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Math Digest

Summaries of Media Coverage of Math

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


January 2005

"Naming Names," by Brian Hayes. American Scientist, January-February 2005, pages 6-11.

People frustrated with finding an unused name to set up an email account or upset because they've had to change their area code, understand that choosing an identifying name or number isn't easy. Hayes writes about the cluttering of "namespaces," the distribution of names in different settings, and the parallel between choosing names and hashing algorithms.

--- Mike Breen

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"How to do an infinite number of things before breakfast," by John D. Barrow. New Scientist, 29 January 2005, pages 28-32.

Can an infinite number of tasks be performed in a finite time? For example, if the first task takes 1/2 a minute, the second 1/4 a minute, the third 1/8 a minute, and so on, then an infinite number of tasks could be performed within 1 minute. The idea of such an "infinity machine" goes back to the mathematician Hermann Weyl (1885-1955). Barrow shows how explorations of this intriguing idea lead to considerations about dynamical systems, black holes, and the twin paradox.

--- Allyn Jackson

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"Wolf Prizes." Random Samples - People, Science, 28 January 2005, page 513.

Gregory A. Margulis of Yale and Sergei P. Novikov of the University of Maryland have been named co-winners of the 2005 Wolf Prize in mathematics and will share US$100,000. The selection committee cited Margulis for his "monumental contributions to algebra," and Novikov for "the introduction of algebraic-geometric methods." The prize will be awarded on May 22 in Jerusalem.

--- Mike Breen

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"Learning from 100 Numbers," by Gilbert Strang. Science, 28 January 2005, pages 521-2.

In this article Gilbert Strang reviews the book The SIAM 100-Digit Challenge: A study in High-Accuracy Numerical Computing. The authors are four of the twenty winners of the challenge, referred to in the book title, which appeared in the January-February 2002 issue of SIAM News (SIAM stands for Society for Industrial and Applied Mathematics). To win the contest, competitors had to compute 10 correct digits in the solutions of 10 different numerical analysis problems that were originally posed to Oxford University graduate students. Ninety-four entries were submitted by teams and individuals.

The book's authors discuss each of the ten problems and their solutions. Strang describes two of the problems, the first requiring competitors to compute a difficult integral. The second, a science problem more like the other contest problems, involves determining the probability of a particular event. Strang enjoyed the books and was "cheered" by the spontaneous teamwork of so many mathematicians previously unknown to each other. For additional information, see the book's Web page.

--- Claudia Clark

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"Romanesque networks," by Steven H. Strogatz. Nature, 27 January 2005.

broccoli The broccoli on your dinner table and the webpage you are currently reading may have more in common than meets the eye. The spatial relationship between the broccoli florets and the interconnection of linked web sites both display the characteristics of self-similar networks, hierarchical trees in which the relationship between groups of nodes resembles that between groups of groups and so on. Scientists working in fractal geometry and statistical physics study self-similar objects by using the properties of an object's intersection with a given lattice. Not all objects, however, occur in a space with a convenient measurement grid. In order to address certain biological and technological networks, mathematicians Chaoming Song, Shlomo Havlin, and Hernan Makse developed a special method for deriving appropriate grids and found that the networks obeyed some of the same laws as their purely theoretical mathematical counterparts. This discovery, coupled with previous links known to physicists between self-similar objects and phase transitions, fosters interesting questions about the state of our world.

See also: "Sizing Up Complex Webs," by Erica Klarreich. Science News, 29 January 2005, page 68.

---Lisa DeKeukelaere

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"Researchers explore mystery, and say gotcha," by Gareth Cook. The Boston Globe, 27 January 2005.
"Secrets of the Venus Flytrap Revealed," by Nell Boyce. NPR's Morning Edition, 27 January 2005.

Venus  flytraps

How does a Venus flytrap snap shut? Without muscles, the plant is still able to close on an insect in a fraction of a second, before the insect can fly away. A group of scientists, led by mathematician Lakshminarayanan Mahadevan, used modeling and high-speed video equipment to construct the shape of a flytrap leaf as it was shutting. The team compared the movement of the flytrap's leaves to the flip of a soft contact lens, which, under force, first holds its shape and then dramatically flips around. After analyzing their model, the scientists found that the plant uses water pressure to keep its leaves just on the brink of slamming shut. An insect landing on a leaf triggers an electrical impulse which pushes the pressure past the point, and the leaves shut. The exact mechanism of how the pressure changes is still unknown, however. The research is reported in "How the venus flytrap snaps," by Y. Forterre, J. M. Skotheim, J. Dumais and L. Madadevan, in the 27 January 2005 issue of Nature.

