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


April 2005

Reviews of The Math Instinct: Why You're a Mathematical Genius (Along With Lobsters, Birds, Cats and Dogs), by Keith Devlin. Review by Elizabeth Sourbut, New Scientist, 9 April 2005; review by Alex Stone, Discover, May 2005; review in Science News, 7 May 2005, page 303.

calculating the catch

Both reviewers note that Devlin describes two types of math: natural and abstract (or symbolic)---the former instinctual and "hardwired into the bodies and brains of organisms," and the latter taught in school, using the language of numbers and symbols. Examples of natural mathematics are animal migration and navigation, diving for prey, and---whether dog or human---running to catch a ball or frisbee. All involve automatic calculations that "on paper, would require the equations of differential calculus." Devlin devotes much of the book to citing examples of animal calculations, and according to Sourbut, suggests that some humans have difficulty with abstract mathematics because the calculations are "out of context." But she concludes, "Fortunately he ends on a positive note. If you understand how symbolic concepts connect to the natural maths you can already do, then it all boils down to practicing until those abstract rules take on a more concrete reality in your mind."

--- Annette Emerson

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"Works in Progress," by Ivars Peterson. Science News, 30 April 2005.

Mac Lane autobiography

Shortly after the death of Saunders Mac Lane (1909-2005), Peterson quotes from Mac Lane's soon-to-be-published autobiography (A.K. Peters). Mac Lane, who started at Yale University at 17 years old and thought he'd major in chemistry, became interested in mathematics, eventually developing the branch of algebra called category theory. In his autobiography he reflects on mathematics and reminisces about his contacts over many years with some of the great mathematicians. Peterson pulls together Mac Lane's thoughts and his own ideas on the importance of mentors and research opportunities to inspire advances in mathematics.

See also:
"Saunders Mac Lane (1909-2005)," by Klaus Peters, Nature, 19 May 2005

--- Annette Emerson

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"Are we nearly there yet?" by Stephen Battersby. New Scientist, 30 April 2005, pages 30-34.

Will there ever be a single physical theory that encompasses all the forces of nature? In the thirty years since the "standard model" of particle physics was established, physicists have hunted without success for a "theory of everything". This article discusses string theory and the associated "M-theory", which string theorists have proposed as a candidate for a theory of everything. "But for now, M-theory exists only as an ideal," Battersby writes. "Theorists can prove that it exists as a mathematical construction, but they can't actually write down its equations and there is no clear route towards doing so." The article presents some physicists' reactions to string theory and M-theory and also discusses an alternative theory called loop quantum gravity. One roadblock is the lack of experimental facilities that could really test the theories, but such facilities may come on line in the future.

--- Allyn Jackson

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"Math Motherlode." NetWatch, Science, 29 April 2005, page 609.

This short item talks about a page on the MAA site that has "tools, animation and other resources" to help improve mathematics skills. There are resources for teachers, too, including a journal with articles about using history to teach math.

--- Mike Breen

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"Making Math Radioactive." Science Friday, hosted by Ira Flatow, National Public Radio, 29 April 2005.

The April 29 edition of NPR's Science Friday featured one hour of mathematics. Host Ira Flatow was joined by Keith Devlin, Sarah Greenwald, Gary Lorden, and Robert Osserman. The guests answered questions of host Flatow and some callers, and talked about how math has played a role in TV programs like "The Simpsons," "Futurama," and "NUMB3RS." Devlin is a frequent guest on NPR and author of The Math Instinct; Greenwald is an associate professor of mathematics at Appalachian State University and a member of the 2005 Mathematics Awareness Month committee; Lorden is Executive Officer for Mathematics at the California Institute of Technology and the math technical consultant for the TV show Numb3rs; and Osserman is Special Projects Director at the Mathematical Sciences Research Institute and chair of the 2005 Mathematics Awareness Month committee. Hear the broadcast on NPR's archive.

--- Annette Emerson

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"Predicting with Unpredictability," by Gianpietro Malescio. Nature, 28 April 2005, page 1073.

Biological randomness, such as genetic mutations and the mixing of parent genes, envelopes our world, and thus it seems fairly logical to harness this randomness in solving mathematical problems. By using random numbers to generate an initial guess to the solution of a problem, we can then perturb the guess with random changes, eventually settling on the most stable outcome. This process is known as a stochastic technique, and it induces the question of how we can obtain a set of random numbers with which to begin. A sequence of true random numbers has no repeating relationship between its elements, but "random" numbers produced by computers are actually the product of some type of algorithm. We can try to capture random numbers by observing physical processes in nature, but how can we tell if these processes are truly random? Only a computer can compare all of the numbers to find out, bringing us to an interesting quandary.

