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Four reviews of mathematics books in American Scientist,
November-December 2007:
"Theorems to Savor": Review of The Art of Mathematics: Coffee
Time in Memphis, by Béla Bollobás. Reviewed by James
Propp. American
Scientist, November-December 2007, pages 536-538.
"A Paradoxical Subject": Review of Mathematics and Common
Sense: A Case of Creative Tension by Philip J. Davis. Reviewed by
Daniel N. Rockmore. American
Scientist, November-December 2007, pages 540-541.
"The Power of Symmetry": Review of Why Beauty is Truth: A
History of Symmetry by Ian Stewart. Reviewed by David W. Farmer. American Scientist,
November-December 2007, pages 544-546.
"Analytical Tools for Evolutionary Processes": Review of
Evolutionary Dynamics: Exploring the Equations of Life by Martin
A. Nowak. Reviewed by Carlos Castillo-Chavez and Carlos Castillo-Garsow. American Scientist,
November-December 2007, pages 546-547.
This issue of American Scientist contains reviews, all favorable, of four mathematics books.
--- Mike Breen
"Reinventing the Wheel," by Mary Andom. Chronicle of Higher Education, 30 November 2007, page A6.
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A group of math students at Saint Norbert College has discovered that changing the shape of the road would allow the wheels on a square-wheeled bicyle to roll smoothly. The shape used is a series of humps, each of which is part of an inverted catenary. As with most research, developing the bicycle wasn't easy, but Terry Jo Leiterman, an assistant professor of mathematics at Saint Norbert, says that "They made many mistakes, but with teamwork and a renewed confidence they made it possible." Although the students were unaware of it when they did their work, in 2004 Stan Wagon (Macalester College) had used the catenary humps idea with a square-wheeled tricycle. His work is described in an April 2004 issue of Math Trek. --- Mike Breen
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"'Professors of the Year' Bring Technical Disciplines Down to Earth," by Paula Wasley. Chronicle of Higher Education, 30 November 2007, pages A8-A9.
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Last month the Council for Advancement and Support of Education and the Carnegie Foundation for the Advancement of Teaching named four professors the 2007 "Professors of the Year." One of the honorees, who took the prize in the category of master's insitutions, is Carlos G. Spaht (pictured at left), a math professor at Louisiana State University at Shreveport. Spaht enjoys teaching and often hands out dollar bills in the classroom. He directs LaPREP, a program that prepares middle-school and high-school students for college-level math, science, and engineering. Spaht's advice to teachers is, "Communicate with your students and build a nurturing relationship with them. Learning will follow." --- Mike Breen
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"Lieber mit oder ohne Zucker? Ja, gerne! (Do you prefer with or without sugar? Yes, I do!)", by George Szpiro. Neue Zürcher Zeitung, 25 November 2007.
This installment of Szpiro's monthly column on mathematics looks at the precision of mathematical language. The title of the article makes allusion to an example Szpiro gives of how language usage in mathematics differs from everyday speech. If one asks, "Would you like your coffee with or without sugar?", one expects the reply to be one in which a choice is made. A reply of "yes" would not answer the question. But in mathematics the word "or" connotes two valid possibilities. So a mathematician would say that "I like coffee with sugar, or I like coffee without sugar" is a true statement. This is why a mathematician could reply "yes" to the question. The article goes on to compare the precision of mathematical language to the language of, say, novels or legal documents.
--- Allyn Jackson
"App State math professor featured on 'Futurama' DVD," by Dale
Neal. Asheville
Citizen-Times, 25 November 2007.
"The
Geekiest Show on TV". Wired, 27 November 2007.
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Futurama recently released a DVD, "Futurama: Bender's Big Score", that includes a 25-minute math lecture by Sarah J. Greenwald (Appalachian State University). Greenwald lectures on mathematical references in the series, which aired on Fox until 2002. One example of math in Futurama is the number 87,539,319 that appears on a cab. The number can be written as the sum of two cubes in three different ways (1673+4363, 2283+4233, and 2553+4143), a reference to the famous Hardy-Ramanujan taxicab story. The show's writers, who together have advanced degrees in mathematics, physics, and computer science, try to include jokes and references that mathematically or scientifically literate people will appreciate, without interfering with the storyline. Greenwald herself earns an allusion: The fictional Greenwaldian Theorem appears on a blackboard in the new DVD. Both Greenwald and Futurama co-creator David X. Cohen lament the portrayal of mathematicians as geniuses or "magic beings." Says Greenwald, "If representations only show the mathematical genius, that's what people expect all mathematicians to be. It's important to look at representations of mathematicians and scientists that appear in pop culture, and critique them and balance those representations for our students so that they can recognize that there are many types of mathematicians." --- Mike Breen
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"Inventor makes shoe-shining easier", Associated Press. NewsOK.com, 26 November 2007.