See also: "In a Snap," by Peter Weiss. Science News, 29 January 2005, page 69.

--- Mike Breen

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"Ein Diplomat mit Liebe für Zahlen und Schach," by George Szpiro. Neue Zürcher Zeitung, 23 January 2005.

This article is about a recent paper on diophantine equations, written not by a professional mathematician but by an Indian diplomat.

--- Allyn Jackson

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"Summers contrite about remarks," by Marcella Bombardieri. The Boston Globe, 20 January 2005.
"Summers storm," by Ruth Marcus. The Washington Post, 22 January 2005.

Comments by Harvard University President Lawrence Summers about women's success in math and science generated much controversy within the Harvard, mathematics, and science communities---as evidenced by web postings, newspaper columns, and letters to the editor around the country. A search for "Lawrence Summers" in The Boston Globe and many periodicals during the week of January 17 in particular reveals the firestorm resulting from his remarks---to date not made public verbatim---which apparently implied that innate differences in women accounted for their low numbers in science professions. Bombardieri reports that Summers responded to the overwhelmingly negative reactions by posting a statement on the Harvard University website. Marcus's piece, published in other newspapers as well, considers the reaction to Summers' impolitic remarks. Both Summers and the question of why women are underrepresented in math and the sciences continue to generate much and impassioned discussion.

See also: "Summers's Comments Draw Attention to Gender, Racial Gaps," by Andrew Lawler. Science, 28 January 2005, pages 492-493;
"Sind wohl die Hormone schuld? (Are Hormones Perhaps to Blame?)," by George Szpiro. Neue Zürcher Zeitung, 29 May 2005

--- Annette Emerson

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"When Laziness Pays," by Erica Klarreich. Science News, 15 January 2005, pages 35-36.

The research described in this article attempts to answer an evolutionary puzzle: "Why do populations of identical organisms sometimes split into two strains, cooperators and cheaters?" (the cheaters are the lazy ones). The two strains are found in many populations, even among yeast cells. If there is a surplus of a desirable commodity, then some cheaters can be supported. They can then thrive while cooperators have to work harder to produce the commodity and sustain the population. The model for this process was developed by Timothy Killingback, Michael Doebels and Christoph Hauert. Killingback gave a talk on the model at the Joint Mathematics Meetings in Atlanta.

--- Mike Breen

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"Hands-on Math Insights," by Bruce Bower. Science News, 15 January 2005, pages 36-37.

A new study suggests that students may learn better when lecturers use gestures that run counter to the technique they are describing. Two psychologists studied grade school students who were learning two particular mathematics problem-solving strategies. Some were taught without gestures, some were taught with gestures that matched the strategy, and the rest were taught with mismatched gestures: gestures appropriate to the other technique. Students taught with the latter technique learned best, although it is not clear why that should be the case. Students taught with no gestures learned worst of all.

--- Mike Breen

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"Cultural Icons." Random Samples - People, Science, 14 January 2005, page 205.

In April, the U.S. Postal Service will release stamps honoring four American researchers "who helped shaped science in the 20th century." The researchers are mathematician John von Neumann, thermodynamicist and mathematician Josiah Willard Gibbs, geneticist Barbara McClintock, and physicist Richard Feynman. Each stamp features a picture of the honoree and an illustration of his or her work.

--- Mike Breen

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"Caltech dons thinking cap for CBS: Math expert advises smart new TV series," by Kimm Groshong. Whittier Daily News, 9 January 2005.

Stars of CBS-TV show Numb3rs

This article provides a little insight into how Caltech (the California Institute of Technology) has influenced the new TV series, NUMB3RS, which premiered on January 23. Gary Lorden, chair of Caltech's math department served as the show's consultant. The premise of the show involves two brothers---an FBI agent and a mathematician---who use their different talents to solve crimes. The episodes make it apparent that "numbers and logic can prove invaluable in detective work." Lorden "answered mathematical questions to inform the writer's scripts and provided much of the show's visual, technical detail." Actor David Krumholtz, who portrays the mathematician, and the producers and writers, visited Caltech to observe the culture of academic mathematicians. The CBS series is now airing on Friday nights at 10:00 p.m.