--- Lisa DeKeukelaere

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"From y-cubed to the GameCube: Math rules at Nintendo," by Flip Morse. The News Tribune, 25 April 2005.

Video Game

This opinion piece from the Tacoma, WA, paper is by the senior vice president for administration at Nintendo of America. In the piece's opening line, Morse writes that "Interactive video games are pure math---or, more precisely, math is the structure behind the design of today's sophisticated games." Morse points out the need for good math skills in all of industry and explains why these skills are important. He is disheartened by the need for math remediation by more than half of the Washington state students who enter community and technical colleges immediately after high school (Nintendo of America is in Redmond, WA), but says that instead of trying to assess blame, now is the time to spread the word to parents, students, teachers, and school administrators about the importance of mathematics.

--- Mike Breen

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"Going beyond Fermat's last theorem," by T. Jayaraman. The Hindu, 25 April 2005.

This article reports on some outstanding new work by Indian mathematician Chandrashekhar Khare and his French colleague J.P. Wintenberger. The work hailed here comprises the first steps toward proving an important open problem known as Serre's Conjecture, named after the Abel-Prize-winning French mathematician Jean-Pierre Serre. A proof of this conjecture, which is related to Andrew Wiles's proof of Fermat's Last Theorem, could open new insights into the Langlands program, which sets forth a vision for unifying number theory and geometry. Khare and Wintenberger have posted their paper on the arXiv, a preprint server widely used by mathematicians, and have submitted the paper to a top journal.

--- Allyn Jackson

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"Baseball's Leading Man of Math Has Some Second Thoughts About the Numbers," by David Leonhardt. The New York Times, 24 April 2005, Sports section, page 3.

Baseball

Baseball keeps, and announces, many stastistics: established figures such as runs batted in and earned run average, and not-so-established figures such as batting average with runners in scoring position and less than two outs. In the last few years Bill James, author of Baseball Abstract, and others have tried to separate meaningful statistics from meaningless ones. A debate has ensued over the idea of a "clutch hitter": one who gets hits in important situations in a game. Earlier James had declared that clutch hitters did not exist; if a hitter was clutch one year, he was not likely to be clutch the next year. That is, the skill did not persist. Now, however, James thinks that earlier conclusions were drawn without enough data to justify the conclusions: Clutch hitters may indeed exist. Leonhardt, who writes each Sunday about statistics and sports, explains the issues and offers a description of statistical noise. James's recent article on the issue, "Underestimating the Fog", and on other perhaps unwarranted conclusions about baseball statistics, is online.

--- Mike Breen

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"Den besten Papst und den besten Song wählen", by George Szpiro. Neue Zürcher Zeitung, 24 April 2005.

What do choosing a pope and choosing the best song in the Eurovision contest have in common? A lot, as it turns out. This article discusses the ideas of mathematician Jean-Charles Borda (1733-1799) about how to create fair voting systems.

--- Allyn Jackson

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"Whatever happened to machines that think?", by Justin Mullins. New Scientist, 23 April 2005, pages 32-37.

This article provides a look back at the history of artificial intelligence, which started with the pioneering work of mathematician Alan Turing, and a look forward at what the future might bring. The 1990s became known as the "AI winter", as disillusionment spread about the promise of AI and as government agencies cut support for AI research. There is today a resurgence of interest in AI, though the field has to some degree splintered into separate areas, such as computer vision and speech recognition---both of which depend heavily on mathematics. The article notes that the mathematical technique of Bayesian statistics has improved some AI systems to the point where they can actually be used in real world systems. Among the examples given are "the despised Microsoft Office paper-clip assistant" and systems that identify fingerprints and irises. A fundamental test of computer intelligence is the "Turing test", proposed by Turing in 1950. You can try the test for yourself at various websites, including http://www.intellibuddy.com, which the article describes as "home to one of the leading artifical intellgences on the planet".

--- Allyn Jackson

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"Saunders Mac Lane, 95, Pioneer of Algebra's Category Theory, Dies", by Jeremy Pearce. New York Times, 21 April 2005.

