# Math Digest

## Summaries of Media Coverage of Math

Edited by Allyn Jackson, AMS
Contributors:
Mike Breen (AMS), Claudia Clark (Northeastern University), Annette Emerson (AMS)

### June 2004

"Herman Goldstine Dies at 90; Helped Build First Computers," by Wolfgang Saxon. New York Times, 26 June 2004, page A12.

Herman Goldstine, who died on June 16, 2004, was a leader in developing the Electronic Numerical Integrator and Computer (Eniac), the first electronic computer (which weighed more than 30 tons). Goldstine received his Ph.D. in mathematics at the University of Chicago in 1936 and later became a permanent member of the Institute for Advanced Study. He was a winner of the National Medal of Science and was director of mathematical sciences research at IBM. In fact, IBM named a postdoctoral fellowship in his honor. The article in the Times features a picture of Dr. Goldstine with Julian Bigelow, J. Robert Oppenheimer, and John von Neumann.

--- Mike Breen

"Best Musical Score (By a Laptop)," by James Barron. New York Times, 26 June 2004, page A13.

John A. MacBain is using statistics to try to take some of the subjectivity out of judging musical competitions. The article does not specify what formula he uses, but does say that he uses Excel to convert judges' scores so that they can be combined and a winner can be chosen. MacBain's method removes the possibility that a factor like playing early in a competition could hurt a competitor. The article outlines the actual process of how the scores are entered and verified, as well as judges' reactions to using their scores and statistics to determine the winner. MacBain's program has been used in the International Violin Competition and the Van Cliburn International Piano Competition.

--- Mike Breen

"Vital Statistics," by Dana Mackenzie. New Scientist, 26 June 2004, pages 36-41.

"The boldest claims about the universe rely on physicists sifting the truth from the millions of measurements they make," the article states. What this means is that, order to understand the phenomena they study, physicists have to understand the data they glean from measurements. As this data becomes increasingly sophisticated and complex, physicists are beginning to realize their need for powerful tools from statistics. The article examines three examples from modern day physics in which statistical tools---or the lack thereof---made a crucial difference.

--- Allyn Jackson

"Now prove it." New Scientist, 19 June 2004, page 4.

This short piece reports on the 8 June news release by mathematician Louis de Branges of Purdue University, who claims to have proven the celebrated Riemann Hypothesis. "Mathematicians have reacted with skepticism," the article says. The paper containing de Branges's results may be found on his web site.

--- Allyn Jackson

Peterson dispels the idea that mathematicians work in solitary pursuit, by using Erdős as an example of one who collaborated extensively with others---as evidenced by what mathematicians refer to as the "Erdős Number." The Erdős number describes the relationship between Erdős and authors who worked with him or one of his associates. Erdős is assigned the number 0; as of the end of 2003, 509 mathematicians had written a paper with Erdős and are forever assigned number 1; 6,984 wrote a paper not with Erdős but with one of his coauthors, so they have an Erdős number of 2---and so on. Peterson notes that Jerrold Grossman (Oakland University, Rochester, MI) worked with Patrick Ion (at Mathematical Reviews ®) and Rodrigo De Castro (Universidad Nacional de Columbia, Bogota) to put together a complete list of Erdős number 1's and 2's. The article notes that many mathematicians enjoy the challenge of determining such networks, and references two websites that show the connectedness of non-mathematicians: the Oracle of Bacon and the Oracle of Baseball.

--- Annette Emerson

"Awards." Random Samples. Science, 11 June 2004, page 1593.

