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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 (2004 AMS Media Fellow), Annette Emerson (AMS), Brie Finegold (University of California, Santa Barbara)


January 2008

"Benjamin Franklin Plays Sudoku," by Julie Rehmeyer. Science News Online, 26 January 2008.

Franklin's 16
            by 16 magic square
16 by 16 magic square, by Ben Franklin. Copyright 2008, Paul C. Pasles.

 

Even though Sudoku presumably wasn't as popular in 18th-century America as it is today, Benjamin Franklin spent a surprising amount of time devising new and complex mathematical puzzles with principles similar to those of this addictive game. In the book Benjamin Franklin's Numbers: An Unsung Mathematical Odyssey, Paul C. Pasles gives an insight into the mathematical musings of this founding father. Inspired by the classic magic squares (squares made up of numbers in which every column, row, and diagonal add up to the same number), Franklin created 8 by 8 magic squares in which each color-coded pattern adds up to 260, and (at left) even a 16 by 16 version in which every "bent row" (^ -shaped) added up to 2056. In fact this last one, which he called "the most magically magical of any magic square ever made by any magician," has the added feature that the numbers in any 4 by 4 subgrid also add up to 2056. Pasles describes many more of Franklin's puzzles, like a "magic circle of circles," and some previously overlooked 8 by 8 and 16 by 16 magic squares that satisfy all the properties of the classic magic squares. The author points out that Franklin also helped lay some of the foundations for statistics, demographics, and decision science, among other areas, and that his capacity for quantitative reasoning is reflected in these overlooked achievements and his clever puzzles alike.

--- Adriana Salerno

 

 

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"Math + Religion = Trouble", by Ron Csillag. Toronto Star, 26 January 2008.

"What is it with God and mathematics?" Csillag asks. "Even as science and religion have quarrelled for centuries and are only recently exploring ways to kiss and make up, mathematicians have been saying for millennia that no truer expression of the divine can be found than in an ethereally beautiful equation, formula or proof." Part of the article consists of musings about relations betweed God and mathematics, and part discusses the new book Irreligion: A Mathematician Explains Why the Arguments for God Just Don't Add Up, by John Allen Paulos. In the book, Paulos uses "logic and probability" to attack some of the best known arguments for the existence of God, such as intelligent design, the anthropic principle, and moral universality. Although these arguments cannot prove God's existence, Paulos also notes that His non-existence cannot be proved either.

--- Allyn Jackson

 

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"Berkeley math institute celebrates 25 years," by Patricia Yollin. San Francisco Chronicle, 25 January 2008, page B1.

Robert Bryant, current Director of the Mathematical Sciences Research Institute (MSRI), talks about how he became interested in math, how the general public perceives math, and what the institute does for the mathematical community and general public. The article points out that more than 1,700 mathematical scientists visit MSRI "in an annual migration that allows them to do ressarch and attend workshops and conferences." One of those researchers quoted is Monica Vazirani, an associate professor at UC Davis, who is spending the semester at MSRI. She aspired to do just that---spend time devoted to her research and bounce ideas off other mathematical scientists on site---since she was an undergraduate at Harvard in 1992. Bryant admits that he "sympathizes with the bemused and befuddled," but as reporter Yollin notes, Bryant "can quickly point to examples of relatively recent mathematics that show up in the real world---in derivative trading and hedge funds, models of the Earth's climate, the so-called unbreakable codes used for secure electronic transactions..." Robert Osserman, special projects director at MSRI, explains the institute's various outreach activities, which include administering the weekly Berkeley Math Circle lectures for local middle and high school students and sponsoring public events such as conversations about math with playwright Tom Stoppard, comedians Robin Williams and Steve Martin, and actor Alan Alda. (The Alda event was mentioned in "Serving up lattes and a quick lecture," by Jackie Burrell, The San Jose Mercury News, 22 January 2008.)

--- Annette Emerson

 

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"Math is a ball!" Don Polec's World, ABC6 TV Action News, 25 January 2008.

The website includes the video segment about Bob Swain, "former teacher and theatrical mathematician [who] put on a presentation at the Leonardo de Vinci Science Center in Allentown [PA] using a thousand old golf balls to illustrate concepts involving polyhedrons and platonic solids." His goal is to get students to think outside the box---or in this case, outside the pyramid.

