# Math Digest

## Summaries of Media Coverage of Math

Edited by Allyn Jackson, AMS
Contributors:
Mike Breen (AMS), Claudia Clark (freelance science writer), Lisa DeKeukelaere (Brown University), Annette Emerson (AMS)

### March 2006

"Lost in Einstein's Shadow," by Tony Rothman. American Scientist, March-April 2006, pages 112-113.

 Following the conclusion of the centennial of Albert Einstein's annus mirabilis, Rothman gives credit to people who were close to making Einstein's discoveries, but who have since been lost in his shadow. Those in the shadow are William Sutherland, Louis Bachelier (who both investigated Brownian motion), Hendrik Lorentz, and Henri Poincaré (who both did work connected with special relativity). Rothman writes about each person's work and the connection to Einstein's results. In papers written before Einstein's, the mathematician Poincaré (pictured) observed that time could be thought of as a fourth dimension, predicted the existence of gravitational waves, and wrote an expression equivalent to Einstein's E = mc2. The article concludes with, "if the history of science has any relevance to the doing of it, surely it is to remind us that science is a collective enterprise and to engender in us a humble awareness that the landscape of science would appear very different had the vast unrecognized majority never existed." --- Mike Breen

"Knot Theory's Odd Origins," by Daniel S. Silver. American Scientist, March-April 2006, pages 158-165.

This article focuses on work in the 1800s by William Thomson (Lord Kelvin) and Peter Guthrie Tait. At the time, although the existence of atoms was known, details about them were unknown. Thomson and Tait came to believe that chemical elements were "knotted tubes of ether" and chemical properties arose from the topological properties of knots. The article contains descriptions and illustrations of Tait's smoke ring experiments which were done to understand knots. Tait classified knots with up to seven crossings, but he and Thomson were unable to make a connection between the elements and knot theory. Despite their "failure," knot theory is a vibrant area of mathematics today.

--- Mike Breen

"Schools Cut Back Subjects to Push Reading and Math," by Sam Dillon. New York Times, 26 March 2006, page 1.

 The increased attention to reading and math in U.S. schools has led to reduced time for other subjects. The No Child Left Behind Act requires annual exams in math and reading and punishes schools that don't meet targets (targets that increase each year). The Center on Education Policy found that over 70 percent of the nation's school districts had reduced time spent on subjects such as history and music. At one school in Sacramento, California, about 20 percent of the students spent five of their six class periods on math, reading, and gym. Chad Colby, a spokesman for the U.S. Department of Education counters, "For every school you point to, I can show you five other schools across the country where students are still taking a well-rounded curriculum and are still making adequate yearly progress." --- Mike Breen

"Ride the celestial subway," by Ian Stewart. New Scientist, 25 March 2006, pages 32-36.

This article describes a new and more efficient way of engineering space travel by using the mathematical theory of dynamical systems. It turns out that the complex interplay of gravitational attraction between celestial bodies, such as the planets in our solar system, creates a network of "tubes" in which spacecraft can be propelled with very little or even no fuel. "The tubes can be seen only with mathematical eyes, because their walls are defined by the combined gravitational fields of all bodies in the solar system," Stewart writes. Junctions linking these tubes are called, in mathematical terms, Lagrange points, after the 19th century mathematician Joseph-Louis Lagrange. To use this "interplanetary superhighway", as the network of tubes has been called, you first calculate which tubes are needed to reach the destination. "You then route your spacecraft along the tube to a Lagrange point," Stewart explains, "and when it gets there you give it a quick burst on the motors to redirect to the next Lagrange point on the route...and so it goes." Through collaborations among mathematicians and space mission engineers, these methods have begun to be used in actual space missions.

--- Allyn Jackson

"Windy City Return." Peer Review, The Chronicle of Higher Education, 24 March 2006, page A10.

Robert J. Zimmer will become president of the University of Chicago on 1 July 2006. Zimmer is a mathematician who has published over 80 research papers and was on the University of Chicago faculty for many years. His most recent position was provost at Brown University. Zimmer succeeds Don Michael Randel who is leaving to become president of the Andrew W. Mellon Foundation.

