# Mathematical Digest

### Short Summaries of Articles about Mathematics

in the Popular Press

"Making Connections": A review of *Six Degrees: The Science of a ConnectedAge,* by Duncan J. Watts. Reviewed by Prabhakar Raghavan. *American Scientist*,July-August 2003.

The reviewer writes: "*Six Degrees: The Science of a Connected Age* [byDuncan J. Watts] offers the lay reader fascinating insights into the wayscience is done, particularly into the interplay of several fields withdistinctive methodologies. Watts argues for a new science that blends graphtheory, stochastic processes and `complexity.' A very entertaining read,especially for nonscientists." As Raghavan notes, Watts suggests that "theclassical theory of random graphs is a failure because for decadesmathematicians overlooked the need to consider more sophisticated models." Thereviewer suggests that this is because "mathematicians like to prove theoremsabout objects they study, and when the objects get too complex for their prooftechniques they back off. In contrast, almost all of the evidence driving theconclusions in *Six Degrees* rests on computer simulations, which allowthe exploration of sophisticated network models without demanding definitivemathematical proof... Watts clearly recognizes this important difference butcould have explained it better; however, the book otherwise nicely contraststhe scientific methodologies from multiple disciplines."

*--- Annette Emerson*