--- Annette Emerson

 

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"Lazy option is best when waiting for the bus". New Scientist, 23 January 2008, page 18;
"Wann es sich lohnt, auf das Tram zu warten (When it pays to wait for the bus)", by George Szpiro. Neue Zürcher Zeitung, 24 February 2008.

calculate how long
            to wait for the bus

 

"Scott Kominers, a mathematician at Harvard University, and his colleagues derived a formula for the optimal time that you should wait for a tardy bus at each stop en route before giving up and walking on", the article says. The orignal research article is available on the arXiv: "Walk versus Wait: The Lazy Mathematician Wins," by Justin G. Chen, Scott D. Kominers, Robert W. Sinnott. The story generated a fair amount of coverage and feedback online.

--- Annette Emerson

 

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"Celia Hoyles: the magic of numbers". The Guardian, 22 January 2008.

Celia
            Hoyles
Celia Hoyles.

 

"Celia Hoyles has always adored a subject that terrifies and repels large sections of the population." So begins this aricle about one of England's leading mathematics educators and chief adviser on math education. Currently chair at the Institute of Education, she has taken charge of the new National Centre for Excellence in the Teaching of Maths. Her enthusiasm about mathematics---its beauty, patterns, proofs, and applications---is obvious. She acknowledges that mathematics has its own language, which can be isolating, but notes that now "mathematicians have to communicate with everybody because mathematical models underpin everything from the financial markets, through animation, to weather forecasting." At one time she appeared on a television show to help the studio audience and viewers at home solve puzzles. She says there is a disconnect between math taught in school and math used in everyday life, and she is interested in "bridging the gap between edicators and practitioners." The article includes details about her life and work and concludes, "Hoyles remains a missionary for maths rather than just for numeracy, determined that more people should enjoy, as she does, the beauty and the wonder."

--- Annette Emerson

 

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"The maths behind group showers," by Philip Ball. Nature News, 18 January 2008.

the Shower
            Temperature Problem

 

When's the best time to take a shower in a youth hostel so that you don't end up under scalding or freezing water? A team of researchers has created "a mathematical model of what happens when everyone in a youth hostel decides to take a shower at the same time." This is but one example of modeling human behavior and looking at optimal group decisions. It turns out that "diverse decision-making behavior," or the "minority game" devised by Damien Challet and Yi-Cheng Zhang, demonstrates that "the more mixed the strategies of decision-making are, the more reliably the game settles down to the optimal average size of the majority and minority groups. The minority game serves as a proxy for many social situations, from changing lanes in heavy traffic to choosing your holiday destination"---to deciding on the best time to take a shower in a hostel where the water system can't cope with lots of demand. The article includes more examples and detailed explanations, as well as links to several original research papers.

--- Annette Emerson

"Alan Alda tackles 'MATH'---and science---in conversation," by Paul Kilduff. San Francisco Chronicle, 17 January 2008, page D26.
"Popular science in a cafe scene," by Jackie Burrell. Contra Costa Times, 22 January 2008.

On 17 January 2008, the Mathematical Sciences Research Institute in Berkeley, California, hosted a conversation between mathematician Robert Osserman and actor Alan Alda. Alda is the host of Scientific American Frontiers on PBS. In the Contra Costa Times article, Osserman is quoted on the popularity of math and science, especially in regard to science cafes or salons: scheduled, casual, gatherings in coffee houses and bars in which scientists talk about their fields to the general public. Osserman says that "CSI sends an undercurrent, a message that science really can be very important. NUMB3RS started out very explicitly talking about how beautiful math is." He also notes that 200 years ago in France, all salons had a mathematician.

--- Mike Breen

 

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"If You Don't Know Your Math, You'll End Up Taking a Bath," by Jonathan Clements. The Wall Street Journal, 16 January 2008, page D1.

Clements writes that "financial recklessness" might be the cause of low consumer saving and high debt. It could be an inability to comprehend compound interest rates (many math teachers know that people have trouble with simple interest rates). Victor Stango (Tuck School of Business) says that people consistently "underestimate the benefits of saving and they underestimate the costs of borrowing." Clements advises consumers to (1) know a loan's finance charge as an annual percentage rate, (2) use online financial calculators, and (3) use the rule of 72 to estimate returns on savings.

--- Mike Breen

 

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"A Mathematical Gem." Random Samples, Science, 18 January 2008, page 263.
"Diamond's chiral chemical cousin," by David Bradley. spectroscopyNOW.com, 15 January 2008.
"Perfect as a Diamond". Research Highlights, Nature Materials, volume 7, number 2, 2008.