Saunders Mac Lane was one of the founders and main developers of category theory, which the article describes as a branch of mathematics that "provides a framework to show how mathematical structures and families of structures relate to one another." He did his doctoral studies at the University of Göttingen, in the era of the legendary David Hilbert, and wrote his dissertation under the direction of Hermann Weyl and Paul Bernays. After positions at Harvard, Cornell, and Columbia universities, Mac Lane went in 1947 to the University of Chicago, where he remained for the rest of his career. Mac Lane is one of the few mathematicians to have served as both president of the AMS and president of the Mathematical Association of America. He also had an important influence on science policy in the United States, serving as vice president of the National Academy of Sciences.

See also: "Saunders Mac Lane (1909-2005)", an obituary by Klaus Peters, Nature, 19 May 2005, page 292.

--- Allyn Jackson

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"Noether's Novelty," by John Derbyshire. National Review Online, 21 April 2005.

Derbyshire recalls that German mathematician Emmy Noether died 70 years ago in April. He describes her as "the greatest female mathematician of the 20th century, and quite possibly of all time." The article places Noether in the context of her time, place and culture---both societal and mathematical. Although she produced "a brilliant paper resolving one of the knottier issues in General Relativity" praised by Einstein, and although David Hilbert fought on her behalf to have her appointed to the faculty at Göttingen during World War I, she had many uphill battles. She won the admiration of colleagues and students but was "ill-paid and un-tenured," and when the Nazis came to power in 1933 she lost her job. While her mathematician brother Fritz emigrated to Siberia, Emmy came to Bryn Mawr in Pennsylvania, where she died two years later. Derbyshire concludes the piece with a quote from her obituary written by Albert Einstein, published as a letter to the editor in The New York Times on May 5, 1935, in which Einstein classifies Noether as one of the "genuine artists, invesigators and thinkers" of the world.

--- Annette Emerson

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"The power of staring," by Michio Kaku. New Scientist, 16 April 2005, pages 48-51.

In this article, physicist Michio Kaku offers a personal look at what fascinates and inspires him in physics. He talks about how Einstein and other geniuses spent a lot of time staring out the window, as idea mingled in their minds. "I find myself spending most of my time staring out the window," Kaku writes. "I see blocks of equations dancing in my head, and I spend hours trying to fit them together." Often these equations display a great deal of symmetry, and the presence of symmetry is one of the deepest mysteries in physics. With symmetry comes beauty. But, Kaku asks, "should beauty alone be a criterion for a physical theory?" He believes so, and in particular finds string theory "gorgeous". He goes on to explain some of the fundamental ideas of string theory and his own contribution to it, which was to write down a field theory of strings. String theory may be wrong, but that possibility does not deter Kaku---the theory itself is so fascinating and beautiful that even if it is wrong it is worthy of a life's work. "Even mathematicians have been startled at the richness and depth of the theory," he remarks. "Some think string theory will live forever as a branch of mathematics."

--- Allyn Jackson

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"Das Auswahlaxiom und seine Konsequenzen (The Axiom of Choice and its Consequences)," by George Szpiro. Neue Zürcher Zeitung, 13 April 2005.

The Axiom of Choice states that, given a collection of sets, one can form a new set by choosing one element from each set in the collection. The axiom is straightforward when applied to a finite collection but a little mind-bending when the collection is infinite. Although the Axiom of Choice is nowadays accepted without any fuss by nearly all mathematicians, there was a time when it raised considerable controversy in the field. Szpiro's article reports on a series of articles by mathematicians Saharon Shelah and Abraham Soifer finding that answers to concrete mathematical problems may depend on whether the axiom of choice is accepted or not.

--- Allyn Jackson

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"The Proof," by John Walters. The Front Porch, 12 April 2005.

This is a 30-minute interview with Dan Rockmore, professor of mathematics and computer science at Dartmouth College, which aired on New Hampshire public radio. Rockmore talks about mathematics in general, the Riemann Hypothesis (about which he's written a book Stalking the Riemann Hypothesis), and his film The Math Life. Rockmore points out that although people may say that they don't like mathematics, most people have early memories of liking math and still have a "lingering curiosity" about it. He also gives examples of the unreasonable effectiveness of mathematics and says that mathematics is "the engine under the hood" for many things we now take for granted, such as buying things online.

--- Mike Breen

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"Capturing the Unicorn: How two mathematicians came to the aid of the Met," by Richard Preston. The New Yorker, 11 April 2005, pages 28-33.

