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), Lisa DeKeukelaere (Brown University), Annette Emerson (AMS)

September 2005

"Group Theory in the Bedroom," by Brian Hayes. American Scientist, September-October 2005, pages 395-399.

Mattress

The writer wants to find a mattress-turn that---over the years---will lead to all feasible mattress positions, so that wear on the mattress will be evenly spread. He uses group theory to discover and show that no such turn exists. Hayes also writes of tire rotation and shows that there is a rotation, or rearrangement, of the tires that if used repeatedly will result in an even distribution of the four tires. The mattress problem is connected with the Klein 4-group, while the tire rotation problem can be associated with the cyclic group of order 4.

--- Mike Breen

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"The Incomplete Gödel": Review of Incompleteness: The Proof and Paradox of Kurt G&oml;del, by Rebecca Goldstein, and A World Without Time: The Forgotten Legacy of Gödel and Einstein, by Palle Yourgrau. Reviewed by Gregory H. Moore. American Scientist, September-October 2005, pages 464-466.

This review provides a lucid explanation of basic ideas contained in Kurt Gödel's celebrated Incompleteness Theorems and presents a brief overview of his life before turning to the books under review. Although Moore appreciates Goldstein's compelling portrait of Gödel, he finds her book to be riddled with errors that in the end erode the reader's confidence. Moore finds Yourgrau's book to be better and recommends it in particular for those wanting to know more about Gödel's unusual ideas about general relativity. But Moore concludes that the best biography of Gödel is still Logical Dilemmas by John Dawson, which was recently reissued in paperback.

--- Allyn Jackson

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"The Music of the Primes," written and presented by Marcus du Sautoy, BBC FOUR, 28 September 2005.

Prime-numbered soccer players

Marcus du Sautoy's "prime numbers only" soccer team. Photo courtesy of Marcus du Sautoy.

Mathematicians may not be the only ones talking about zeta functions and the Riemann Hypothesis---not after a television program presented in September 2005 on the BBC, entitled The Music of the Primes. Written and presented by Oxford University mathematics professor Marcus du Sautoy, author of a book by the same name as the television show, this hour-long program explores some of the fascinating work done with prime numbers, from Euclid to the present day. After a brief primer on prime numbers, du Sautoy begins with Euclid’s proof that an infinite number of primes exist. But this is no dry recitation: He uses images of people sitting around restaurant tables in different prime-number-size groups to explain the concept. Throughout this 50-minute program, du Sautoy uses familiar and humorous images like these to present what could otherwise be intimidating concepts to nonmathematicians.

du Sautoy then discusses Gauss's search for the number of primes---which led him to discover an approximation for their distribution---followed by Bernhard Riemann’s discovery of a connection between the distribution of prime numbers and the zeros of what was subsequently known as the Riemann zeta function. In this part of the program, a miniature du Sautoy is pictured standing on the complex plane, where the Riemann zeta function is defined, watching in amazement as the first few zeros of the function sprout vertical columns of light, which "line up." This image allows the viewer to "see" Riemann's conjecture.

du Sautoy goes on to discuss the further discoveries of mathematicians such as mathematicians G. H. Hardy, Srinivasa Ramanujan, and Hugh Montgomery, and physicist Freeman Dyson. Periodically, he includes the observations and insights of current mathematicians. And along the way, he visits the places where his subjects lived and worked, telling stories about their lives that may invite even greater interest in these brilliant individuals and their work. A website has more information about du Sautoy and this program.

--- Claudia Clark

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Reviews of Coincidences, Chaos and All That Math Jazz, by Edward Burger and Michael Starbird:
"Mathematics made fun," by Lisa Palmer.The Boston Globe, 16 October 2005;
"Math for laughs all in author's equation," by Paul Grondahl. Albany Times Union, 16 October 2005;
Review by Ben Longstaff. New Scientist, 10 September 2005.

A book about higher mathematics without equations? Yes, it's the recently published Coincidences, Chaos, and All That Math Jazz. The author, Edward Burger, a Williams College professor of mathematics, explains to Boston Globe correspondent Lisa Palmer that he wanted to reach a wide audience. "Some books say they are for the general public, but you open them up and see all these equations. Our book ... is for math fans and math-phobes."

Burger aims to make higher mathematics concepts more accessible to people: He has used everything from origami to storytelling to teach mathematics to his students and the public. One of his lessons---determining whether it is possible to tie one's ankles together with a rope, remove one's pants, turn them inside out, and put them back on without cutting the rope---demonstrates the creative thinking he wants to inspire in others. "This is [one of the challenges] I put out to people," he says. "You have a surprising discovery when you begin to think about it." When students ask "Why?" he adds, "I know I've met them on their terms."

The piece in the Albany Times Union is similar, but also mentions Burger's stand-up comedy career. Burger was in Albany for the University at Albany's Writers Institute fall writers series.

