# Math Digest

## Summaries of Articles about Math in the Popular Press

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

### May 2005

"George Dantzig," The Telegraph, 27 May 2005;
"George B. Dantzig Dies at 90; Devised Math Solution to Broad Problems," by Jeremy Pearce, The New York Times, 23 May 2005;
"Weekend Edition: A Mathematician Who Solved Major Problems," hosted by Scott Simon, with guest Keith Devlin, National Public Radio", 21 May 2005;
"Vanguard Mathematician George Dantzig Dies," by Joe Holley, The Washington Post, 19 May 2005, page B06;
"George Dantzig, 90, noted statistics theorist," by Howard Mintz, The San Jose Mercury News, 17 May 2005.

 Dantzig, who died on May 13 at age 90, was known for two major contributions: linear programming and the "simplex method," an algorithm for solving linear programming problems. He developed both while serving as chief of the combat analysis branch of the U.S. Air Force during World War II. Devlin noted that after the war, when food was scarce, Dantzig's pioneering work was put to use to figure out a "minimum-priced, optimal diet" for the U.S. population, after which the government directed farmers to produce certain crops and animals. Devlin concluded that Dantzig's work had and continues to have a great impact in this computer age in which many variables must be juggled to get optimal results. Holley summarized Dantzig's inventions as having "revolutionized planning, scheduling, network design and other complex functions intergral to modern-day business, industry and government." Dantzig was awarded the National Medal of Science by President Gerald Ford in 1975. --- Annette Emerson

Reviews of Incompleteness: The Proof and Paradox of Kurt Gödel:
"Review of Reviews"
The Week, 11 May 2005;
"Gödel's Universe," by Martin Davis, Nature, 5 May 2005, pages 19-20;
"Waiting for Gödel," by Polly Shulman, The New York Times, May 1, 2005, page 20.

 Kurt Gödel and his work have been the subject of at least two works published this year. One is Incompleteness: The Proof and Paradox of Kurt Gödel, written by novelist and philosophy professor Rebecca Goldstein. The other, A World Without Time: The Forgotten Legacy of Gödel and Einstein, was written by another philosopher, Palle Yourgrau. Reviews of these works have appeared in various news outlets, including Nature and The New York Times. Writing for Nature, Martin Davis, a visiting scholar at University of California, Berkeley, discusses Gödel's incompleteness theorem and the mathematical thinking that led up to this influential result. Apart from a few inaccuracies and apparently unjustifiable assumptions that appear in these books, Davis finds the books to be "well written" explanations of some of Gödel's accomplishments. Polly Shulman of The New York Times calls Goldstein's book "a touching intellectual love story" of Gödel's "romance ... with mathematical Platonism". Noting that Goldstein focuses on both the man and his ideas, Shulman provides the reader with an introduction to Gödel's incompleteness theorem. ---Claudia Clark

"Abel prize awarded to Peter Lax," BBC NEWS, UK Edition, 25 May 2005;
"A-bomb pioneer wins mathematics prize," CNN.com, 24 May 2005.