See also:
"'Numb3rs'," by Sara Lipka. The Chronicle of Higher Education, 18 February 2005, page A8;
"Math is hip." Random Samples---People, Science, 4 February 2005, page 671.

--- Annette Emerson

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"Bridging the gap," by Ben D. MacArthur and Richard O.C. Oreffo. Nature, 6 January 2005.

Researchers (in the Bone and Joint Research Group at the University of Southampton, UK) are using mathematical models in the emerging field of tissue engineering. One of the goals of tissue engineering is to produce replacement tissue. Currently the work involves the expertise of scientists across several disciplines---"cell and molecular biologists, clinicians and materials scientists"---but mathematicians are now collaborating, providing models. "In these models, cells are considered as distinct entities (or agents) positioned on an appropriate lattice, and simple cellular behaviours are prescribed, which, on their own or on the local scale, are insufficient to produce pattern. But on the global scale, structure is seen to emerge from long-range summation of these low-level behaviours. Such models are now being incorporated into practical work programmes to explore the behaviour of stem-cell systems and mechanisms of tissue regulation." Another new direction of research is using "complex network theory to analyse the 'shape' of phenotypic regulatory mechanisms."

--- Annette Emerson

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"Go with the throw," by Erica Klarreich. New Scientist, 1 January 2005, pages 42-44.

juggling torches

Many mathematicians are also jugglers. This article discusses the mathematics of "site swaps", which form a notation for recording juggling patterns. Site swaps were first created in 1985, and they have spawned the creation of many new juggling patterns---as well as a few new theorems. In the picture, Henry Segerman, a mathematics graduate student at Stanford University, juggles torches.

--- Allyn Jackson

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"For some girls, the problem with math is that they're good at it," by Cornelia Dean. New York Times, 1 February 2005, page D3.
"Harvard chief's words on innate differences lack basis in science," by Sharon Begley. Wall Street Journal, 28 January 2005.
"Off the Record." by Kyra Gottesman. Oroville Mercury Register, 5 February 2005.

Cornelia Dean served as science editor for the New York Times from 1997 to 2003. In her essay, she recalls some of the laugh-while-groaning moments she encountered while editor, in which male scientists could not quite seem to grasp the notion that the person holding this influential position was a woman. What she could never laugh at, though, was a memory from seventh grade. On a mathematics aptitude test, she proved herself to be several years ahead of the other kids. "The results were posted and everyone found out... A girl really good in math! What a freak! I resolved then and there on a career in journalism." Her essay was written on the occasion of remarks by Harvard president Lawrence Summers, who suggested that perhaps those who say there are biological reasons men perform better in math might have a point. The jury is still out on that question; in the meantime, Dean points out, there are plenty of social and cultural barriers to women's participation in math and science that need to be dismantled.

Sharon Begley's article delves into whether the research behind Summers' remarks is as airtight as it is sometimes assumed to be. She also notes that the simultaneous ticking of the biological and tenure clocks means that many women will opt out of demanding careers in science and math.

The controversy over Summers' remarks simmered for weeks afterward. See also the following Math Digest entry:
"Summers contrite about remarks," by Marcella Bombardieri. The Boston Globe, 20 January 2005.
"Summers storm," by Ruth Marcus. The Washington Post, 22 January 2005.

--- Allyn Jackson

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"Prime-Time News," by Keith Devlin. Discover, January 2005, page 42.

This issue of Discover contains the annual feature the "Year in Science." Mathematician Keith Devlin covers one of the top math stories of 2004. "What no mathematician had proved until this year is the long-standing conjecture that prime numbers come in arbitrarily long, finite arithmetic progressions." He briefly presents the historical breakthroughs by the Greeks, Jacques Hadamard of France, Charles de la Vallée Poussin of Belgium, Johannes van der Corput of the Netherlands, and--in 2004--the "nonconstructive existence proof" by Ben Green, then of the University of British Columbia, and Terence Tao of UCLA. The issue also includes Count Down: Six Kids Vie for Glory at the World's Toughest Math Competition, by Steve Olson, on the list of Top Science Books of the Year.

--- Annette Emerson

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