--- Claudia Clark

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"Alle Wege führen nach Paris---und Anchorage" ("All Roads Lead to Paris---and Anchorage"), by George Szpiro. Neue Zürcher Zeitung am Sonntag, 25 September 2005.

This article discusses a study of the worldwide network of airline flights. Mathematically, this network bears much similarity to other familiar networks, such as the Internet, in that it has many nodes that are connected to only a few other nodes, plus a few hubs that are connected to many nodes. But with the airline network, the busiest airports are not necessarily the most crucial. Anchorage and Port Moresby in New Guinea are in a certain sense more important than London, Paris, or Chicago.

--- Allyn Jackson

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"Mothers Driving Cycles": Review of Ecological Orbits: How Planets Move and Populations Grow, by Lev Ginzburg and Mark Colyvan. Reviewed by Günter Wagner. Science, 23 September 2005, page 2001.

In this review, Yale professor of ecology and evolutionary biology, Günter Wagner, praises the recently published book. Wagner writes that this book "may well turn out to mark ... a transition from what was considered unthinkable—namely a rigorous and nontrivial theory of population dynamics akin to a law of nature—to a real scientific achievement." He compares classical population dynamical theory—which "treats organisms as tokens for bookkeeping ... endowed with arbitrary probabilistic rules of transformation (death rates, birthrates, etc.)"—to Ginzburg and Colyvan's model, where organisms are treated as "real physical non-equilibrium systems" whose chances of reproduction or survival "depend on their abilities to acquire a share of the energy available to the population." Wagner goes on to explain how this different perspective influences their mathematical model. "The Ginzberg equations respect a law of inertia," he states: These equations incorporate the fact that healthy mothers have healthier offspring than less healthy mothers. The fact that this new model has led to explanations for well known but less well explained phenomenon is one of the reasons Wagner cites for the model's importance. Wagner also agrees with the authors that the management of endangered populations and the control of less desirable ones are a few of the areas that could benefit from the application of this theory.

--- Claudia Clark

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"Playing Patterns." NetWatch, Science, 23 September 2005, page 1971.

NetWatch gives a short description of the site WolframTones. The tones are called "A New Kind of Music" and are based on cellular automata. Users can choose genres, like jazz or country, and can see how the music is generated.

--- Mike Breen

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"For Fry's It's a Prime Time to Support Higher Math," by Michael Hiltzik. Los Angeles Times, 20 September 2004.

Fry's Electronics, the chain of megastores that stretches across California and the Southwest---and that has plans to grow yet bigger---sports an unusual sideline: It funds a mathematics institute. John Fry, president of Fry's Electronics, was a mathematics major in college and has a longstanding love of the subject. He began funding the American Institute of Mathematics in the late 1990s, and AIM has since grown into "one of the most remarkable academic institutes in the country," as the article puts it. AIM, which nowadays also receives funding from the National Science Foundation, is located in a space right next to the Fry's Electronics store in Palo Alto, California. "[T]he institute has been devoted to cracking the most elusive problems in higher math by organizing workshops that bring together leading experts for top-level brainstorming," the article states. The article also discusses the Riemann Hypothesis, which is one of the biggest outstanding challenges in mathematics today and which has been the focus of some of the research AIM has supported. (Read more about AIM in A Different Kind of Institute, in the December 2005 issue of Notices of the AMS.)

--- Allyn Jackson

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"Chaos", by James Yorke. New Scientist, 17 September 2005.

This brief piece on chaos is a contribution to a special feature on "Big Ideas" in the 17 September 2005 issue of New Scientist. Yorke ventures to say that the most successful people are those who are good at devising a plan B. He writes: "Chaos theory is an area of science and mathematics that deals with plans B to Z, describing unstable situations where small changes can cascade into larger and larger long-term effects." Chaos and unpredictability are woven into everyday life, yet it took a long time for scientists to realize how the phenomenon of chaos relates to their own subject. "I continue to wonder, if nearly all scientists missed this pervasive phenomenon, what other obvious phenomenon might we all be missing now?"

--- Allyn Jackson

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"Dirac's hidden geometry," by Graham Farmelo. Nature, 15 September 2005.

Paul Dirac

Farmelo presents the mystery of Paul Dirac, the renowned physicist who used his own methods to present quantum mechanics. His early works on the topic "repeatedly took theoretical physicists by surprise." Few of Dirac's papers included diagrams, yet he claimed that his approach was fundamentally geometrical and that his preference was geometry. He reportedly claimed that he used projective geometry when developing quantum mechanics, yet those early publications did not indicate just how. After a talk in 1972 at Boston University, moderator (and eminent mathematician and scientist) Roger Penrose "gently turned to him and asked point-blank how this geometry talk had influenced his early quantum work. Dirac gave his trademark shake of the head, and declined to speak. Dirac died 12 years later, still having never clarified the point."