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Richard Neal, who taught mathematics for 20 years at the Unviersity of Oklahoma, has invented a machine to shine shoes without getting polish on shoe shiners. The Shoe Horse, for which Neal has filed a patent, "holds the shoe so you don't have to," and is being demonstrated and sold at a mall in Oklahoma. Neal, who now devotes himself to inventing, says "Everything we create is mathematical. There's always been a question of whether mathematics is invented or discovered. But a lot of mathematicians think of themselves as inventors. Mathematicians create axioms, or statements, and ask what those axioms imply." --- Annette Emerson
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"Mathematics plus": Review of The Jinn from Hyperspace, by Martin Gardner. Reviewed by Justin Mullins. New Scientist, 24 November 2007, page 60.
This brief review notes "Martin Gardner's status as a legend of popular mathematics and science writing". The book features essays on a wide variety of topics, such as homeopathy and false memory syndrome, as well as physics and math. The review calls the essays "clear, closely argued and entertaining".
--- Allyn Jackson
"Decoding Encrypted Internet Messages," by Scott Simon on Weekend Edition Saturday. National Public Radio, 24 November 2007.
"Math Guy" Keith Devlin talks with host Simon about the mathematics of encryption---and decryption---that makes your online purchase and medical records secure. Devlin explains how the RSA system, developed in the 1970s by Ron Rivest, Adi Shamir, and Leon Adleman, establishes secure communication, and how the system is now under scrutiny. Devlin says that there are two possible ways the system could be broken: one way is by a mathematician discovering a fast method to find prime factors, and the other danger---more-likely---is by a computer chip containing a mere arithmetic flaw that would allow a hacker to crack computer security systems.
--- Annette Emerson
"Famous math whizzes," by Beth Beasley. BlueRidgeNow.com (Times-News Online), 21 November 2007.
Gaynelle Patterson's "Famous Mathematician Project" at the Rosman Middle School in North Carolina is reportedly a great success for a class of sixth-graders and their parents and teachers. The program, which blends math, history, and language arts, will be presented again at the Transylvania County Schools' Technology Showcase next semester. Each of the forty-five students searched for "famous mathematicians" on Google and, after further exploration and research, presented a two-minute presentation and written report on "the era of their mathematician of choice, including some personal background, major inventions of the time period, and of course, why they were famous." Each student wore a costume to portray the mathematician, which made the project especially fun and entertaining. Among the famous mathematicians portrayed were Carol Ruth Karp, Ernest William Brown, Marjorie Lee Browne, Marie-Sophie Germain, and Ernst Karl Abbe.
--- Annette Emerson
"A Probable Killer?" Random Samples, Science, 16 November 2007, page 1045.
In 2001, Lucia de Berk, a Dutch nurse, was convicted of murdering seven patients, yet there were questions about the statistics used to convict her. On 29 October 2007, a panel recommended that the case be reopened and it is now in the hands of the Dutch Supreme Court. See an earlier Digest for more information.
--- Mike Breen
"Study Compares States' Math and Science Scores With Other Countries,"
by Sam Dillon. New York
Times, 14 November 2007.
"Illinois math, science scores compare favorably with world," by
Carlos Sadovi. Chicago
Tribune, 14 November 2007.
"City Schools Gain, Yet Still Lag Nation," by Nancy Zuckerbrod. Associated Press, 15 November
2007.
Five years ago, the Trends in International Mathematics and Science Study (TIMSS) showed that, among 50 countries, the United States ranked above average in mathematics. However, Asian nations, such as Japan and Singapore, outranked the U.S. In an attempt to apply international standards to test results from states within the U.S., a new report statistically links the results of the 2005 and 2007 National Assessment of Educational Progress (NAEP) to the 2003 TIMSS. Gary W. Phillips, who wrote the report Chance Favors the Prepared Mind, once held the position of acting commissioner of the National Center for Education Statistics, the federal entity that administers NAEP. Journalist Sam Dillon does not mention the specific statistical means by which Phillips linked the studies, but provides a bar graph directly comparing the 8th grade math skill levels of U.S. states to foreign countries. While Massachusetts ranks almost as high as Japan, Mississippi ranks with Moldova, where there are hardly any requirements for becoming a teacher. It is striking to look at the differing testing styles of the NAEP and the TIMSS. Researcher Gage Kingsbury warns that there are a "flock or difficulties" with Phillips' study and that we should not jump to compare the rigor of education in the US with that of other countries based solely on test scores. The Times article ends with a quote that provides information easily obtained from the 2003 TIMSS study as if that information were new and encouraging: "We're in the top half of the table, and a number of states are outperforming the majority of the nations in the study. But our performance in math and science lags behind that of the front-running Asian nations." The Tribune article notes that Illinois students would finish about 10th in a list of countries, including the US, while Zuckerbrod reports findings that urban students in the US trail the national average, although students in Austin, Texas, and Charlotte, North Carolina, were above the US average.
