May 2005
"George Dantzig," The Telegraph, 27 May 2005;
Reviews of Incompleteness: The Proof and Paradox of Kurt Gödel:
"Abel prize awarded to Peter Lax," BBC NEWS, UK Edition, 25 May 2005;
"Third Time Proves Charm for PrimeGap 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
"Learning curve." Random SamplesPeople, Science, edited by Yudhijit Bhattacharjee, 27 May 2005.
"Juggling the Numbers," by Jeffrey Brainard. The Chronicle of Higher Education, 27 May 2005, pages A2123. 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 onetenth 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
"Mathematician lauded for (corrected) research," by Glennda Chui. San Jose Mercury News, 25 May 2005. 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
"Effectiveness of biometric ID system in doubt", by Shaun Waterman. United Press International, 23 May 2005. 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 5050 chance of catching suspected terrorists, even if their prints are on file". The article goes on to describe the system, called USVISIT, 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, spherepacking, and the Königsberg Bridge Problem.  Mike Breen
Articles on the Sudoku puzzle craze: 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 ninebynine grid. Each row and column as well as each smaller, threebythree subsidiary gridthese are indicated by slightly bolder linesmust 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." See also:  Mike Breen
"As easy as 1, 1, 2, 3 ...," by Jonathan Jones. The Guardian, 12 May 2005. 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, 37cent 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
"Learn to love the equation," by Marcus du Sautoy. The Guardian, 9 May 2005.
"Late Author, Teacher Demystified Calculus for Thousands." All Things Considered, hosted by Robert Siegel, National Public Radio, 9 May 2005.
"Nature journalist scoops £10,000," by Mark Peplow. news@nature.com 9 May 2005. 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 wideranging 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 mathematicsrelated articles for Nature.  Annette Emerson
"'Math guy' has a knack for numbers," by Esther Landhuis. Mercury News, 9 May 2005. 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
"Who's Counting: Math in Narratives," by John Allen Paulos. ABCnews.com, 1 May 2005. In his May 2005 column, Paulos reports on an upcoming international conference on Mathematics and Narrative (scheduled for July 1215 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; 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 Londonbased 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
"Surprise! TV Gets the Math Right," by Lauren Aaronson. Popular Science, May 2005.

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