--- Mike Breen

"Congress Examines Science Teaching," by Jeffery Brainard. The Chronicle of Higher Education, 24 March 2006, page A28.

At a U.S. House of Representatives subcommittee hearing on improving math and science education, college officials said that improving math and science education requires colleges to improve undergraduate instruction, especially that of future school teachers. The officials said that math and science departments should "provide financial rewards and support from colleagues to encourage faculty members to devote more effort to teaching over research." Daniel L. Goroff, vice president and dean of faculty at Harvey Mudd College, recommended expanding the budget for the National Science Foundation's division of undergraduate education, which is slated to be cut under President Bush's proposed 2007 budget.

--- Mike Breen

"Book, How Do I Love Thee? Let Me Count the Words," by Noam Cohen. New York Times, 19 March 2006, Week in Review, page 3.

Software at Amazon.com called Text Stats analyzes books by counting the number of big words in a book and how long its sentences are. Some literary scholars appreciate Text Stats, saying that it can answer questions about authorship and influence, while others see it as a gimmick. Software analysis of texts has been around for a while, but Amazon's software automates the process and puts the results on the Internet. The article includes word counts (presumably ignoring words like "the") for Stephen Hawking's A Brief History of Time ("universe" is the most used word with a count of 535) and Mickey Spillane's The Mike Hammer Collection, Vol. 1 ("get" tops the list with 714 appearances).

--- Mike Breen

"Film to celebrate maths genius," by Soutik Biswas. BBC News, 16 March 2006.

 Srinivasa Ramanujan The media in India and England reported extensively on the announcement that British film director Stephen Fry and India's Dev Benegal plan to make a film about Indian mathematician Srinivasa Ramanujan and Cambridge mathematician G.H. Hardy. Ramanujan was born to a poor family in 1887, dropped out of college, and became obsessed with mathematics. Largely self-educated, he wrote many letters and mathematicial theorems to many mathematicians until Hardy and his peers recognized the genius of Ramanujan's work. The two then collaborated. Benegal asserts in the article that "Ramanujan's work and ideas are the DNA of what powers digital technology today. When your automated teller machines divide and arrange your money before coughing it up, they are all using Ramanujan's partition theory." Both film directors Benegal and Fry share a passion for the subject despite the same cultural and linguistic barriers that existed between Ramanujan and Hardy. The directors are being praised for bringing to the public the life and work of Ramanujan and for aiming to make a major feature film rather than a documentary or television program. Among the other articles on this topic are the following: The Statesman - India ("Now showing - digital age's debt to Ramanujan," by Leonard Doyle, 18 March); The Mumbai Mirror - India ("Doing it by numbers," 17 March 2005); The Khaleej Times Online ("Stephen Fry to make film on Indian math genius Ramanujan," 24 March 2006); "Dev Benegal's dream project ready to take off," by Subhash K. Jha. Hindustan Times, 6 April 2006; "Squaring the Circle," by Geeta Doctor, The Hindu, 23 April 2006. --- Annette Emerson

"Mathematischer Beweis einer intuitiven Idee (Mathematical proof of an intuitive idea)", by George Szpiro. Neue Zürcher Zeitung, 15 March 2006.

This article discusses recent work by the French mathematician Michel Talagrand concerning the ad hoc ideas about so-called "spin glasses" that were proposed the Italian physicist Girorgio Parisi 25 years ago. Talagrand has proven that these intuitive ideas are mathematically correct.

--- Allyn Jackson

"National Pi Day," the subject of The Daily One Minute Trivia Challenge on 88Slide.com, 14 March 2006.

 "Mathemagician" Dr. Arthur Benjamin (Harvey Mudd College) presents the number pi and poses the day's trivia question, which can be viewed on the Archives link at the 88Slide.com website. --- Annette Emerson

"Today's Lesson About the Brackets: Don't Always Follow the Crowds," by Bryan Clair and David Letscher. New York Times, 13 March 2006, Section D, page 5.
"Bracketology," by Chad Garrison. Riverfront Times, 22 March 2006.
"Oops. A Few End Up Afloat in the Pool," by Michael S. Schmidt. New York Times, 28 March 2006.