--- Brie Finegold
"Surfer dude stuns physicists with theory of everything",
by Roger Highfield. Daily
Telegraph, 14 November 2007.
"Einstein on a snowboard", by Steve Farrar. Times Online, 18
November 2007.
"Is mathematical pattern the theory of everything?", by Zeeya Merali.
New Scientist, 17
November 2007.
"Geometry is All". The
Economist, 22 November 2007.
These articles report on a paper, "An Exceptionally Simple Theory of Everything", which was posted in November 2007 on the arXiv preprint server. This paper makes the extraordinary claim of presenting a unified "theory of everything" that incorporates all the known forces including gravity. The search for such a theory has been a central occupation of modern physics, so the claim is major---as is the skepticism greeting it. The author of the paper is Garrett Lisi, a physicist without an academic affiliation who, according to the articles, spends much of his time surfing and snowboarding. It is not easy to understand from the news reports just what it is that Lisi has done, but apparently he attempts to use the exceptional Lie group E8 as a sort of template for associating elementary particles and forces. E8 was the subject of worldwide news reports in the spring of 2007, after the American Institute of Mathematics in Palo Alto, California, announced that a team of mathematicians had carried out an enormous calculation to elucidate the group's structure (see the Math Digest summary of the media coverage about E8). At the time of this writing, Lisi's work was being discussed on blogs, such as Not Even Wrong, maintained by Peter Woit, a mathematician at Columbia University. Perimeter Institute physicist Lee Smolin is quoted by New Scientist as calling Lisi's work "fabulous" and saying that "It is one of the most compelling unification models I've seen in many, many years." But Oxford mathematician Marcus du Sautoy told the Telegraph he thinks Lisi's work is "a long shot". For his part, Lisi is maintaining his sense of humor. "It's either going to be exactly right, or spectacularly wrong," he told New Scientist. "I'm the first to admit this is a long shot. But it ain't over till the LHC sings." (The LHC is the Large Hadron Collider, a high-energy testing facility that could be used to verify his claims.)
--- Allyn Jackson
"Talk of the Town: A Firefighter's Theorem," by Lizzie Widdicombe. The New Yorker, 12 November 2007.
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The journey from casual observation to theorem is vividly portrayed in Lizzie Widdicombe's account. Just hours before he died doing his job in August, firefighter Bobby Beddia mentioned that that his age, 53, was the same as the last two digits of his birth year, 1953. Little did he know that his amusing observation would travel through a chain of mathophiles and inspire a recreational math theorem. Barry Cipra, a freelance mathematics writer, heard the firefighter's story and coined the term "Beddian age." Cipra then proved a theorem concerning the number of people who have reached their Beddian age in a given year. Sparking a series of conversations, Bobby Beddia showed that the observation of patterns is an addictive and exciting game that can last a lifetime. --- Brie Finegold
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"Fractals can't separate the fakes from the Pollocks," by Mark Buchanan. New Scientist, 10 November 2007, page 11.
This article discusses attempts to use fractals to authenticate the abstract paintings that Jackson Pollock created by letting paint drip in a seemingly random way on a canvas. In 2003, Richard Taylor of the University of Oregon offered to use his fractal methods to authenticate some paintings claimed to be by Pollock. Now researchers at Case Western Reserve University have done new analyses and got results different from what Taylor found. They conclude that the fractal method of authenticating the paintings cannot be trusted.
--- Allyn Jackson
"1 PhD + 9 Songs = 1 Cool Album," by Robert Everett-Green. The Globe and Mail Online, 10 November 2007.
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Recording artist Dan Snaith just released his fourth album and is about to set off on a European tour-while he works on his Ph.D. in number theory from the University of Toronto. Snaith likens math to musical compositions because both require fitting small ideas together in new ways to create a final product. Originally interested in jazz music, Snaith shifted his focus to electronic pop music around the same time he undertook serious study of mathematics. In his early albums, Snaith's "puzzle pieces" were layers created by individual instruments and pieces of equipment. For his recent album, Snaith's new approach was to create the melody without using the electronic equipment, resulting in a return to a more classical, jazz-like style. --- Lisa DeKeukelaere
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"Good stories, Good Math," by Julie Rehmeyer. Science News Online, Week of 10 November 2007.
