fractions a challenge. This new book focuses on integers, which McKellar's research showed to be the next stumbling block for students. She says she never imagined her first book would do so well (her publisher asked her to write another volume), and she receives emails from students on how helpful the books are. In both books she tries to address the problem of girls "dumbing themselves down" because they don't think being smart and being interested in math makes them attractive. McKellar cites the recent article in Science on the recent national report on math and gender that found that girls score as well as boys but that, she notes, "did not say [girls] are as interested in math and did not say they are going into math careers." She responds to some calls from the radio program listeners, addressing math education, math concepts, and her own experience in middle and high school. She reveals that she plans to write a third book, on algebra, but in the meantime plan to continue acting and promoting awareness of her books and math for young girls.
--- Annette Emerson
"A mind-bending reef." New Scientist, 5 July 2008, page 48.
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This brief piece includes a picture of a crocheted "coral reef" from the Institute of Figuring, which celebrates aesthetic aspects of mathematics and science. The institute teamed up with mathematician Daina Tamina of Cornell University, who created crocheted models in order to visualize hyperbolic geometries. The models "worked perfectly, and even led to some new results, since Taimina could test out her equations by crocheting them," the article says. It turns out that hyperbolic structures appear in coral growth, and Taimina's crocheting technique led to the creation of the institute's "Hyperbolic Crochet Coral Reef", which was on display in London in August. --- Allyn Jackson
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"How hard can it be?", by Ian Stewart. New Scientist, 21 June 2008, pages 46-49.
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This article uses the "postage stamp problem" to discuss the deeper problem known as "P vs. NP". The latter is one of the main outstanding problems in computer science today, and the Clay Mathematics Institute has offered a US$1 million prize for its solution. The postage stamp problem is the following. If you have a supply of, say, 2 cent stamps and 5 cent stamps, then there are only two values of postage you cannot make with these stamps, namely 1 cent and 3 cents. It is a general fact that, given an unlimited supply of stamps of certain denominations, there is always a key value above which any postage total can be put together with the stamps. The million-dollar question, as Stewart has framed it, is, What is that key value? The postage stamp problem is NP-complete, meaing that it appears to be much more difficult than problems solvable by polynomial-time algorithms. But recent work involving large stamp denominations has shown that particular cases of the postage stamp problem can be solved quickly. Perhaps, then, only certain cases of NP-complete problems are really hard to solve and most cases one is likely to encounter are solvable. This could have practical implications, Stewart notes. "Even if the method that your bank uses to encrypt your account information is NP-complete `in general'---which is more than can be proved for most practical encryption systems---the particular version that your bank is using might nevertheless be insecure." --- Allyn Jackson
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"Ancient Symmetries": Review of Solving Stonehenge: The new key to an ancient enigma, by Anthony Johnson. Reviewed by Nick Saunders. New Scientist, 21 June 2008, page 53.
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The Stonehenge monument has fascinated people for centuries. Many mystical and even outlandish interpretations have been proposed to explain the monument's creation and purpose. This book examines some of the mathematical and engineering aspects exhibited at Stonehenge. "No one denies that those who authorized Stonehenge had access to mathematical and constructional talent," the reviewer, an archeologist, writes. "But archeologists are rightly wary of ancient geometries `hidden' in a monument's layout." He found the book to be "refreshingly free from the lunacies of the past." --- Allyn Jackson
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"Grand designs", by Marcus du Sautoy. New Scientist, 14 June 2008, pages 38-41.
This article takes a historical approach to describe the work of the 2008 Abel Prize winners, John Thompson and Jacques Tits. du Sautoy begins his story about symmetry with Niels Hendrik Abel, the 19th-century mathematician for whom the prize is named. "Just as molecules can be broken down into atoms like sodiumm and carbon, or numbers can be built out of the indivisible primes such as 3, 5, and 7, the mathematicians of Abel's generation discovered that symmetrical objects can be decomposed into indivisible symmteric objects," he writes. These were named "simple groups", and they are the "atoms of symmetry". Thompson received the Abel Prize for his monumental proof, with Walter Feit, of the odd-order theorem, which provides a conenction between the symmetry of shapes and prime numbers. Tits received the prize for constructing higher-dimensional geometric settings to explain symmetries of simple groups of a special kind. Finally, the article discusses the discovery of "the monster", an enormous simple group that is characterized as "sporadic" because it does not fit into the standard classification of simple groups. But the monster is not an "anomalous freak with no relation to reality", du Sautoy notes. "[T]he symmetries of the monster might actually underpin some of the deepest ideas of string theory".
--- Allyn Jackson
"Sin cities," by Mark Buchanan. New Scientist, 3 May 2008, pages 36-39.
This article discusses recent efforts to use mathematical modeling and computation to understand crime patterns in cities. One idea basic to this work is "routine activity theory", which puts the emphasis not on the deviant mind of the criminal but on the human habits and environments out of which crimes emerge. Routine activity theory suggests that "crime is a normal, if undesirable, outcome of ordinary social interactions." Often crimes like burglary spread like a communicable disease. This makes sense in the context of routine activity theory, which says burglars spend their time on routine, non-criminal activities and then commit crimes in areas they are familiar with. "Finding solutions to crime is much easier once a trend has been identified," the article says, "and now mathematically minded criminologists say that computer models based on routine activity theory have the potential to make sense of a far more complex mix of social and physical factors that may influence crime." Researchers have found that remarkably similar crime patterns show up in cities spread around the globe. Another key notion is "space syntax", which provides a way to describe how cities are built out of smaller elements of space, such as parks, roads, buildings, etc. Detailed study of the use of space and its influence on people "can explain a lot of human interaction, including crime."
--- Allyn Jackson
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