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Math Digest

Summaries of Articles about Math in the Popular Press

Edited by Allyn Jackson, AMS
Contributors:
Mike Breen (AMS), Claudia Clark (freelance science writer), Annette Emerson (AMS)


December 2004

"Snowflakes made easy," by Mark Peplow. news@nature.com, 31 December 2004.

Peplow writes about mathematician Cliff Reiter of Lafayette College, who is using cellular automata to create snowflakes. Reiter uses cellular automata because he found that models that use differential equations weren't "aesthetically pleasing." His research is published in "A local cellular model for snow crystal growth" in the February (2005) issue of Chaos, Solitons & Fractals (Vol, 23, Issue 4, pages 1111-1119). Videos showing the growth of Reiter's snowflakes can be viewed online.

--- Mike Breen

 

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"How math enriches our lives," by Arthur Michelson. The Providence Journal, 30 December 2004.

Michelson, a middle school teacher in Menlo Park CA, bemoans the fact that many American students and adults don't think math is important. Why do I need math in "real life"? Michelson notes that math is not just about computation, geometric proofs, and balancing a checkbook. He offers that math "has intrinsic value. It is about discipline, precision, thoroughness and meticulous analysis. It helps you see patterns, develops your logic skills, teaches you to concentrate and to separate truth from falsehood. These are abilities and qualities that distinguish successful people." He goes on to show a few examples of how math helps one make financial decisions, evaluate false claims, and determine risk.

--- Annette Emerson

 

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"Taming the Hyperbolic Jungle by Pruning Its Unruly Edges," by Dana Mackenzie. Science, 24 December 2004, pages 2182-2183.

equivalence            classes of Kleinian group

Mackenzie writes about two results in three-dimensional topology, specifically having to do with hyperbolic manifolds. Both results are proofs of statements conjectured in the 1970s. The first result - that a major category of manifolds must have well-behaved ends - was proved by Ian Agol in Tameness of hyperbolic 3-manifolds and by Danny Calegari and David Gabai in "Shrinkwrapping and the taming of hyperbolic 3-manifolds". The second result is in "The classification of Kleinian surface groups, II: The Ending Lamination Conjecture" by Yair Minsky, Jeffrey Brock, and Richard Canary. They showed how to classify the well-behaved ends and showed that the shape of such an end determines the shape of the manifold. The article has background on hyperbolic geometry and Kleinian fractals, aw well as some nice illustrations. (Image created by David J. Wright and Bill Casselman.)

--- Mike Breen

 

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"The Return of a Beautiful Mind": Interview with John Nash. Interviewed by Michael Brooks. New Scientist, 18 December 2004, pages 46-49.

In this fascinating interview, John Nash reflects on his fame and his bouts with mental illness, which in recent years has taken the form of caring for his mentally ill son, also a mathematician. Asked whether the Nobel Prize changed his life, he replied: "It changed everything for me." But in fact some things have not changed: He said he is still living in the same house in Princeton. "I still don't have enough money to buy a mansion," he said.

--- Allyn Jackson

 

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"Gödel and Einstein: Friendship and Relativity," by Palle Yourgrau. The Chronicle of Higher Education, 17 December 2004, pages A9-A10.

Goedel and Einstein

Yourgrau writes about the relationship between Albert Einstein and Kurt Gödel while both were at the Institute for Advanced Study. He points out that each enforced a limitation within their subjects: Gödel on proof, and Einstein on an object's speed. Yet these limitations actually opened up new horizons of research. Yourgrau wonders why the Einstein-Gödel friendship is hardly mentioned in biographies of Einstein. He also writes about solutions by Gödel to the field equations of general relativity and their implications for the laws of nature.

--- Mike Breen

 

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"The Mathematician's Literary Companion." NetWatch. Science, 17 December 2004, page 2009.

Book

Professor Alex Kasman of the College of Charleston has a website listing more than 450 literary works that feature mathematical themes, characters or examples. The list can be viewed in a format sorted either by author, title or publication date. According to this short article, "the portrayals of mathematicians range from sympathetic to scathing." A scathing quote from Jonathan Swift's Gulliver's Travels is included.

--- Mike Breen

 

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"The Designated Hitter as Moral Hazard," by Daniel H. Pink, and "Sabermetrics for Football," by Paul Campos and Jonathan Chait. New York Times Magazine, 12 December 2004, page 63 and pages 91-92 (respectively).