 Bryan Clair and David Letscher are two math professors at St. Louis University who have a strategy to help people win NCAA Basketball Tournament office or online pools. Part of their strategy is to stay away from picking teams to win that many other people are picking. They admit that they don't have a formula to guarantee winning a pool, but their predictions will be different from others so that following their advice may bring success if a long-shot team does win. Clair and Letscher constructed entries based on the size of the contest: small (for most offices), middle (for pools of around 5000 contestants), and mega (for pools with millions of entries, such as ESPN's). The 28 March 2006 Times article is about Russell Pleasant, one person (of four) who correctly picked the 2006 Mens' Final Four in ESPN's online contest. Russell may be proof that it is better to be lucky than good. He picked George Mason University, when he meant to pick George Washington University (which brings to mind the saying, "First in war, first in peace, and first in the Washington, D.C. bracket."). --- Mike Breen

"Improving math ed -- Bush right about that; But where are the teachers coming from?", by Jonathan David Farley. San Francisco Chronicle, 12 March 2006.

Farley agrees with President George Bush's statement, in the 2006 State of the Union address, that the United States must improve mathematics education. But, Farley notes, there are not enough teachers with strong enough math backgrounds to address this challenge. He also points out the need for more inspirational teaching of mathematics and notes how the television program NUMB3RS is now being used by many mathematics teachers to spark students' interest. Farley also sees the use of mathematics in counterterrorism research as a way to engage students and presents a few specific examples of such research. "High school students could learn algebra, trigonometry, calculus and logic while also learning concrete applications involving homeland security," he writes. "No longer would students yawn and ask, `What is math good for?' Beauty could defeat both terror and boredom."

--- Allyn Jackson

"All Square," by Ivars Peterson. Science News, 11 March 2006, pages 152-153.

Manjul Bhargava (Princeton University) and Jonathan P. Hanke (Duke University) have proved a result in number theory whose history goes back a long way. In 1770, Lagrange showed that every positive integer could be written as the sum of at most four squares. In the early 1900s Ramanujan found 53 other sums involving multiples of squares, called quadratic forms (for example, w2 + 2x2 + 2y2 + 7z2) that can be used to represent every positive integer. One question is if there are other quadratic forms that represent all integers, and another is if there is a way to test if a given quadratic form does represent all positive integers. Bhargava has found other quadratic forms, adding to a list that mathematicians for more than 50 years had thought was complete. In 1993, John H. Conway (Princeton) and his student William Scheeberger found that a certain class of quadratic forms could be tested on numbers no larger than 15 and conjectured that a similar test could be found for a much broader class of quadratic forms. Bhargava and Hanke have now proved that conjecture (which involves a test on numbers no larger than 290). Bhargava presented the result at the International Conference on Number Theory and Mathematical Physics held at SASTRA University in India in December 2005. A sidebar in the article on Bhargava states that his mother, a math professor, encouraged his interest in mathematics and introduced him to the tabla, an Indian musical instrument. Bhargava compared patterns in the two: "The goal of every number theorist and every tabla player is to combine these patterns, carefully and creatively, so that they flow as a sequence of ideas, tell a story, and form a complete and beautiful piece."

--- Mike Breen

"Untying a math mystery," by Margaret Wertheim. The Los Angeles Times, 6 March 2005.

 Wertheim's piece touches on the complexities of knot theory and notes that researchers in the field may contribute to unraveling the mysteries of DNA and quantum computing. Ken Millett (University of California, Santa Barbara) is cited both for his being "part of a team that discovered a strange new way of classifying knots" in the 1980s and for his involvement in a program that recruits math and science undergraduates to become classroom teachers. The article was also published in the The San Jose Mercury News ("Mysteries of nature pose knotty questions for mathematicians," 8 March 2006). --- Annette Emerson

"The Limits of Mathematics." by Ivars Peterson. Science News Online, 4 March 2006.