When the textile conservators at the Cloisters Museum (part of the Metropolitan Museum of Art) in New York City took down the legendary Unicorn Tapestries for restoration in 1998, they set off a chain of events that would culminate with two mathematicians and a supercomputer named "It" constructed from parts purchased at Home Depot. With the tapestries off the wall and resting in a bed of water for cleaning and preservation, the museum arranged for them to be photographed in minute detail, a process that took two weeks and produced volumes of image data. Their goal was to align all of the photographs using computer software to produce a single image of each tapestry so precise that each thread would be visible. The amount of data collected was so massive, however, that no computer could be found that could perform the necessary computations. Enter brothers David and Gregory Chudnovsky and their homemade computer, nicknamed "It." After a first pass over the data, they realized that the photographs could not be stitched together because the gradual changes in the lighting and the shape of the tapestries had caused inconsistencies between the images. Fitting them together into a clear, coherent picture required months of intense computational trials, interpolating the color of each pixel from the shade of those around it. The final product gave the museum its finished photograph and the mathematicians another fun puzzle to count as solved.

--- Lisa DeKeukelaere

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"InterViews: Mathematics, with Joel Cohen," National Academies website, 11 April 2005.

This interview with mathematician Joel Cohen is one of a series on the InterViews program of the National Academies. Cohen is a professor at Rockefeller University whose lab studies populations and quantitative theories relevant to them. Listeners may use RealPlayer to hear Cohen discuss his background, mathematical interests, and current research. The tracks of his interview are as follows: Mathematics is Like a Microscope (on his early fascination with science); All Around the World (on infectious diseases affecting millions around the world); Mosquitoes and Monkeys (on his research on malaria and on collaborative research); Science, Policy and Legislation (on mapping populations to help affect policy); The Blind Men and the Elephant (on his investigations of food webs); and Beauty in Unlikely Places (in which Cohen relates the patterns that mathematics and science explore to music, poetry, and even humor).

--- Annette Emerson

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"Mathematical fluency is no easy equation," by Gary Robbins. Orange County Register, 9 April 2005, pages 19 and 21.

Robbins begins his column with, "I was feeling dumb about being stupid in mathematics" but soon feels better when he discovers that even the star of the CBS-TV show NUMB3RS needs help writing equations (people from the Caltech math department have written some equations for the show). He closes the column with "As long as the cashier gives me the right change at 7-Eleven, I really don't care. And the next time someone tells me, 'Math is the only universal language,' I'm going to say, 'Really? Then why do so few of us speak it?'" The ironies are that Robbins is the Register's Science Editor and that this column appeared during the National Council of Teachers of Mathematics annual meeting in Anaheim (where the Register is published).

--- Mike Breen

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"Manuscripts as Fossils," by Erica Klarreich. Science News, 9 April 2005, page 231.

Can mathematical models used in population biology shed light on the percentage of ancient, hand-printed manuscripts that have survived to this day? Apparently, yes, according to an article recently published in Science by Cornell University paleontologist John Cisne, and discussed by Erica Klarreich in this issue of Science News. Cisne focuses on four widely-read scientific works of the Venerable Bede, an 8th century scholar whose manuscripts have been studied and cataloged extensively.

As Cisne notes in his article, application of his logistic model yields results that are in "remarkably good" agreement with those from existing paleographically-based models. For example, Klarreich notes, "Cisne estimates that the likelihood that a popular medieval text would have gone extinct between its creation and the present day is less than 7 percent." If applied to all 35 of the Venerable Bede's texts, this would mean the extinction of no more than 2 or 3 texts. In fact, 3 of Bede's texts are known to be extinct. At the same time, Cisne recognizes that the characteristics of Bede's four scientific works are not present in all ancient manuscripts. For example, these texts were "theologically neutral"---and less likely to be targeted for destruction for religious or political reasons. They therefore had the more or less "constant death rate" assumed in the model. However, Cisne notes, "This is how science works---you find a first-order model that works in simple situations, then go on to look at complex situations and see if the model can be modified".

In the future, Cisne also plans to use information theory to answer another question: How accurate is transcription as a method for transmitting information? Time, and mathematics, will tell.

--- Claudia Clark

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"Science Journal," by Sharon Begley. The Wall Street Journal, 8 April 2005, page B1.

