Math Digest

May 2006

• "Gauss's Day of Reckoning," American Scientist Online, May-June 2006
• "Science & Technology: Future Focus, Training the Next Generation," The Crisis, May-June 2006
• Articles about the awarding of the Abel Prize to Lennart Carleson, May 2006
• "Number power": Review of Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills, by Paul J. Nahin, New Scientist, 27 May 2006
• "Math Professor's Work Adds Up to an International Award," KBCI-TV (Boise, ID), 24 May 2006
• "How Einstein struggled with his grand theory---and the maths," The Guardian (UK), 22 May 2006
• "The answer isn't teaching to the test," The Colorado Springs Business Journal, 19 May 2006
• "Finding Common Ground in the U.S. Math Wars," Science, 19 May 2006
• "Learning beyond the classroom," USA Today, 17 May 2006
• "New Math---Recent Algorithmic Art at LACDA," Artdaily.com, 17 May 2006
• "The NSA's Math Problem," The New York Times, 16 May 2006
• "Ex-University President to Lead U.S. Math Panel," The New York Times, 15 May 2006;
  "Well-Balanced Panel to Tackle Algebra Reform," Science, 19 May 2006
• "George Lenchner, 88, Dies After Life By the Numbers," New York Times, 14 May 2006
• "Algebra and Its Enemies," TCSDAily.com, 8 May 2006
• "Speed Theater," The San Francisco Chronicle, 7 May 2006
• "Wired for math," Science News, 6 May 2006
• "Free will---you only think you have it," New Scientist, 6 May 2006
• "Math teacher wins TV spot," Chicago Tribune, 4 May 2006
• "Math + letter writing = free Puffs tissues," WNDU-TV (South Bend, IN), 3 May 2006
• "Ask.Com's Friendly Math Professor Does TV Show and Tell," Brandweek.com, 3 May 2006
• "When Slide Rules Ruled," Scientific American, May 2006
• "America's 100 Best," Reader's Digest, May 2006
  

"Gauss's Day of Reckoning," by Brian Hayes. American Scientist Online, May-June 2006.

Carl Friedrich Gauss.

One of the more famous anecdotes about Carl Friedrich Gauss tells of the young schoolboy who astounded his teacher by using a clever trick to sum the numbers from 1 to 100. Writer Brian Hayes developed a few questions about this story, however: how did the teacher know that Gauss's solution was correct, and how did the other students attempt to solve the problem? Hayes's hunt for answers led him through a literature search to a surprising conclusion: Gauss's tale is an accumulation of embellishments on an originally plain story. The earliest version of the anecdote, written just after Gauss died, mentions a quickly solved arithmetic summation, but no details about the numbers involved or Gauss's method of solution. Since then, different authors have inserted their own numbers to make the story interesting and plausible. While Hayes does not criticize embellishment as an important tool of storytellers, he does worry that inaccuracies in the anecdote may discourage future math students. In the absence of a smart, Gauss-style solution, he says, students who must solve problems "the hard way" may doubt their talent and ability to succeed. --- Lisa DeKeukelaere

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"Science & Technology: Future Focus, Training the Next Generation," by Victoria L. Hudson et al. The Crisis, May-June 2006, pages 34-35.

Jonathan Farley, one of five people profiled in the article, is on the cover of this issue of The Crisis. His profile has information about his education---he is one of four brothers to graduate from Harvard---and early scholarly work as well as his plans for the future: This month, Farley becomes chair of the department of mathematics and computer science at the University of the West Indies. His research area is lattice theory, which he has recently applied to homeland security. "We're not coming up with anything that's going to stop terrorists or catch Osama Bin Laden. We're creating tools that enable decision makers to make more logical decisions rather than relying on intuition or guesswork."

--- Mike Breen

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"Swedish mathematician scoops Abel Prize," Independent Online (South Africa), 24 May 2006;
"Lennart Carleson of Sweden awarded with Abel mathematics prize." Pravda (Russia), 23 May 2006;
"Abel Prize awarded to Swedish mathematician," New Kerala (India), 23 May 2006;
"Abel prize awarded to Swedish mathematician," by India eNews (India), 23 May 2006.

