## Math Digest |

- "Circles of friends: What maths tells us about us",
*The Economist,*30 September 2004 - "Doing a number on terrorism: A conference at Rutgers focused on how math could be applied to the fight against terrorists,"
*Philadelphia Inquirer,*10 October 2004 - "Play it again, John": Review of
*Theory of Games and Economic Behavior: Sixtieth-Anniversary Edition*, by John von Neumann & Oskar Morgenstern,*Nature*, 30 September 2004 - "Pedigrees for all humanity,"
*Nature*, 30 September 2004 - Special issue on randomness,
*New Scientist*, 25 September 2004 - "New Light on Newton,"
*Science*, 24 September 2004 - "For Fry's, It's a Prime Time to Support Higher Math,"
*The Los Angeles Times*, 20 September 2004 - "Naturally patterned": Review of
*The Colours of Infinity*, by Ian Stewart, Benoit Mandelbrot, et al,*New Scientist*, 18 September 2004 - "Dali's immortality of the soul,"
*Nature*, 16 September 2004 - "Google Entices Job-Searchers with Math Puzzle,"
*NPR Morning Edition*, 14 September 2004 - Articles on biometrics: "How to Stop Identity Theft,"
*Discover*, October 2004, and "Iris ID," ABC News.com, 13 September 2004 - "Browns Town 1964: Frank Ryan," Cleveland Browns web site, 6 September 2004
- "Solving a Knotty Problem,"
*The Chronicle of Higher Education*, 3 September 2004

**"Circles of friends: What maths tells us about us". ***The Economist,* 30 September 2004; "Doing a number on terrorism: A conference at Rutgers focused on how math could be applied to the fight against terrorists," by Matt Crenson. *Philadelphia Inquirer,* 10 October 2004.

These two articles discuss mathematical research presented at a meeting at DIMACS, the Center for Discrete Mathematics and Theoretical Computer Science at Rutgers University. The meeting explored applications of mathematics to understand social networks. The particular branch of mathematics used here is graph theory, which studies phenomena that arise in simple models of nodes and links connecting the nodes. The article first article emphasizes applications of graph theory to modeling terrorist networks. Is it possible, for example, to know whether a terrorist cell has been disabled by knowing how many of its members are in custody and what their functions in the cell were? Graph theory may be able to help analyze such situations. The second article discusses the terrorism example only briefly before going on to discuss, for example, using graph theory to model the spread of sexually transmitted diseases in social networks. An Associated Press article emphasizing the terrorism applications was carried by several newspapers around the world.

*--- Allyn Jackson*

** "Play it again, John": Review of Theory of Games and Economic Behavior: Sixtieth-Anniversary Edition, by John von Neumann & Oskar Morgenstern. Reviewed by Karl Sigmund. **

This review includes a brief overview of the mathematical contributions of John von Neumann and Oskar Morgenstern and quotes from a review of the original edition of their classic work: "Posterity may regard this book as one of the major scientific achievements of the first half of the twentieth century" (*Bulletin on the American Mathematical Society*, 1945). The reviewer of the new edition of *Theory of Games and Economic Behavior* notes that the work---specifically the theory of two-person zero-sum games, analyses of situations of pure competition---gave birth to the field of game theory, which led to John Nash's equilibrium concept, and which ultimately led to work resulting in several Nobel Prizes in economics. Morgenstern's idea that "economic predictions are in principle inconsistent, because they cause agents to act in a different way from that predicted," and von Neumann's "'maximin' solution, yielding the highest guaranteed payoff" led to the concept that "mixed strategies can be optimal, even if an adversary manages to guess them." Sigmund asserts that the book's value is mainly of historical interest but points out that it "marked a turning point in economics, challenging it to become a mathematical discipline at last."

*--- Annette Emerson*

** "Pedigrees for all humanity," by Jotun Hein. ***Nature*, 30 September 2004.

Consider the idea that all of the humans living on the earth today come from some common ancestor and that at some point in the past (known as the IA point), each person on earth was either an ancestor of everyone, or no one, alive today. How long ago would the most recent common ancestor (MRCA) have lived? When would the "identical ancestor" (IA) point have occurred? In an existing model of genealogical ancestry, mating is assumed to be random, which may explain why the MRCA is estimated to have lived at the improbably recent time of 1400 AD!