--- Annette Emerson

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"New study sums up math debate," by Jamie Talan. Newsday, 13 September 2005.

A study by Harvard University psychologists says that children already have a basic understanding of mathematical concepts, such as order and addition, before entering school. Former AMS President Hyman Bass (University of Michigan) is quoted: "It's important for teachers to know what preschoolers bring to the table. They [teachers] should build on this rather than undermine what they [students] already know and enjoy." The article concludes by summarizing a previous study in which Asian and American parents were asked what they thought determined mathematical success. For Asian parents it was hard work, whereas American parents thought it was talent. "Just this difference in perception, Bass said, could leave an indelible mark on a child. American children who don't grasp a concept might feel incompetent and humiliated, while an Asian child 'might view it as a moment to return to the work and persist,' Bass said."

--- Mike Breen

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"Eine Formel fürs passende Geschenk" ("A formula for the appropriate gift"), by George Szpiro. Neue Zürcher Zeitung am Sonntag, 11 September 2005.

This article discusses a recent research paper in game theory, written by two mathematicians, Peter Sozou und Robert Seymour, and published in the Proceedings of the Royal Society. In the paper, the authors investigate what kind of gift a suitor should give a lady whom he wants to impress. It turns out that "extravagant" gifts, such as an invitation to a restaurant or flowers, are optimal. Such gifts display the buying power of the suitor but cannot be sold for money by gold-digging females.

--- Allyn Jackson

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"The Dismal Rhetoric of Economics; Teaching Math With Pineapples." Melange, The Chronicle of Higher Education, 9 September 2005, page B4.

Pineapple

The Melange section of the Chronicle of Higher Education runs excerpts from books on different subjects. The second portion of this week's feature has an excerpt from Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas, by Ed Burger and Michael Starbird. A selection follows. "What leads to deep mathematical ideas? Counting the spirals on the prickly facades of pineapples and pine cones or looking closely at the chaotic creases created by folding a piece of paper. Surprisingly quickly we can move from a silly observation to a profound mathematical insight. A little logical thinking goes a long, long way. After we see a pattern on a pine cone, just a few easy steps take us to the discovery of a number pattern that has an organic life of its own and expresses itself in paintings, architecture, and music.... Ideas---intriguing, surprising, fascinating, and beautiful---are truly at the heart of mathematics."

--- Mike Breen

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"The Kidney Connection: Math Makes A Match," by Anita Hamilton. Time Online, 4 September 2005.

Patients waiting for a kidney transplant may now have a much better chance of survival due to a mathematical algorithm for finding compatible donors. The algorithm, used in a program designed by a transplant surgeon and a mathematician, matches patients who have a willing but incompatible donor with other pairs in a similar situation. Though currently underutilized, the program sharply decreases the time a patient must wait for a donor, increasing the survival odds for the 62,000 Americans on the transplant list and lessening the national economic burden of interim dialysis treatment by as much as $750 million.

--- Lisa DeKeukelaere

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"Hey, Jerk. I'm Talking to You" by Eric Wills. The Chronicle of Higher Education, 2 September 2005, page A6.

In the September 2, 2005 issue of the Chronicle of Higher Education, writer Eric Wills reports on a new device that rates a cellphone user's level of involvement in a conversation. The Jerk-O-Meter, as it is known, is an academic research project developed at MIT. The software uses mathematical algorithms to measure vocal stress, mirroring behavior, how much each person talks, and who drives the conversation. A rating is calculated, and, as a result, the Jerk-O-Meter user receives messages ranging from "Don't be a jerk" to "Wow, you're a smooth talker." Computerized trials have been 90 percent accurate; so far, human trials have been conducted informally among colleagues. In Wills' words, software creator Anmol B. Madan says that "no jerks have been singled out." If it becomes available commercially, that could change. There is more information on the Jerk-O-Meter and related projects online.

--- Claudia Clark

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"Symmetry by numbers": Review of The Equation that Couldn't be Solved: How Mathematical Genius Discovered the Language of Symmetry by Mario Livio. Reviewed by István Harittai. Nature, 1 September 2005, page 34.

Symmetry

The work of Evariste Galois was the gateway to a powerful investigation of the role of symmetry in our world, as expounded by Mario Livio in The Equation that Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry. Livio tells Galois’s brief but compelling life story, a tale of rejection by universities and death by duel at a young age, and provides a larger picture of the scientists and theories that led up to and resulted from Galois’s discoveries. The reviewer credits the book for its liveliness and the number and variety of supporting topics that it details, such as crystallography, the Rubik's Cube, and string theory. He argues, however, that it goes too far in asserting the omnipresence of symmetry, thereby actually hindering understanding of the concept.

--- Lisa DeKeukelaere

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