# Mathematical Digest

### Short Summaries of Articles about Mathematics

in the Popular Press

"Know thy neighbor," by Mark Buchanan. *New Scientist*, 17 January 2004, pages 32-35.

This article discusses the concept of "small worlds" in network theory. This concept is often described using the "six degrees of separation" experiment, which was carried out by psychologist Stanley Milgram in the 1960s. In the experiment, people were given letters to be sent to a recipient unknown to them. The people sent the letters to friends whom they thought might be socially closer to the recipient; those friends sent the letters to their friends, and so on. Surprisingly, most of the letters reached the recipient in just 6 steps---hence the phrase "six degrees of separation". In the 1990s, mathematicians Steven Strogatz and Duncan Watts investigated this phenomenon and found that, when they worked with mathematical networks that consist simply of points and links between the points, throwing in just a few links between widely-spaced points greatly decreased the number of steps needed to get from a point to any other. Their work spurred a great deal of subsequent research into network theory, and this research could have substantial implications for designing networks like the Internet.

*--- Allyn Jackson*