These two short articles, involving mathematical analyses of sports, are from the Fourth Annual Year in Ideas issue of the New York Times Magazine. The first idea is from a paper presented by John-Charles Bradbury and Doug Drinen (University of the South) at the Joint Mathematics Meetings in Phoenix last January. The paper examined the reason for a higher rate of hit-batsmen in baseball's American League (AL) when compared to the National League. The pair examined many factors and concluded that the AL's designated hitter rule, which effectively keeps AL pitchers from batting, accounts for a large part, if not all, of the difference. Sabermetrics, the subject of the second idea, employs statistical analysis to coaching or managerial decisions. Very popular in baseball, sabermetrics is now starting to come into use in football as well. Two analyses cited here are David Rowe's (University of California, Berkeley) on "going for it" on fourth down and Harold Sackrowitz' on two-point conversions. Bill Belichick and the New England Patriots, winners of two of the past three Super Bowls, used the advice from both.

--- Mike Breen

 

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"Teen wins $54,000 by doing the math," by Susanne Quick. Milwaukee Journal Sentinel, 12 December 2004.

Po-Ling Loh, a senior at James Madison Memorial High School in Madison, Wisconsin, won second place in the 2004-05 Siemens-Westinghouse Competition in Math, Science and Technology. Her total prize money from the national and local competitions was US$54,000 in college scholarships. Loh's project was Closure Properties of D2p in Finite Groups. She was advised by Michael Ashbacher at Cal Tech who said, 'Very few people can cope with the abstraction and rigor that are necessary to do creative mathematics, ... Po-Ling has that kind of ability...' Loh's interest in that area of number theory came from a number theory class she took from Martin Isaacs (University of Wisconsin). The article concludes with Isaacs' assessment of Loh's future: "'She will make a real contribution to mathematical research,' he said, adding that he wouldn't be 'surprised if she will eventually be one of the great mathematicians of the 21st century.'"

--- Mike Breen

 

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"Poppy Seed Bagel Math." Weekend Edition, National Public Radio, 11 December 2004.

Bagel

The question is: How to spread poppy seeds evenly across the surface of a bagel? Ed Saff talks about the problem and the more general question of how to evenly distribute points on a curved surface. He explains why it is a hard problem and points out some of its applications. Saff also explains that although the method he and Doug Hardin have found is precise, it would not be cost-effective for bagel-makers. This NPR interview resulted from the article Discretizing Manifolds via Minimum Energy Points by Saff and Hardin (both at Vanderbilt University) in the November 2004 issue of the Notices.

--- Mike Breen

 

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"Parallel Worlds": Review of János Bolyai, Non-Euclidean Geometry, and the Nature of Space by Jeremy J. Gray. Reviewed by Fernando Q. Gouvêa. Science, 10 December 2004, pages 1893-1894.

This book is the first in a series from the Burndy Library in which facsimiles of resources from the library are published, so that they can be available to a wider audience. This book contains Bolyai's original Latin publication from 1932 on non-Euclidean geometry, an 1896 translation by George B. Halsted, and a lengthy 'preface' by Jeremy Gray. The reviewer calls Gray's preface a "delight," and writes that Gray gives "a very full account of the story of the Parallel Postulate, the discovery of non-Euclidean geometry, and the impact of these ideas from the mid-19th to the early 20th century."

This book was also reviewed by Brian Hayes in American Scientist, May-June 2005, pages 275-276.

--- Mike Breen

 

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"Circumferential Curiosities": Review of π: A Biography of the World's Most Mysterious Number by Alfred S. Posamentier and Ingmar Lehmann. Reviewed by Eli Maor. Science, 10 December 2004, page 1894.

Maor enjoyed this book, which is mostly about "curiosities associated with π." One included curiosity is the value of π to 100,000 places. Another is that the world record for memorizing digits of π belongs to Hiroyuki Goto, who has memorized over 42,000 digits of π. Maor would have enjoyed the book more had it had fewer typos; he hopes that a future edition will be edited more thoroughly.

--- Mike Breen

 

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"Misleading Numbers in the News: A Look at Numbers behind Social Security, Illegal Immigrants and Iraqi Civilians Killed," by John Allen Paulos. ABCNEWS.com, 5 December 2004.

Temple University professor of mathematics, John Allen Paulos, considers 3 examples of "misleading, dubious or uncertain numbers" that appear in today's news.

The first example considers the current proposal to cut the average American's Social Security contribution from 6.2% to 4.2% of his income, the balance to be placed in private investments. While typically-and erroneously-reported as a diversion of 2% of Social Security funds into private investments, this in fact represents a more significant 32% diversion of social security funds.