2006 Abel Laureate Lennart Carleson was received by Norway's Crown Prince Haakon and Queen Sonja. (Photo: Scanpix/Abel Prize/Norwegian Academy of Science and Letters.)

News sources around the world picked up the news of the Abel Prize ceremony held in Oslo on May 23. Norway's Queen Sonja awarded the 2006 Abel Prize to Swedish mathematician Lennart Carleson. The Abel Prize website includes photographs, a video of the prize announcement, and a wealth of information about Carleson, the Abel Prize, and related events. --- Annette Emerson

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"Number power": Review of Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills, by Paul J. Nahin. Reviewed by Matthew Killeya. New Scientist, 27 May 2006, page 54.

This book tells the tale of the famous Euler formula, which provides a beautiful relation among the numbers e, pi, and i. The reviewer calls the tale "remarkable" but also notes that the book is filled with equations and therefore is a "challenging read".

--- Allyn Jackson

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"Math Professor's Work Adds Up to an International Award," by Paul Fredericks. KBCI-TV (Boise, ID), 24 May 2006.

Justin Moore, an associate professor of mathematics at Boise State University, won the 20,000-euro prize (about US$25,000) in the Young Scholars' Competition at the Horizons of Truth Gödel Centenary 2006 in Vienna, Austria. The competition took place April 27-29 and was held in honor of Kurt Gödel who was born April 28, 1906. At the competition, 10 finalists presented proposals on research related to Gödel's work. Moore's first-place prize---presented by Garry Kasparov---was for his project "The continuum and aleph-2." Also receiving 5000-euro (about US$6300) prizes were Mark Van Atten of the Institute of History and Philsophy of Science and Technology of the University of Paris I, whose project is "Gödel and German Idealism", and Eli Ben-Sasson of Technion-Israel Institute of Technology, whose project is "Searching for a conditional answer to Gödel's question".

--- Mike Breen

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"How Einstein struggled with his grand theory---and the maths," by James Randerson. The Guardian (UK), 22 May 2006.

The young Albert Einstein.

A collection of Albert Einstein's letters and papers will go on sale in London in June for US$1.5 million. The 15 manuscripts and 33 letters written between 1933 and 1954 were held by Ernst Gabor Straus, a young mathematician who collaborated with Einstein at Princeton Unviersity. The papers were never studied before because no one except the Straus family knew they existed. David McMullan (Plymouth University, UK) notes that the papers show that Einstein used and needed help from mathematical colleagues: "Straus' mathematical virtuosity gave a framework to Einstein's intuitive vision of the universe." The papers---to be sold as a single collection---also include some of Einstein's "scientific doodles and scribbled equations", some of his thoughts on academia, and a letter from Erwin Schrödinger. The article concludes with a brief chronology of Einstein's life and publications. --- Annette Emerson

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"The answer isn't teaching to the test," by John Hazlehurst. The Colorado Springs Business Journal, 19 May 2006.

Google lures job applicants by the ingenious method of testing---teasing---those interested with a math question on a billboard on Highway 101: Those who know the answer go to the website, where they are greeted with a harder problem to solve, after which they are invited to email their resumés. This prompts Hazlehurst to recall how he learned to love math (largely by the inspiration of an unconventional teacher and the challenge of Fermat's Last Theorem) and how---despite politicians now fighting over "teaching to the test"---there are still ways students and others can "connect with mathematics." He cites a city-wide competition sponsored by Alex Soifer of the University of Colorado at Colorado Springs, video games, and chess clubs, all of which provide "environments that nurtured today's Internet magnates," including the Google group. --- Annette Emerson

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"Finding Common Ground in the U.S. Math Wars," by Jeffrey Mervis. Science, 19 May 2006, pages 988-90.