In this article, writer Sharon Begley discusses a new book written by Dartmouth College professor of mathematics Dan Rockmore. On his website, Rockmore describes the text, Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers, as a "non-technical account of the history of the Riemann Hypothesis." While Begley attempts to provide an accessible introduction to the mathematics for a lay audience, some of the information could mislead the reader. For example, prime numbers are not as regularly spaced as her article would seem to imply, and some of the infinite sets she compares---all numbers divisible by two versus all numbers divisible by nine---are, contrary to what is stated in the article, all of the same size. For a lively discussion of this article, and of issues involved in presenting mathematics to a general audience, go to this website on The Math Forum.

--- Claudia Clark

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"Math teacher resets the learning curve," by Tracey Wong Briggs. USA Today, 5 April 2005.

John Mahoney is a math teacher at Benjamin Banneker Academic High School in Washington, D.C. Banneker wrote a widely used almanac and was part of the team that designed the blueprints for Washington, D.C. The article relates Mahoney's approaches to teaching mathematics at the school and tells of his switch from a private school to Banneker. Coincidentally, the school is on Euclid Street in Washington.

--- Mike Breen

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"Dem Geheimnis der Primzahlen auf der Spur": Review of Die Musik der Primzahlen (Music of the Primes), by Marcus du Sautoy. Reviewed by George Szpiro. Neue Zürcher Zeitung, 3 April 2005.

Szpiro liked this book exploring the mysteries of prime numbers, which was published in a German translation in 2004. See also the Math Digest entry about a review of the original English version of the book.

--- Allyn Jackson

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"Born to Count." NetWatch, Science, 1 April 2005, page 29.

Francis Galton (1822-1911) did work in several diverse areas, including statistics and meteorology. This site is a virtual library of Galton's texts, paper, and letters. Among Galton's achievements are putting the use of fingerprints on a firm foundation, and the statistical techniques of correlation and regression.

--- Mike Breen

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"Math + Crime = Hit," by Rebecca Smith Hurd. Wired, April 2005.

One of the creators of the TV show NUMB3RS," Cheryl Heuton, is interviewed regarding the premise of the program and her thoughts on mathematics. She notes that years ago she was influenced by Science Guy Bill Nye. She was struck by his enthusiasm and inspiring message to young people to study math and science. Heuton emphasizes that the accuracy of the mathematics in the show is very important--that mathematician Gary Lorden (at Caltech) and others are consulted. When asked--both by Wired and previously by mathematicians at Caltech -- "Will you ever run out of ways to apply math to crime?" her apt reply was "Do you think you're ever going to run out of problems?" She also relayed with enthusiasm that mathematicians have been sending in ideas. Hurd reports that "NUMB3RS" is a hit for CBS, with 12 million viewers each Friday night, and notes that the program is up for renewal in April, "which happens to be Mathematics Awareness Month."

--- Annette Emerson

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"Eiffel Equation," by Alex Stone. Discover, April 2005, page 12.

Eiffel Tower

The Eiffel Tower has an elegant shape, yet Alexander-Gustave Eiffel didn't have modern engineering when he designed the tower. Engineer Patrick Weidman found an 1885 memo which unlocked the secret of the tower's shape. Stone writes that the shape of the tower is an "exponential function of the natural logarithm." (No details of the function are given, however.) With the special shape, fewer diagonal trellises are needed, which allows the tower to be more aesthetically pleasing.

--- Mike Breen

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"Stay Patient, Stay Alive," by Joshua Foer. Discover, April 2005, pages 26-27.

Traffic

Traffic accidents worldwide kill more than a million people each year--about the same as the number of people who die from malaria. This article presents some mathematical and statistical analysis of traffic and of driver behavior. For example, although cars in one lane are moving faster than those in another lane, drivers in the first lane may still think that they are in the slower lane. This can lead to aggravation and unnecessary lane-changing, neither of which is desirable. Mathematicians Bryan Dawson and Troy Riggs of Union University (TN) found that drivers also misjudged speeds: "Drivers going faster than average will exaggerate how slow other traffic is going; those going slower will exaggerate how fast others are going," which also makes drivers want to change lanes.

--- Mike Breen

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Review of Chance: A Guide to Gambling, Love, the Stock Market & Just About Everything Else, by Amir D. Aczel. Reviewed by Alex Stone. Discover, April 2005, page 80.

Alex Stone calls this book an easy-to-follow guide to probability. The review concludes with, "Odds are the book won't make you richer, but it might enrich your appreciation of that beautiful branch of mathematics that, as Aczel gracefully puts it, 'Is humanity's attempt to understand the uncertainty of the universe.'"

--- Mike Breen

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