Paulos then considers the figures given for the number of people illegally crossing the U.S.-Mexican border. U.S. border agents note that they apprehend about 1 million people every year attempting to cross the border, and estimate that 3 times as many make it across. But freelance journalist Ben Winograd has noted a few problems with these numbers. First, the "1 million" figure represents the number of apprehensions, not the number of people: Winograd notes that many people repeatedly attempt the crossing. Secondly, he asks, how can one estimate the number of people not apprehended when they haven't been caught?

For the final example, Paulos looks at the estimates given for the number of Iraqi civilians killed in the current war. He gives some reasons-including small sample size, not quite random sampling of the population, and less than certain assumptions-to be "skeptical (but not dismissive)" of the figure of 100,000 reported in a study recently appearing in the Lancet. While this may be too large, he notes that the 15,000 figure given by Iraqi Body Count may be too small: the reality, Paulos guesses, lies somewhere in between.

--- Claudia Clark

 

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"Take a Chance," by Erica Klarreich. Science News, 4 December 2004, pages 362-364.

Klarreich writes about random- and pseudorandom-number generators, which are used in expected settings such as shuffling a virtual deck of cards at an online poker site, and in unexpected ones such as an archaeologist choosing which quadrants to survey at a big dig. Billions of random numbers are needed each day, so good random-number generators are in demand. Bias in a random-number generator can lead to unwanted consequences: For example, a website's online transactions might no longer be secure if a hacker could exploit the bias. Klarreich describes effective random-number generators and the faults of some others.

--- Mike Breen

 

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"Shiing-Shen Chern, 93." Milestones, Time, 20 December 2004.
"Math giant." Random Samples - People, Science, 17 December 2004, page 2037.
"Shiing-Shen Chern, 93, Innovator in New Geometry, Dies," by Kenneth Chang. New York Times, 7 December 2004, page A25.

 

S-S Chern

Shiing-Shen Chern was a Chinese-American mathematician who did major work in differential geometry. He had positions at the Institute for Advanced Study, the University of Chicago, and the University of California, Berkeley. In addition, he helped found the Mathematical Sciences Research Institute in Berkeley and was its first director. A 1998 interview with Allyn Jackson was published in the Notices of the AMS. One student was so taken by Chern's teaching that after winning the lottery he created a foundation to honor him. (Photograph by Peg Skorpinski.)

--- Mike Breen

 

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"Students Show Mixed Science, Math Scores," by Ben Feller. Newsday, 15 December 2004;
"Hong Kong, Finland Students Top High School Test of Applied Skills," by David Grimm. Science, 10 December 2004, page 1877;
"The Last Time You Used Algebra Was ...," by Donald McNeil, Jr. New York Times (Week in Review), 12 December 2004, page 3;
"Math and Science Achievement," by Rodger W. Bybee and Donald Kennedy. Science, 28 January 2005, page 481.

Results of two international tests in math and science were released recently. The 2003 Trends in International Mathematics and Science Study (TIMSS) released its statistics based on tests given to fourth and eighth graders last year. In the TIMSS math rankings, Singapore students from both grades finished first, of 44 countries participating. U.S. fourth graders finished 12th, while eighth graders finished 15th. The study showed improvement in the math scores of U.S. minority students. The TIMSS webpage has all results from 2003 and earlier years. In a study of how well students apply their knowledge - the Program for International Student Assessment (PISA) - Hong Kong students finished first, while U.S. students finished 24th. The PISA test was given to 270,000 15-year olds in 41 countries, also in 2003. More information is at the organization's website. The third article is reaction to the poor U.S. scores on the latter test. Two sample questions from the test are included in a sidebar. McNeil's thesis is that "In all but the most arcane specialties (like teaching math), the need for math has atrophied." After making his case, McNeil quotes others' reaction to his thesis. He concludes with a quote from his daughter's math teacher: "...kids don't study poetry just because they're going to grow up to be poets. It's about a habit of mind. Your mind doesn't think abstractly unless it's asked to - and it needs to be asked to from a relatively young age. The rigor and logic that goes into math is a good way for your brain to be trained."

--- Mike Breen

 

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"What Makes Beautiful Minds," by Sylvia Nasar. FastCompany, December 2004, page 50.

John Forbes Nash, Jr.

 

Nasar, whose book A Beautiful Mind was the source of the film by the same name, concludes the article about John Nash and his achievements with "The most surprising reaction to the movie came from high school students who told me they were intrigued by the world of mathematics, that they thought it was cool. It's like F. Scott Fitzgerald's definition of what makes a first-rate mind: the ability to hold two opposing ideas at the same time. I think it's great that they think of mathematics and Russell Crowe together. Great stories do inspire, and a story that can spark an interest in pursuing original ideas is about as creative as anything I can think of."