Recent years have seen many disputes in the mathematics community and in communities across the U.S. about how mathematics should be taught. The Common Ground Iniatitive is a six-member group of mathematicians and mathematics educators created in 2004 to find agreement on issues in math education. Richard Schaar, former president of the calculator division at Texas Instruments, leads the group, which issued a three-page document of principles in math education, from kindergarten to high school. Schaar says that the document is not a curriculum, indeed the most that Common Ground participants hope to achieve is "to influence the process by which states develop standards, adopt textbooks, and develop the assessment tools to measure what students should be learning." The article lists seven areas of agreement among the group:

• Automatic recall of basic facts
• Judicious use of calculators
• Fluent use and understanding of basic algorithms
• Fractions as a foundation for algebra
• Careful choice of real-world problems
• Teachers at the core of good instructions
• Mathematical knowledge of teaching

--- Mike Breen

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"Learning beyond the classroom," by Tracey Wong Briggs. USA Today, 17 May 2006.

Michael Viscardi.

This article is about the 20 students named to the 2006 All-USA High School Academic First Team. The list includes three---Brett Harrison, Daniel Litt, and Michael Viscardi (pictured here)---who have done some significant mathematics projects. Harrison's work on Seymour's Conjecture will appear in the American Mathematical Monthly; Litt constructed a combinatorial proof of the Chan-Robbins-Yuen Theorem; and Viscardi's work on the Dirichlet problem will be published in Computational Methods and Function Theory. All three won Karl Menger Memorial Prizes at the recent Intel International Science Fair. Litt and Harrison are quoted in the article. Litt says, "If I excel, I think it's because I'm essentially interested in everything. I've never found a subject that's not interesting to me." Harrison says, "If education is the search for truth, math is the most definitive truth. It lays the fundamental rules for every other science...I really think the motivation for pure math research, above every other research, is the purest form of intellectual curiosity and search for truth." The article includes individual profiles of all 20 students, nine of whom are going to Harvard and three to Yale. Each student received a trophy and US$2500. --- Mike Breen

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"New Math---Recent Algorithmic Art at LACDA." Artdaily.com, 17 May 2006.

International artists are exhibiting works at the Los Angeles Center for Digital Art. Andy Lomas, Nathan Selikoff, Charles Fairbanks, Hollis Cooper, Tim Quinn, Thomas Briggs, and Milos Rankovic are exhibiting works created using computer algorithms, math-based image generators, and/or customized software, and the author provides a brief profile of each and an overview of the process used to generate the images.

--- Annette Emerson

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"The NSA's Math Problem," by Jonathan David Farley. The New York Times, 16 May 2006.

Mathematician Farley writes in this Op-Ed that "it's very unlikely that the type of information one can glean from [telephone customer records] will help us win the war on terrorism." He explains that without additional data, graph theory and social network analysis (which try to determine key players and patterns) don't provide the complete or accurate picture, especially given the NSA's assumption that you can figure out "who might be a terrorist based on calling pattterns." Farley explains the flaws and suggests that "formal concept analysis, a branch of lattice theory" could shed more light, although using math is just one tool which cannot be used exclusively and can be used unwisely. See also "The NSA is tap, tap, tapping," by Jonathan David Farley, The San Francisco Chronicle, 9 July 2006. --- Annette Emerson

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"Ex-University President to Lead U.S. Math Panel," by Diana Jean Schemo. The New York Times, 15 May 2006;
"Well-Balanced Panel to Tackle Algebra Reform," by Jeffrey Mervis. Science, 19 May 2006, page 982.

Last January, President Bush unveiled a plan to spend US$250 million to improve math education in elementary and middle schools. The plan, which is intended to help the U.S. maintain a competitive edge in math and science, involves the creation of a National Math Panel that will balance opposing viewpoints to formulate a nationwide strategy for math education. While older teaching plans involved rote memorization of equations, newer strategies focus more on the concepts that drive the formulas than on simply producing the correct solution. Larry R. Faulkner, the former president of the University of Texas at Austin and the newly selected chair of the Math Panel, views his role as a "shepherd" for the interests involved in the fiery debate between these conceptual and formula-based teaching approaches.

--- Lisa DeKeukelaere

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"George Lenchner, 88, Dies After Life By the Numbers," by Margalit Fox. New York Times, 14 May 2006.