K_4 crystal
The K4 crystal. Image created by Hisashi Naito.

 

These articles report on work of mathematician Toshikazu Sunada, who has investigated mathematical properties of crystals. He examined the diamond crystal and found that it has two special properties, which he called "maximal symmetry" and "the strong isotropic property". Only one other crystal, which Sunada calls the K4 crystal, shares these two properties with the diamond. Sunada's work is described in his article "Crystals that Nature Might Miss Creating", which appeared in the February 2008 issue of the AMS Notices. In the article, Sunada stated his belief that the K4 crystal had not been synthesized in nature. But after the article appeared he found out from crystallographers that in fact it does appear in various compounds, including liquid crystals, and has been known for decades by other names.

--- Allyn Jackson

 

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"Nerds, geeks, superstars," by Helen Dalley. The Sydney Morning Herald, 13 January 2008.

Terry Tao
Terry Tao at the 2008 Joint Mathematics Meetings. Photo by Tony Badeaux of Convention Photo by Joe Orlando, Inc.

 

Dalley begins the article writing about Australian champions that every Aussie recognizes: swimmer Cathy Freeman and rugby player John Eales, and then asks how many readers recognize the picture of 2006 Fields Medalist Terry Tao that accompanied the article? She says that Tao "should be as revered as they and other sports stars are in Australia." In addition to listing Tao's many accomplishments, the article also lists many uses of mathematics, such as error-correcting codes in DVDs and encryption methods in electronic transactions. Tao points out that math is not for nerds. He uses the example of the Page Rank algorithm, which has made Google's founders billionaires.

--- Mike Breen

 

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"Small Infinity, Big Infinity," by Julie Rehmeyer. Science News Online, 12 January 2008.

In this article, Julie Rehmeyer uses the example of two separate proofs that the real numbers are uncountable, presented in simple terms for the non-mathematician, to emphasize that two entirely different methods can arrive at the same conclusion. She points out that this idea may provide new ideas for mathematical progress. Rehmeyer starts with the concept of infinity and Georg Cantor's proof from the late 1800s that the natural numbers (1,2,3…), which you could count forever, lead to a "countable" infinity, while the set of all real numbers, which can have an infinite number of nonrepeating digits after the decimal, is "uncountable"---a different, larger type of infinity. Cantor's proof entails showing that it is impossible to set up a counting scheme that will index the real numbers to the natural numbers, a set theory approach. In contrast, a game theorist proved the same result by setting up a choosing game and tying the possibility of a given player winning to whether the pool of items from which they chose was countable.

--- Lisa Dekeukelaere

 

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"Mathematician Proposes Another Way of Divvying Up the US House," by Eric Hand. Nature News, 8 January 2008.

If you divide the US population by the number of seats in the House of Representatives, 435, you should get the ideal number of individuals per representative. Next, divide the population of each state by this ideal number, and you should get the number of representatives per state---right? Not quite. The problem is fractions of representatives, and since the 1850s multiple methods have been used to decide which states get to round in which direction. Each method has its drawbacks, however, and can place an unfair advantage with either the larger or the smaller states, depending on the mathematical rule used to determine the rounding. Mathematician Eric Edelman has developed a new method that attempts to find the ideal balance of representatives between states by determining which of 385 scenarios minimizes the difference between the most under- and over-represented states. Even this method, however, faces difficulties in an accurate execution. Edelman presented his method in an invited address at the January 2008 Joint Mathematics Meetings in San Diego.

--- Lisa DeKeukelaere

 

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"Zahlen und Formeln sind die heimlichen Herrscher des 21. Jahrhunderts (Numbers and formulas are the secret rulers of the 21st century)", by Norbert Lossau. Welt am Sonntag, 6 January 2008.

This article is a celebration of mathematics and appeared at the start of the "Jahr der Mathematik", or Mathematical Year, which is taking place throughout Germany during 2008. The article includes brief sketches of some intriguing mathematical problems and concepts, such as Fermat's Last Theorem and the notion of infinity. There is also a sidebar with a short interview with Günter Ziegler, a mathematician at the Technical University of Berlin and president of the German Mathematical Society. The Mathematical Year activities include museum exhibits in Paderborn and Bonn, a staging of the "Kangoroo" mathematics contest for schoolchildren, and special events at the 2008 Science Summer festival in Leipzig. For more information, visit the Jahr der Mathematik web site.