In a recent issue of *Nature*, researchers Rohde, Olson and Chang describe both of their methods for determining the MRCA and the IA dates. Both models allow for migration. The first model, chosen for tractability and theoretical insight, involves the use of probabilistic analysis. A second model that incorporates known migration patterns and population density was analyzed computationally using Monte Carlo simulations. The results of the first model fall somewhere between the more conservative and less conservative results from the second model: in the second model, the more conservative mean MRCA date was 1415 BC and the less conservative mean date was 55 AD, while the corresponding mean IA dates were 5353 BC and 2158 BC, respectively.

The second model was also used to calculate genetic common ancestry, with quite different results. Partly because DNA is inherited in rather large segments from our predecessors, Hein notes that "not many generations ago (about six), members of our pedigree existed that did not contribute to us genetically."

*--- Claudia Clark*

** Special issue on randomness: "In the lap of the gods", by Ian Stewart; "What are the chances?", by Robert Matthews; "The jumble cruncher", by John L. Casti and Cristian Calude. ***New Scientist*, 25 September 2004, pages 29-37.

** "New Light on Newton." NetWatch, ***Science*, 24 September 2004, page 1881.

Those who want to learn more about Isaac Newton, about both his scientific and non-scientific sides, can visit The Newton Project. According to this short article, the site is "an online storehouse of documents that range from his early notebooks to never-before-published commentary on the Book of Revelation."

*--- Mike Breen*

**"For Fry's, It's a Prime Time to Support Higher Math," by Michael Hiltzik. The Los Angeles Times, 20 September 2004.**

The American Institute of Mathematics is in Palo Alto, California, next to a Fry's Electronics. The location is no accident, as Fry's helps fund the institute. Most of this article is about the work and history of the institute, which brings together mathematicians to work on problems. Peter Sarnak and institute director Brian Conrey are quoted about the institute's mission. Also, the article gives some information on the Riemann Hypothesis, on which the institute held its first workshop.

*--- Mike Breen*

** "Naturally patterned": Review of The Colours of Infinity, by Ian Stewart, Benoit Mandelbrot, et al. Reviewed by Kenneth Falconer. **

**"Dali's immortality of the soul," by Alison Abbott. Nature, 16 September 2004, page 247.**

A new documentary, *The Dali Dimension*, tells of Salvador Dali's passion for science and how that passion is reflected in his art. The film premiered in Barcelona in September and will be show in several European countries. The article mentions Thomas Banchoff and René Thom and begins with a quote from Dali: "Thinkers and literati can't give me anything. Scientists give me everything, even the immortality of the soul."

*--- Mike Breen*

**"Google Entices Job-Searchers with Math Puzzle," by Andrea Shea. NPR Morning Edition, 14 September 2004.**

Google advertised for engineers by putting the following problem on banners in Harvard Square in Boston and on a billboard in Silicon Valley: "First 10-digit prime found in consecutive digits of e.com." Those who solve the problem can get to a website where they can submit their resumes to Google. An MIT graduate student said that it took him the better part of a day to solve the problem, but upon reflection he felt that it was the kind of problem that a "precocious sixth grader could do."

See also:

"Google's creative search for elite programmers," by Michael Liedtke. *San Francisco Chronicle*, 24 October 2004.

*--- Mike Breen*

**"Browns Town 1964: Frank Ryan," by Terry Pluto. Cleveland Browns, 6 September 2004.**

This chapter, from *Browns Town 1964*, is about Frank Ryan, the quarterback for the Cleveland Browns in their NFL championship season of 1964. During the season, Ryan was working toward his Ph.D. in mathematics and earned the degree from Rice University the following spring. Although most of the chapter is about football, Ryan also talks about how sportswriters had difficulty dealing with his abilities in mathematics. Said Ryan, "I came quickly not to like the media's interpretation of my interest in math...It was pretty demeaning of what I was trying to do. I don't think that I ever acted like the 'flaky egghead' they called me. It shows you how deficient the sports world was that they had to seize on those sorts of hooks to get a story out. It was pretty pathetic journalism." Ryan retired from football in 1970. He taught mathematics at Rice and has now retired from teaching.

*--- Mike Breen*

**"Solving a Knotty Problem," by Isolde Raftery. The Chronicle of Higher Education, 3 September 2004, page A6.**

Colin Adams, a mathematics professor at Williams College, has created a comic book about knots. "Knot Man" is the superheroine, and "Knot Cat" is her canine companion. The comic book is aimed at high school students. Says Adams, "If you excite students about the material, they'll go on learning it." Adams will also be creating a comic book on bubbles with his Williams colleague, Frank Morgan.

*--- Mike Breen*

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