In 1979, George Lenchner founded the Mathematics Olympiads for elementary and middle school students. As a math teacher on Long Island, NY, in the 1950s, Lenchner started the first scholastic math league outside of New York City, and an article he published in a national teachers' magazine inspired the creation of similar leagues across the country. Lenchner's Olympiads, which currently serve more than 100,000 students in all 50 states and more than two dozen foreign countries, are one of the few such organizations that involves so-called "mathletes" at the grade-school level.

--- Lisa DeKeukelaere

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"Algebra and Its Enemies," by Kenneth Silber. TCSDAily.com (Technology, Commerce, Society: A Publication of Tech Central Station), 8 May 2006.

Islamic scholar al Khwarizmi (790-840).

Silber covers the reaction to an Op-Ed piece written by Richard Cohen in The Washington Post. As Silber reports, Cohen dimissed math as something that "can now be done by a computer or a calculator" and stated it's a "lie" that calculus teaches reasoning. Silber notes that science bloggers and journalists have argued both sides of each issue, and he enlightens us with a brief review of a new book, Unknown Quantity: A Real and Imaginary History of Algebra, by John Derbyshire. Notable for Silber "is just how slow progress often was" as algebra developed from its origins in Mesopotamia and Egypt to now. Algebra originated with the Islamic scholar al-Khwarizmi, who wrote a book on the subject. In fact, the word "algebra" comes from the Arabic al-jabr, meaning "completion." Silber notes that while Derbyshire finds it depressing that perhaps symbolic algebra doesn't come naturally to humans, he considers it inspiring that humans have made such progress in inventing and learning the subject. Silber marvels that humans "can do it at all. No thanks to some pundits, though." --- Annette Emerson

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"Speed Theater," by Sam Hurwitt. The San Francisco Chronicle, 7 May 2006.

PlayGround exposes emerging playwrights in San Francisco to a variety of topics, from which they must write a 10-page play in five days (to be submitted for review for possible performance at the Berkeley Repertory Theater). The Mathematical Sciences Research Institute (MSRI) has partnered with PlayGround on topics for three years, but this year was the first time that MSRI hosted a briefing on their topic, "zero sum game." Mathematicians Elwyn Berlekamp, David Einsenbud, and Aaron Spiegel gave presentations.

--- Annette Emerson

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"Wired for math," by Carolyn Gramling. Science News, 6 May 2006, page 286.

The study summarized in this article suggests that the human brain can process numerical information fairly early in life. Researchers studied four-year-olds and adults viewing a stream of computer images. The researchers found that in both groups the same region of the brain---the intra-parietal sulcus---was active when the number of objects in the images changed. Says lead researcher Jessica Cantlon, "The take-home message is that by at least four years [of age], your brain is learning how to deal with quantitiative information. The same brain circuits appear to be important for doing mathematical tasks your whole life." The research results are published in the open-access journal Public Library of Science Biology.

--- Mike Breen

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"Free will---you only think you have it," by Zeeya Merali. New Scientist, 6 May 2006, pages 32-36.

This article juxtaposes two recent developments, one in physics and one in mathematics, which both have implications for the question of whether human beings have free will. The theory of quantum mechanics suggest that randomness is inherent in the universe. As Merali puts it, quantum mechanics tells us that "you cannot predict the outcome of an experiment; you can only estimate the probability of getting a certain result." If physical reality were actually deterministic, you could, given a sufficient amount of sufficiently precise data, predict the outcome of experiments with total certainty. Now physics Nobel laureate Gerard 't Hooft has put the finishing touches on a theory that says there is a deeper layer of physical reality that is deterministic. This theory in turn suggests that the idea of human free will is an illusion and that all our actions are deterministic. In the mathematics camp are John H. Conway and Simon Kochen, who have proved an intriguing mathematical result showing that, if human beings have even the slightest bit of free will, then so do particles---and hence physical reality is not deterministic. Conway believes that he does have free will: "I believe I am free to drink this cup of coffee, or throw it across the room," he is quoted as saying. Thus he and Kochen believe there must be a flaw in 't Hooft's theory. As it happens, the theory deals with physical reality at a scale that is inaccessible by current experimental methods. Since it has not been tested experimentally, no one knows for sure whether the theory truly reflects reality.