 Norwegian Crown Prince Haakon of Norway awarded the 2005 Abel Prize to Peter Lax in Oslo, Norway, on Tuesday May 24. The BBC item includes a brief biography of Lax, described as an "inspirational figure," and summarizes his important mathematical work as having "provided new approaches to partial differential equations, which are used to describe non-linear systems such as the motion of gases." The CNN piece focuses on Lax's contributions to the Manhattan Project at Los Alamos, New Mexico, in 1945, although the article cites the lifetime achievements for which Lax was recognized and awarded the US$980,000 Abel Prize. (Photo courtesy of New York University.) See also: "Math genius tames complex systems," by Anna Salleh, ABC News in Science, 27 May 2005; "Math Prize Press Survey Disproves Hungarian Genius Theory," Pestiside.hu: The Daily Dish of Cosmopolitan Budapest, 27 May 2005. --- Annette Emerson Return to Top "Third Time Proves Charm for Prime-Gap Theorem," by Barry Cipra. Science, 27 May 2005. Sometimes the old adages offer good advice: "If at first you don't succeed, try, try again." Number theorists Dan Goldston and Cem Yildirim would probably agree. After two years and two proofs that each contained an error, Goldston, Yildirim and more recent contributor János Pintz, have with input of other mathematicians proven an important prime number theory result. As writer Barry Cipra notes in the May 27th issue of Science, "On average, the gap between a large prime p and the next prime number is approximately ... log p. But the actual gap between two primes may be far from average. Number theorists long ago proved that there is no upper limit on how large the gap can grow, relative to log p." Now Goldston, Yildirim, and Pintz, have proven that "the smallest possible gap [between consecutive prime numbers] continues to shrink relative to log p, as the numbers increase." While perhaps not a surprising result, mathematicians may find it useful in proving other results, in particular the famous "twin prime" conjecture. Seems worth a try. --- Claudia Clark Return to Top "Learning curve." Random Samples-People, Science, edited by Yudhijit Bhattacharjee, 27 May 2005.  Photograph courtesy of Weber Shandwick/ExxonMobil. Science notes under "Nonprofit World" that golf pro Phil Mickelson and his wife Amy have teamed up with ExxonMobil to promote elementary school scence and math education. In July the Mickelson ExxonMobil Teachers Academy enrolled about 200 teachers from across the country in a workshop "aimed at creating a sense of inquiry and problem-solving ability in students." Mickelson helped to promote awareness of the importance of science and math education in TV spots that aired during the 2005 Masters Tournament. In ExxonMobil's announcement of the partnership and program Mickelson says "Amy and I are eager to support education programs that open up the world of science and math to young people. It's our hope that these young people will become the scientists and engineers of tomorrow." --- Annette Emerson Return to Top "Juggling the Numbers," by Jeffrey Brainard. The Chronicle of Higher Education, 27 May 2005, pages A21-23. This article examines the shift in grant money for partnerships between schoolteachers and math and science educators in colleges or universities, from the National Science Foundation (NSF) to the U.S. Department of Education. A chart at the end of the article shows that Education Department funding for such programs has gone from less than one-tenth that of NSF's in 2002 to more than four times NSF's in the proposed 2006 budget. Bush administration officials contend that the Education Department is better positioned to help school districts, while Jere Confrey, a math education professor at Washington University in St. Louis, says that the NSF pays more attention to quality and is a better source of ongoing efforts. The author notes that the Education Department programs are smaller than NSF's and run for a shorter time, but have a wider reach (money is awarded to all 50 states). --- Mike Breen Return to Top This article reports on the latest twist in the saga of an attempt to prove an important result in number theory. Two years ago, Daniel Goldston, a math professor at San Jose State University, and his Turkish colleague Cem Yalcin Yildirim of Bogazici University, announced they had proved this result, which mathematicians consider to be a huge advance. The result is related to the renowned Twin Primes Conjecture, which asks whether there are infinitely many prime numbers that differ by 2 (e.g., 5 and 7 are twin primes because the differ by 2). Goldston and Yildirim attempted to answer a somewhat different question: Are there infinitely many pairs of primes that are closer together than average? Trouble was, their proof was not quite right. Within weeks of its appearance in preprint form, other mathematicians pointed out errors that caused the proof to collapse. But now, with a new collaborator, Hungarian mathematician Janos Pintz, Goldston and Yildirim have produced a new version of the proof. This version has been vetted by those who found errors in the earlier attempt and is receiving accolades. --- Allyn Jackson Return to Top This article discusses a report in the Proceedings of the National Academy of Sciences by two researchers at Stanford University, Lawrence M. Wein and Manas Baveja; Bajeva is in Stanford's Institute for Computational and Mathematical Engineering. The report uses a mathematical model to evaluate the effectiveness of the system the United States depends on for using fingerprints to identify foreign visitors. The first sentence of Waterman's article summarizes the report's conclusion: "The Department of Homeland Security's$10 billion system for using fingerprints to check the identity of foreign visitors has only about a 50-50 chance of catching suspected terrorists, even if their prints are on file". The article goes on to describe the system, called US-VISIT, and discusses how Homeland Security officials have reacted to the report.

--- Allyn Jackson

"Count Him In," by Linton Weeks. Washington Post, 23 May 2005, page C1.