--- Allyn Jackson

 

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"Free journal-ranking tool enters citation market," by Declan Butler. Nature, 3 January 2008.

A new tool, similar to Google's PageRank, calculates the impact factor of research papers---of interest to authors, institutions, libraries, and journal publishers. The SCImago Journal & Country Rank database, launched in December 2007, provides a way for users to generate "on-the-fly statistics of publisher research papers for free." As Butler points out, not all citations are equal. "Those coming from journals with a higher SJR (SCImago Journal Rank) are given more weight." The article goes on to present both positive and negative feedback to the ranking system metric and its results.

--- Annette Emerson

 

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Math in "The Year in Science 2007." Discover, January 2008.

Two-dimensional
            representation of E_8
Computer-generated two-dimensional representation of E8, made by John Stembridge and based on a hand drawing made in the 1960s by Peter McMullen.

 

Four stories about mathematics made Discover's annual January issue covering the top 100 science discoveries or breakthroughs in 2007:

  • #38: "Math Advance Threatens Computer Security," by Stephen Ornes, page 45. A group of researchers factored the Mersenne number 21,039 - 1. More specifically, knowing that 5,080,711 was one of this Mersenne number's factors, the team found the factors of (21,039 - 1)/5,080,711---a 1017-bit, 307-digit number---using the special number field sieve algorithm. (Note: the Discover article incorrectly equates the Mersenne number above with its 307-digit factor.) Team member Arjen Lenstra predicts this discovery will have serious ramifications for computer security in the next decade.
  • #47: "248-Dimensional Math Problem Solved," by Jessica Ruvinsky, page 49. A team of mathematicians mapped the 248-dimensional Lie group E8. The matrix representing the irreducible representations of E8 and the relationships between them contains over 200 billion entries. This four-year effort is part of a larger project, known as the Atlas of Lie Groups and Representations.
  • #56: "Calculus Was Developed in Medieval India," by Stephen Ornes, page 52. British researchers George Gheverghese Joseph and Dennis Almeida reported finding evidence that the infinite series was first developed in the 14th century by Indian mathematicians. Joseph and Almeida also believe that this information made its way via Jesuit missionaries to Europe, where it may have eventually influenced Isaac Newton and Gottfried Wilhem Leibniz.
  • #59: "Math Breakthrough Spotted on Mosques," by John Bohannon, page 53. Two physicists studying periodic and nonperiodic tilings in medieval Islamic architecture found quasi-crystalline Penrose patterns in the Darb-I Imam shrine, built some 500 years before such patterns were discovered by mathematicians in the West.

See previous Math in the Media items on the E8 development and on the similarity between mosaics in medieval mosques and quasi-crystalline patterns.

--- Claudia Clark

 

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"Why do strings of holiday lights end up in giant knots?", by Corey Binns. Popular Science, January 2008.

holiday
            lights

 

Before you pack up your holiday lights you may want to read this article. Mathematicians have long studied knots. As Binns puts it, "the ingredients of a knot are simple: a string with one loose end, one loop and some movement to push the end through the loop." After some experimentation, researchers suggest that holiday decorators follow these simples steps when packing up those strings of lights for storage so they won't be tangled when you pull them out next year: "Eliminate loose ends by plugging the two ends of each strand into each other, box them in a tight squeeze, and put them in a spot in your garage where they won't get jostled."

"Knots, unraveled," by Josie Glausiusz (Discover, February 2008) also covers how "extension cords and computer cables have an irritating tendency to tie themselves into knots," and quotes Doug Smith (University of California at San Diego) on current research on knots.

--- Annette Emerson

 

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"Formula For Disaster," by Michael Behar. WIRED, January 2008.

Although his first love was art, computer scientist Jos Stam says, "I started coding just for the beauty of it." A math and computer science major in college, he won an Oscar in 2005 for his improvements in rendering smooth objects. Now he works for a company that produces Maya, a leading piece of three-dimensional modeling software for creating special effects used in movies. His aim is to create physics-based modeling software that produces realistic interactions among natural phenomena such as wind, smoke, and rain. An animator would feed in certain initial or boundary conditions, and the scene would be created. Once initiated, the program takes over, leaving the animator hands-free, unlike current methods that involve costly manual tweaking. Michael Behar writes that to improve special effects "animators have to rely on mathematical finesse, not processing brawn." This statement is borne out in Stam's work, which uses the mathematics of physics. Although "formula", "polygon", and "equations" are the only math-related words used in the article, handwritten differential equations with captions explaining their significance decorate the pages. The handwriting evokes a sense of the artistic as opposed to the cold technicality usually associated with math.

