Mathematical Digest

Short Summaries of Articles about Mathematics
in the Popular Press

"A Better Web Through Higher Math," by Stephen H. Wildstrom. BusinessWeek online, 22 January 2002.

"Concepts from graph theory may hold the key for everything from delivering Internet content more quickly to tracing hack attacks." Wildstrom reports that the Joint Mathematics Meetings in San Diego (January 2002) included three sessions on "probabilistic methods in combinatorics and the Internet," at which 21 papers were presented. "The most common approach is to consider the World Wide Web as a graph. In mathematical terms, a graph has nothing to do with the familiar stock market fever chart or graphical representations of data. Instead, it is simply a collection of points, called vertices, and lines joining them, called edges. This turns out to be an ideal way to model the Web; each page is considered a vertex, each hyperlink an edge. It works just as well for the physical Internet: In this case, every router is a vertex and each communications channel an edge." Wildstrom summarizes some of the applications, and proposes that these and sessions in other areas of research may well contribute to future Web and software improvements. After all, he reminds us, "One of the beauties of research in theoretical mathematics is that even the researchers generally have no idea of what will turn out to be practical. More than 150 years after Galois died, the theory that bears his name proved critical to the development of error-correcting codes that make compact disks reliable and practical."

--- Annette Emerson

American Mathematical Society