A recent study of pre-school-aged children by researchers at the University of Waterloo showed a correlation between narrative skills and mathematical ability two years later. Children who included perspective from multiple characters while telling a story based on wordless picture book later showed higher aptitude in mathematics---but not reading, spelling, or general knowledge. Mathematician Keith Devlin attributes this finding to the fact that both math and language rely on the ability to visualize complex relationships between abstractions. This explains why other aspects of story-telling, such as sentence length and vocabulary, which depend less on visualization, had no correlation to mathematical skill in the children studied. The study's finding indicates children may be able to absorb the key idea of abstraction earlier than previously thought.
--- Lisa DeKeukelaere
"Math Error Could Compromise Cryptographic Systems," by Thomas
Claburn. Information
Week, 9 November 2007.
"Adding Math to List of Security Threats," by John Markoff. The New York Times, 17 November
2007.
"Microprocesor math bugs pose security risk, warns cryptographer," by
Jaikumar Vijayan. Computerworld, 19 November
2007.
Adi Shamir (Weizman Institute of Science), who along with Ronald Rivest and Leonard Adleman developed the RSA encryption algorithm, wrote a research note that said that encryption codes could be attacked by taking advantage of math errors in microprocessors. A single message sent to computers that had the faulty microprocessors could break any RSA key running on those computers. The Times article about Shamir's note caused some alarm last month as many people wondered if their computers could be vulnerable to attacks from individuals or government agencies. After the publication of the Times article, Shamir emailed Computerworld to say that his note "was not meant to cause alarm but to raise awareness of an important issue." In the Computerworld piece cryptographer Bruce Schneier said that Shamir's idea should not be ignored but that the attack he described is very theoretical, and added, "Shamir's math is beautiful. But it did sound like a bit of fearmongering to me."
--- Mike Breen
"Math on Fire," by Julie Rehmeyer. Science News Online, Week of 3 November 2007.
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When fighting wildfires, or even managing prescribed burns, one of the challenges firefighters face is the unpredictable nature of fire: it is affected by a multitude of factors, including weather, terrain, and the weather created by fire itself. Writer Julie Rehmeyer reports on the work of a team of mathematicians, computer scientists, fire scientists, and meteorologists working to develop a tool for making more accurate predictions of fire behavior than can be done with existing equipment. This tool includes a software model that can calculate the probabilities of various scenarios, based upon both fire and weather patterns. It also includes some sensors to be used from the air to identify fire hotspots and other sensors to be used on the ground to measure such variables as smoke, carbon monoxide, temperature, and humidity. This data, along with regular weather updates, would be sent every half-hour to a supercomputer, which would use the model to calculate new probabilities and send them to handheld computers the firefighters would carry. The initial version of the software model is now complete and is being tested on existing fire data. Jan Mandel, the lead researcher in the project and a mathematician at the University of Colorado at Denver, has more information about this project on his website. --- Claudia Clark
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"Scientists Fete China's Supreme Polymath," by Richard Stone. Science, 2 November 2007, page 733.
In October 2007, scientists met at the Partner Institute for Computational Biology in Shanghai to celebrate the 400th anniversary of the publication of the first six volumes of Euclid's Elements in Chinese, and to examine the legacy of its Chinese translator, Xu Guangqi. Born in Shanghai in 1562, Xu was "a fascinating polymath who spread his interests far and wide for a specific purpose: statecraft," notes Dagmar Schäfer of the Max Planck Institute. Xu was introduced to the ideas of Euclid in 1600 with the arrival in China of Italian Jesuit Matteo Ricci, a student of European mathematician Christopher Clavius. Realizing the importance of planar geometry and other mathematical ideas to progress in China, Xu and Ricci translated several volumes of Euclid's Elements into Chinese, introducing late Ming Dynasty intellectuals to Western logic. In addition, with the Jesuit's assistance, Xu would become a leader in the reform of the Chinese calendar. Stone writes that "the reams of data used to justify the revision amounted to the first scientific collaboration between scientists in Europe and the Far East."
--- Claudia Clark
"Theoretical Plumber," by Gregory Mone. Popular Science, November 2007.
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Martin Bazant, associate professor of applied mathematics at the Massachusetts Institute of Technology, has been named one of Popular Science's "Brilliant 10" for 2007. Bazant's studies of fluids at the microscopic level are "helping others to build portable diagnostic labs, miniature drug-infusion devices, and more." The mathematics he uses "describes how electrodes spaced throughout a channel could move fluid along like a miniature conveyer belt." Mone describes Bazant as a theoretician who is interested in real-world applications---perhaps in part because Bazant comes from a family of civil engineers. --- Annette Emerson
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