In the early 20th century, mathematician David Hilbert dreamed of "codifying the methods of mathematical reasoning and putting them within a single framework." So writes Ivars Peterson in this issue of Science News Online. In such a system, there would be a definite procedure for deciding whether a proposition follows from certain axioms. A few decades later, mathematicians such as Kurt Gödel and Alan Turing proved that such a procedure is impossible. Their work, and the ongoing work of mathematician Gregory Chaitin, author of the book The Limits of Mathematics, is the subject of Peterson's article.

Gödel recognized the incompleteness of a system as basic as elementary arithmetic, using just the whole numbers and the operations of multiplication and addition, Chaitin noted in his recent book, Meta Math. Peterson goes on to explain some of Chaitin's own work, including his proof that "no program can generate a number more complex than itself." (Chaitin defines a number's complexity as "the length of the shortest computer program (or set of instructions) that would spew out the number.") He notes that Chaitin has conversely shown that "it is impossible for a program to prove that a number more complex than the program is random." (For Chaitin, a sequence of numbers is random if it cannot be generated by an algorithm significantly shorter than itself.)

For further information on Gregory Chaitin's work, see his article "The Limits of Reason" in the March 2006 issue of Scientific American.

--- Claudia Clark

"Number cruncher": Review of Letters to a Young Mathematician, by Ian Stewart. Reviewed by Justin Mullins. New Scientist, 4 March 2006, page 54.

In this book, Ian Stewart writes letters to an imaginary niece who is studying to become a mathematician. Justin Mullins's review says that Stewart "shows us how mathematicians work, rest and play, and what kind of jokes they tell each other... As a mentor for a budding mathematician, he is remarkably good company."

Another review of this book:
"Clever proof that math has its charms": Reviewed by Paul A. Robinson Jr., Christian Science Monitor, 25 April 2006.

--- Allyn Jackson

"Researchers use math to explain dolphins' dance," by Judy Siegel-Iztkovich. The Jerusalem Post, 2 March 2006.

 Although a dolphin's leap from the water and subsequent twisting in the air seems effortless and playful, in fact, neither is true. The force of the dophins' spins in the air removes parasites from their bodies, which is why they do it, according to researchers Daniel Weiss, Frank Fisch, and Anatoly Nicastro. How they do it has been explained by the three researchers' mathematical model. The spin begins in the water, which offers more resistance than air. When the dolphin emerges from the water, it encounters less resistance, so that the last twist in the water allows for more spins in the air (up to seven, according to the team). Previously it was thought that a helicopter-like motion of their tails caused the dolphins' pirouettes, but the dolphins lack of flexibility rendered that explanation invalid. --- Mike Breen

"Largest US math group calculates in Providence," by Tim Lehnert. The Providence Phoenix, 1 March 2006.

 AMS headquarters in Providence, Rhode Island. A reporter came to the AMS headquarters in Providence to learn about the Society. The article reported on the AMS's membership, mission, and programs based on a tour and talk with the Public Awareness Officers. --- Annette Emerson

"The Elusive Goal of Machine Translation," by Gary Stix. Scientific American, March 2006.

Since the 1950s, corporate and academic researchers have been attempting to develop fully automatic, high quality translation programs with relatively little success; some say it can never be accomplished, while others believe that new statistics-based programs are well on their way. The first generation of translation programs was rule-based: they used enormous lexicons and sets of guidelines developed by linguists on when to use which participle. The newer statistics-based programs compute the probability that a word is translated correctly using large libraries of text given in multiple languages. The boom of the world wide web has led to advancements in the statistical programs by increasing the amount of bilingual text available for the libraries and creating a demand for translation that drives further research, but disagreement persists on the accuracy of these programs and their potential for further improvement.