The People section of Random Samples lists two mathematicians who recently won awards. Shiing-shen Chern of Nankai University in Tianjin, China received a one million dollar prize from the Shaw Prize Foundation for "his role in developing global differential geometry." Mikhael Gromov of France's Institut des Hautes Études Scientifiques and the Courant Institute of Mathematical Sciences at New York University won the US$150,000 Frederic Esser Nemmers Prize in Mathematics "for his contribution to modern geometry." The Nemmers Prize is awarded by Northwestern University. --- Mike Breen "Mighty prime." New Scientist, 5 June 2004, page 7. "Another Mersenne." Random Samples, Science, 11 June 2004, page 1592. The largest known prime number is now 224,036,583 - 1 -- a number with over seven million digits. The number was discovered in late May by Josh Findley's computer as part of the Great Internet Mersenne Prime Search (GIMPS). Mersenne primes are primes of the form 2p - 1, where p is prime. Findley's prime number is the 41st known Mersenne prime, and the seventh discovered by GIMPS since its inception in 1996. --- Mike Breen Isaac Asimov's science fiction "Foundation" novels were published over 50 years ago, but the new science described in them---"psychohistory", in which scientists use equations to calculate human behavior---is no longer the stuff of fiction. The article describes how mathematics is now commonly used in research and reported in science journals to predict voting patterns, crowd behavior, stock market trends, fads, rumors, and more. The field of "statistical mechanics math" is now being used to study more than gas and chemical reactions and magnetic materials: it is used to study problems such as traffic flow. The mathematics of networks---used to study the connectedness of molecules in gases---is applied to study TV networks, the electric power grid, airports linked by direct flights, the internet and the spread of disease. "Science today has more to work with---the mathematics of statistical physics, economic game theory and networking with modern neurobiology, brain scanning and anthropological experiments," and much of it can be used to explain or predict human behavior. --- Annette Emerson "Cracking the DaVinci Code," by Keith Devlin. Discover, June 2004, pages 65-69. In this article, Keith Devlin writes about the number (1 + √5)/2, known to have been calculated by Euclid around 300 B.C., and more recently referred to as the "divine proportion" or "golden ratio." This value and Fibonacci's famous sequence appear in the recent best-selling mystery, The DaVinci Code, as do a number of popular misconceptions regarding these mathematical entities. For example, Devlin points out that it's not necessarily true that the Greeks integrated the golden ratio into their architecture. It's also questionable that humans, in general, prefer the golden ratio above any other proportion. And why would the ratio of a person's belly-button height to overall height---which doesn't exactly equal the golden ratio anyhow---be more "divine" than any other ratio of human proportions? On the other hand, it's true that certain 20th century artists, including Salvador Dali, used the divine proportion in their paintings. And both Fibonacci numbers and the golden ratio clearly appear in nature: in the position of leaves around a stem, the number of clockwise and counterclockwise spiral patterns of seeds in a sunflower, or the number of petals on most flowers. It's a matter of efficiency, as mathematicians and scientists are discovering. But regardless of the veracity of the claims surrounding the golden ratio and Fibonacci numbers, Devlin notes that people persist in believing these stories. And that's a puzzle that neither he nor the book attempts to solve. --- Claudia Clark "A Confederacy of Smarts," by Gary Stix. Scientific American, June 2004, pages 40-45. The confederacy in this case is Microsoft Research. While other companies' research divisions are shrinking, Microsoft's is growing---currently numbering 700 researchers. Understandably, most of the article is about computer science. There is, however, a sidebar on page 42 profiling three researchers, including mathematicians Susan Dumais and Michael H. Freedman. Another sidebar has excerpts from an interview with Microsoft founder Bill Gates. --- Mike Breen "Thumbing His Nose at Academe, a Scholar Tries to Auction His Services," by Richard Monastersky. The Chronicle of Higher Education, 28 May 2004, page A15. "Theorems for Sale," by Erica Klarreich. Science News, 12 June 2004, pages 376-377. "Six Degrees of Erdős," NetWatch, Science, 16 July 2004, page 317. In April 2004, William A. Tozier auctioned his services as a co-author on eBay. The winner of the auction would receive Tozier's help writing a paper. Tozier has an Erdős number of 4, so one of the benefits of winning the auction was an Erdős number of at most 5. Tozier said that the auction began as a joke but as he was contacted by people who "expressed a frustrated desire to do research," the auction became serious. Jose Burillo, an associate professor of mathematics at the Polytechnic University of Catalonia (Spain), was offended by the auction and offered an inflated bid of over US$1,000 to end the bidding. Erica Klarreich writes that Burillo was declared the original winner of the auction but because his was a protest bid, Tozier wound up contacting the next-highest bidder. That bidder backed out of the auction because of a lack of time. As of publication of the articles, no winner had been declared. Tozier said that any payment he receives would be used to start an online community for scientific collaboration.

--- Mike Breen

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