The "him" is Dan Rockmore, professor of mathematics and computer science at Dartmouth College. He and Weeks spent an afternoon together in Manhattan, during which Rockmore pointed out many instances where mathematics can be found. Among the mathematics topics that the two ran across in the course of the afternoon were: apportionment problems, Fibonacci numbers, the Riemann Hypothesis (about which Rockmore has written Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers), the Poincaré Conjecture, sphere-packing, and the Königsberg Bridge Problem.

--- Mike Breen

Articles on the Sudoku puzzle craze:
"Can you digit?" by Tim Dowling.
Guardian Unlimited, 20 May 2005;
"Insanity by numbers," by Justin McCurry. Guardian Unlimited, 17 May 2005.

Sudoku is a puzzle involving numbers and logic that has swept Japan and is sweeping Great Britain. These articles discuss the game, the craze, strategy, and the frustration that results when a puzzle seems unsolvable. McCurry describes the game as follows: "The aim is to place a number between one and nine in the empty 'cells' contained inside a nine-by-nine grid. Each row and column as well as each smaller, three-by-three subsidiary grid---these are indicated by slightly bolder lines---must contain the numbers one to nine, without omission or repetition." (Readers might recognize these as examples of Latin squares.) Puzzlers are presented with grids that have some numbers already filled in, and the challenge is to complete the puzzle according to the requirements. According to one person who supplies puzzles to newspapers, those created by humans are more elegant than those created by computer. Dowling gets advice from mathematicians Marcus DuSautoy and Robin Wilson, but is still stymied by the puzzles.

The article "Sudoku craze 'could revive interest in mathematics'," by Roger Highfield, appeared in the 11 October 2005 issue of The Telegraph (U.K.). The article quotes mathematician Sir Michael Atiyah: "... he believes that the puzzle could kindle more interest in the subject among young people. 'All kinds of mathematical games are a good thing,' said Sir Michael, who was speaking to mark his appointment today as the new President of the Royal Society of Edinburgh."

"We can work it out. Or maybe we can't...," Guardian Unlimited, 11 December 2005;
"Mind-bending Swiss genius returns," by Thomas Stephens. Swiss Info, 22 August, 2005;
"Sudoku's puzzling journey,"
BangkokPost, 22 August 2005;
"An Sudokus rätseln Mathematiker schon lange," by George Szpiro. Neue Zürcher Zeitung, 26 June 2005;
"Sudoku: The puzzle everyone's talking about," by Allan Koay, The Star Online, 20 June 2005:
"Sudoku Math," by Ivars Peterson, Science News Online, 18 June 2005;
"Forget crosswords. Britons now like their puzzles with numbers," by Mark Rice-Oxley, The Christian Science Monitor, 31 May 2005;
"The mind of Mr Sudoku ...," by the Features Editor, Belfast Telegraph Digital, 21 May 2005.

--- Mike Breen

The Fibonacci sequence continues to inspire artists and architects. The author cites an article published in The Fibonnaci Quarterly journal in 1964 that demonstrated how Johann Sebastian Bach's Art of the Fugue "has a mathematical perfection," and notes that a contemporary chamber music ensemble has adopted the name Fibonacci Sequence and is performing in a U.K. music festival. The author speculates that humans have a desire to seek and see harmony (he mentions the Greeks and Romans, Da Vinci, Kepler), and that while the "modern movement, Dada, feedback and Duchampian chance" have come along, "here we are, still asking the same questions as Pythagoras."

--- Annette Emerson

"US gives stamp of approval to scientists." News in Brief, Nature, 12 May 2005, page 137.

Nature covers the news of the U.S. Postal Service's issuance of four, 37-cent stamps commemorating scientists including mathematician John von Neumann, geneticist Barbara McClintock, and physicists Josiah Willard Gibbs and Richard Feynman. "The US Postal Service has put out stamp series before on such themes as inventors or architects, but this is the first group of stamps featuring scientists."