--- Allyn Jackson

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"Math teacher wins TV spot," by Grace Aduroja. Chicago Tribune, 4 May 2006.

Sheila Hardin, a math teacher at Oak Park and River Forest High School in Illinois, was selected in an online sweepstakes to make a cameo appearance on the CBS-TV show NUMB3RS next season. Hardin was nominated by her student, Kevin Binder, who will also travel to Hollywood for the filming and who said that Hardin is "really encouraging and gets you excited about math." The contest received about 28,000 entries from almost 8,000 students. Hardin's selection was announced in St. Louis at the annual meeting of the National Council of Teachers of Mathematics. She was notified that she had won by e-mail, but deleted most of the messages, thinking that they were spam. When she opened one of the messages and called the number, to ask that the e-mails stop, she found out that she had won. The article concludes with Hardin's reaction to being nominated: "I was really excited and touched. Every time a student recognizes you in any way, it reminds you that you're doing something."

--- Mike Breen

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"Math + letter writing = free Puffs tissues," by Stephanie Stang. WNDU-TV (South Bend, IN), 3 May 2006.

Procter and Gamble printed five simple arithmetic problems on some of its boxes of Puffs tissues. Rochester, Indiana English teacher Lauri Wilhite tried the problems but couldn't get the answers printed on the box, so she asked the math department for help. It turned out that three of the five answers were wrong. For example, 1 + 7 x 4 - 5. The answer on the Puffs box is 27, but the correct answer is 24 because multiplication is done before addition and subtraction. The three wrong problems were all calculated left to right instead of following the standard order of operations. In fact, the two correct answers on the box were correct because the left-to-right calculation agreed with the order of operations. Wilhite's students at Rochester Middle School wrote Procter and Gamble about the errors, and Dave Minifie, Puffs Brand Manager, went to the school to apologize for the mistake. He said that the company would send the school 5000 boxes of Puffs (the school goes through about 1000 boxes a year) to atone for its mistake. Now that the company knows the order of operations, it may have to work on units: When this segment aired, Procter and Gamble had sent nine boxes to the school instead of nine pallets of boxes.

--- Mike Breen

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"Ask.Com's Friendly Math Professor Does TV Show and Tell," by Jenny Holland. Brandweek.com, 3 May 2006.

The website Ask Jeeves has been relaunched as Ask.com. It claims search capabilities superior to those of Google and uses an algorithm called ExpertRank, developed by former Rutgers University math professor Apostolos Gerasoulis. Ask.com is advertising its relaunch with a series of unscripted TV commercials featuring the exuberant Gerasoulis himself using the search engine. Data from March 2006 shows the search engine with 6 percent of the market, compared to Google's 43 percent. One ad ends with Gerasoulis saying, "Google is big, that's for sure. If you notice, through evolution, the biggest animals go first."

--- Mike Breen

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"When Slide Rules Ruled," by Cliff Stoll. Scientific American, May 2006, pages 80-87.

Stoll describes several aspects of the slide rule, including its invention, its different forms, and its heyday when slide rules were as common as the electronic calculator is today. He explains logarithms, which are the basis for slide rules, and has instructions on how to use a slide rule. Also included in the article is a diagram that can be cut out and assembled into a slide rule. The article points out that the designer of one of the first electronic calculators used a slide rule in the design process, so Stoll assumes that at night the huge slide rule on his wall whispers to his Pentium, "Watch out, you never know when you're paving the way for your own successor." --- Mike Breen

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"America's 100 Best." Special issue of Reader's Digest, May 2006, page 96.

Math makes the magazine's America's Best list this year. Ranking numbers 30 and 31 are NUMB3RS (the TV program, for "inspiring new mathematicians") and Edward Burger of Williams College (for his book, Coincidences, Chaos, and All That Math Jazz: Making light of weighty ideas, from which Reader's Digest quotes: "What allows us to discuss sex, drugs and death with such quantitative glee? Welcome to statistics.").

--- Annette Emerson

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