--- Annette Emerson

 

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"The Case of the Pilfered Planet: Did the British Steal Neptune?" by William Sheehan, Nicholas Kollerstorm, and Craig B. Waff. Scientific American, December 2004, pages 92-99.

In the early 1800s, Uranus was thought to be the outermost planet yet scientists could not reconcile its observed orbit with theoretical predictions based on Newton's laws of gravity and motion. In 1846 French mathematician Urbain Jean Joseph Le Verrier stated that another planet---now named Neptune---must exist, affecting Uranus' orbit, and indicated where to look for it. This led to the discovery of Neptune a few months later. One year before Le Verrier's prediction, Englishman John Couch Adams had done calculations about a hypothetical planet and left a sheet of paper about his work at the home of George Biddell Airy. Adams has shared credit with LeVerrier for the discovery of Neptune but historians of science have been unable to examine the paper since the 1960s. The crucial document has recently become available. Based on their examination of the paper and other related documents, the authors conclude that "Adams does not deserve equal credit with Le Verrier for the discovery of Neptune. ... The achievement was Le Verrier's alone."

--- Mike Breen

 

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"Optics and Realism in Renaissance Art," by David G. Stork. Scientific American, December 2004, pages 76-83.

 

Van Eyck

One example of early realism in art is Portrait of Giovanni Arnolfini and His Wife, painted by Jan van Eyck in 1435. Both people in the painting have a photographic quality to them. In addition, the painting includes a convex mirror that shows how the subjects and their surroundings appear from behind. In seeking to answer why realism occurred then, David Hockney recently theorized (in Secret Knowledge: Rediscovering the Last Techniques of the Old Masters) that Renaissance painters used lenses and mirrors to project images on canvas, which were then traced by the artists. In this article, David Stork uses projections, geometry, and the theory of mirrors to examine Hockney's theory, especially in regard to van Eyck's art, and concludes that the evidence does not support his claim.

--- Mike Breen

 

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"Best of what's new," edited by Eric Hagerman and Suzanne Kantra Kirschner. Popular Science, December 2004.

 

Bose photo

The long section highlights the best in new gadgets, cars, photography, computing, aviation, health, recreation, home tech, and more, and is introduced with a definition of algorithm: "a procedure for solving a mathematical problem in a finite number of steps that often involves repetition of an operation, or doing something over and over and over until you get it right." The editors note that the term and process is used in the development of most of the best new products and technologies covered in the issue. Of particular interest is the article "Better living through curiosity," by Tom Clynes, which gives an in-depth history and profile of Amar Bose, who was trained in mathematics at the Massachusetts Institute of Technology, where he also taught courses and stressed problem-solving. While teaching, Bose went into acoustics and electonics research, then founded Bose Corporation (known for its innovative and high-quality music systems), which in recent years delved into new territory---an automotive suspension system that uses electromagnetic motors instead of springs or hydraulics. It is this new "outrageously inventive car suspension system" that gets the magazine's "best of what's new" Grand Award. Bose continues to lead his successful company in solving as yet unrevealed problems. In answer to the question of "how he accounts for the impact he has had on such diverse fields" he notes that he once asked his mentor, famed mathematician Norbert Weiner, the same question and the response was "insatiable curiosity." The photograph show Amar Bose (center) with mathematicians Y.W. Lee (left) and Norbert Wiener (right) at MIT's Research Laboratory of Electronics in 1995. Photo courtesy of Bose Corporation.

--- Annette Emerson

 

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"The Cerebral Jongleur," by Bill Donahue. Discover, December 2004.

Juggling--it's math

What kind of cult is "siteswapping"? Juggling, of course. The article profiles Allen Knutson (University of California, Berkeley), "an authority on algebraic combinatorics, which involves, among other things, the counting of intersecting lines in multidimensional spaces. The number sequence he's uttering would be familiar to anyone who knows siteswap, a mathematical language that describes juggling routines. Siteswap codifies motion by assigning each throw a number." The higher the number, the higher the throw. Odd-number throws are passed from one hand to the other. Even-number throws are tossed and caught by the same hand. Computer programmers, mathematicians, and engineers---"siteswapping numbers jugglers"---enjoy the challenges and joys of the putting the patterns into practice and practicing the patterns. Donahue's article provides a nice explanation of siteswapping and its appeal. (Photo: Allen Knutson (left) and Greg Warrington, juggling cucumbers.)

--- Annette Emerson

 

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