--- Lisa DeKeukelaere

"2006 mathematics prize announced," BBC News, U.K., 23 March 2006.
"Swede Wins Abel Mathematics Prize," Sci-Tech Today, 23 March 2006.
"Swede wins Abel Prize," Aftenposten, Norway, 23 March 2006.
"Swedish Mathematician Wins $920,000 Prize for Work on 'Difficult and Deep Problems'," by Jason M. Breslow. The Chronicle of Higher Education 24 March 2006. "Prize for mathematician who paved way for iPod," by James Randerson. The Guardian (U.K., Technology section), 24 March 2006. "Wave work wins top maths prize," ABC Science Online, Australia, 24 March 2006. Schwede erhält den Abel-Preis für Mathematik: Auszeichnung für Lennart Carleson (Swede receives Abel Prize in Mathematics: Honor for Lennart Carleson)," by George Szpiro. Neue Zürcher Zeitung, 24 March 2006. "Life begins at N = 40," by Marcus du Sautoy. NewScientist.com, 1 April 2006. "Awards: Add It Up." Newsmakers, Science, 7 April 2006, page 51.  Lennart Carleson. Photograph courtesy of The Abel Prize/The Norwegian Academy of Science and Letters. On 23 March 2006 the Norwegian Academy of Science and Letters announced that the 2006 Abel Prize is being awarded to Lennart Carleson (Royal Institute of Technology, Sweden). The prize amount is over US$900,000 and in mathematics is comparable to the Nobel Prize in other sciences. The Abel Committee citation says: "Carleson's work has forever altered our view of analysis. Not only did he prove extremely hard theorems, but the methods he introduced to prove them have turned out to be as important as the theorems themselves." HRH King Harald will present the Abel Prize to Carleson at an award ceremony in Oslo 23 May. The news release was posted on several newswire services (UPI, Reuters, EurekAlert) and was published in or generated coverage in media worldwide. See also the Abel Prize website. --- Annette Emerson

"Math Professor Wins a Coveted Religion Award," by Dennis Overbye. New York Times, 16 March 2006.
"Cosmologist wins 2006 Templeton Prize," by Jenny Jackson. Ottawa Citizen, 16 March 2006.
"Cosmologist Barrow bags prize for divinity." News in Brief, Nature, 23 March 2006, page 396.

 Black hole monster in a spin releases energy, from NASA. John D. Barrow, mathematical sciences professor at the University of Cambridge and cosmologist, has won the US$1.4 million dollar Templeton Prize for 2006. Barrow has published over 400 research papers and 17 books, the most recent being The Infinite Book: A Short Guide to the Boundless, Timeless and Endless. The prize "recognizes people who have bridged the schism between religion and science." Previous winners include Freeman Dyson, Aleksandr Solzhenitsyn, and Mother Teresa. The award will be presented at Buckingham Palace on 3 May 2006 by the Duke of Edinburgh. --- Mike Breen Return to Top "Math whiz, 17, hits big time with research," by Becky Bartindale, San Jose Mercury News, 7 March 2006. "He's a math all-star," by Becky Bartindale. San Jose Mercury News, 15 March 2006. "Science's New Guard," by Ben Harder. Science News, 18 March 2006, page 166. Winners of the Intel Science Talent Search were feted at a banquet in Washington, D.C. on March 14. Shannon Babb of American Fork High School in Utah won the competition and a US$100,000 scholarship for her study of pollution in a Utah river system. Three students who did math projects finished in the top ten. Yi Sun of the Harker School in San Jose, CA, won second place and a $75,000 scholarship for his study of the winding number of random walks. Nicholas Michael Wage of Appleton, WI. won fourth place and a$25,000 scholarship for his study of Paley graphs. Kimberly Megan Scott of Wellesley, MA, won tenth place and \$20,000 scholarship for her study of Ehrenfeucht-Fraisse games. The Mercury News articles are about Yi Sun. One was published before the final results and gives some of his background. The other came out after the banquet and quotes the judges' impression of him: "Delightful, bright, energetic and clearly an all-star who has already shown excellent leadership in science and to whom we will look for future leadership." The Science Service website has more information about all the winners and their projects.

--- Mike Breen