--- Brie Finegold

 

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Math in "The Year in Science 2007." Discover, January 2008.

Two-dimensional
            representation of E_8
Computer-generated two-dimensional representation of E8, made by John Stembridge and based on a hand drawing made in the 1960s by Peter McMullen.

 

Four stories about mathematics made Discover's annual January issue covering the top 100 science discoveries or breakthroughs in 2007:

  • #38: "Math Advance Threatens Computer Security," by Stephen Ornes, page 45. A group of researchers factored the Mersenne number 21,039 - 1. More specifically, knowing that 5,080,711 was one of this Mersenne number's factors, the team found the factors of (21,039 - 1)/5,080,711---a 1017-bit, 307-digit number---using the special number field sieve algorithm. (Note: the Discover article incorrectly equates the Mersenne number above with its 307-digit factor.) Team member Arjen Lenstra predicts this discovery will have serious ramifications for computer security in the next decade.
  • #47: "248-Dimensional Math Problem Solved," by Jessica Ruvinsky, page 49. A team of mathematicians mapped the 248-dimensional Lie group E8. The matrix representing the irreducible representations of E8 and the relationships between them contains over 200 billion entries. This four-year effort is part of a larger project, known as the Atlas of Lie Groups and Representations.
  • #56: "Calculus Was Developed in Medieval India," by Stephen Ornes, page 52. British researchers George Gheverghese Joseph and Dennis Almeida reported finding evidence that the infinite series was first developed in the 14th century by Indian mathematicians. Joseph and Almeida also believe that this information made its way via Jesuit missionaries to Europe, where it may have eventually influenced Isaac Newton and Gottfried Wilhem Leibniz.
  • #59: "Math Breakthrough Spotted on Mosques," by John Bohannon, page 53. Two physicists studying periodic and nonperiodic tilings in medieval Islamic architecture found quasi-crystalline Penrose patterns in the Darb-I Imam shrine, built some 500 years before such patterns were discovered by mathematicians in the West.

See previous Math in the Media items on the E8 development and on the similarity between mosaics in medieval mosques and quasi-crystalline patterns.

--- Claudia Clark

 

 

Return to Top

"Why do strings of holiday lights end up in giant knots?", by Corey Binns. Popular Science, January 2008.

holiday
            lights

 

Before you pack up your holiday lights you may want to read this article. Mathematicians have long studied knots. As Binns puts it, "the ingredients of a knot are simple: a string with one loose end, one loop and some movement to push the end through the loop." After some experimentation, researchers suggest that holiday decorators follow these simples steps when packing up those strings of lights for storage so they won't be tangled when you pull them out next year: "Eliminate loose ends by plugging the two ends of each strand into each other, box them in a tight squeeze, and put them in a spot in your garage where they won't get jostled."

"Knots, unraveled," by Josie Glausiusz (Discover, February 2008) also covers how "extension cords and computer cables have an irritating tendency to tie themselves into knots," and quotes Doug Smith (University of California at San Diego) on current research on knots.

--- Annette Emerson

 

 

Return to Top

"Formula For Disaster," by Michael Behar. WIRED, January 2008.

Although his first love was art, computer scientist Jos Stam says, "I started coding just for the beauty of it." A math and computer science major in college, he won an Oscar in 2005 for his improvements in rendering smooth objects. Now he works for a company that produces Maya, a leading piece of three-dimensional modeling software for creating special effects used in movies. His aim is to create physics-based modeling software that produces realistic interactions among natural phenomena such as wind, smoke, and rain. An animator would feed in certain initial or boundary conditions, and the scene would be created. Once initiated, the program takes over, leaving the animator hands-free, unlike current methods that involve costly manual tweaking. Michael Behar writes that to improve special effects "animators have to rely on mathematical finesse, not processing brawn." This statement is borne out in Stam's work, which uses the mathematics of physics. Although "formula", "polygon", and "equations" are the only math-related words used in the article, handwritten differential equations with captions explaining their significance decorate the pages. The handwriting evokes a sense of the artistic as opposed to the cold technicality usually associated with math.

--- Brie Finegold

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