--- Annette Emerson

 Mathematician du Sautoy reports that an advertising firm in the U.K. has taken to using a mathematical equation in a poster campaign to promote Smirnoff Ice, assuming that the formula would increase the credibility of the product. Rather than appealing only to nerds, "it is a mark of the subject's changing fortunes that mathematical equations have become sufficiently intriguing for brands to sponsor a formula." The author cites examples of mathematics used to promote ideas as well as products: "a formula for parallel parking; a formula to predict the future of a marriage; even a formula to help British people understand their fear of eating with chopsticks." Du Sautoy lists some of the most famous equations: Einstein's e=mc2, innocent-looking equations of chaos theory, and equations to explain the motions of heavenly bodies and the behavior of electrons and to predict solar eclipses. He wishes that people could summon up equations other than e=mc2. --- Annette Emerson

 NPR's Siegel interviews high school math department chair Ameilia Zimmerman about the late Louis Leithold. Leithold, who died on April 29, wrote a number of calculus books. After teaching many years at the university level, he started in his 70s teaching calculus at Malibu High School. Zimmerman notes that while the average score on the AP Calculus test is 3.01, Leithold's students scored an average 4.6. He was "legendary at the College Boards." He routinely assigned 2 to 3 hours of homework and would build up anticipation towards the day celebrating the Fundamental Theorem of Calculus. Leithold was the subject of the 1988 film "Stand and Deliver." Hear the entire interview on the NPR archive. --- Annette Emerson

Nature journalist Philip Ball has been awarded the prestigious Aventis Prize for his book, Critical Mass. He received the £10,000 (US\$19,000) award on May 12 from Robert May, the president of the Royal Society, London, and Dirk Oldenburg, who is on the board of the pharmaceutical company Aventis. Fellow author Bill Bryson (chair of the Aventis Prize judging panel) summarized why Ball was awarded the prize: "This is a wide-ranging and dazzlingly informative book about the science of interactions. By explaining the mathematics of human group behavior, Critical Mass explores the efforts of physicists and social scientists to describe the patterns behind economic crashes, stampeding crowds and the development of traffic jams." Ball often writes mathematics-related articles for Nature.

--- Annette Emerson

He's the "Math guy" on NPR, the creator of the PBS series "Life by the Numbers," and the writer of numerous books and articles on mathematics for the public. He's Keith Devlin. And writer Esther Landhuis profiles this "preacher" of mathematics in an article in the May 9 San Jose Mercury News. Devlin's interest in mathematics, and desire to share this with others, began when he was a teenager studying the calculus: "I could see the beauty, the aesthetics, the challenge," recalls Devlin. After earning his Ph.D. in mathematics and teaching for a few decades, Devlin was ready to "spread [his] wings." But not ready to leave mathematics behind. In fact, through his first math column, and the TV shows, books, and articles that followed, Devlin has spread the word about the pervasiveness of mathematics in everyday life, and has made difficult concepts more accessible to a very large audience.

---Claudia Clark

In his May 2005 column, Paulos reports on an upcoming international conference on Mathematics and Narrative (scheduled for July 12-15 in Mykonos, Greece). Academics there will explore the interplay between the Narrative of Math and the Math of Narrative. Paulos explains that the math of narrative uses mathematical ideas to study narrative techniques: "hypertext, recursion theory, combinatorics and other mathematical notions," and logic. He describes mathematical metaphors and "notions of probability and statistics" and predicts that "an increasing appetite for abstraction as well as other aspects of contemporary culture will insure [sic] that the confluence of mathematics and narrative will intensify."

--- Annette Emerson

"Harvard professor offers services as Hollywood mathematician," by Michael Kunzelman, Associated Press, 1 May 2005;
"Divide and Conquer," by Vanessa Jones. Boston Globe, 17 May 2005.

Jonathan Farley, a professor at Harvard University, has started a consulting company to help media projects get their math and science right. "Plenty of films and TV shows employ military experts, police officers or doctors to serve as technical advisers, but Farley believes his company -- Hollywood Math and Science Film Consulting -- fills an unmet need," the AP article reports. Farley's company, which he founded with London-based biochemist Lizzie Burns, has helped producers of the new television program NUMB3RS, which features a mathematician as a main character. With assistance from Harvard postdoc Anthony Harkin, Farley not only uncovers mathematical errors in scripts but also advises the producers on getting the culture of mathematics right. Not all of their suggestions have been followed, but they are enthusiastic about the show. "Farley and Harkin both hope the show inspires youngsters to consider careers in math," the AP article says.

This AP story was printed in newspapers across the United States. Read more about NUMB3RS in this entry in the Math Digest; see also the Math Digest entry below.

--- Allyn Jackson