Stalking the Riemann Hypothesis

In 1998 the Mathematical Sciences Research Institute in Berkeley, California had a three- day conference on "Mathematics and the Media". The purpose of this conference was to bring together science writers and mathematicians to discuss ways to better inform the public about mathematics and new discoveries in mathematics. As part of the conference, they asked Peter Sarnak, from Princeton University, to talk about new results in mathematics that he felt the science writers might like to write about. He chose as his topic "The Riemann Hypothesis". This is generally considered the most famous unsolved problem in mathematics and is the major focus of Sarnak's research.

In his talk, Sarnak described some fascinating new connections between the Riemann Hypothesis, physics and random matrices. He used only mathematics that one would meet in calculus and linear algebra. Sarnak's lecture can be found here under "Mathematics for the Media" .

The coments of the science writers is best illustrated by the writer who said that she felt the way she felt when she was in Germany and went to a party of her German friends. When she to talk to them, at the beginning confersation she could understand them but once they got going in the conversation there was no hope.

Dan helped the chance group write three special issues of Chance News called Chance on the Primes to help Chance News better understand Sernac's talk. But even here we assumed a knowledge of basic mathematical concepts.

With this book Dan attempts to describe the Prime Number Theorem and its history to the general public. He does this bye explaining the relevant mathematical concepts in terms of concepts famililer to his readers. For example the exponentila function and rate of increase are discussed in terms of the spread of a rumor.and the logarithm in terms of the Rickter scale. Densisty is described in the notion of population density. Having discussed density. The average number of people per square mile living in South Dekota is quite different from that of New Jersey. Dan writes:

Similarly, we can ask how many prime numbers "live in the neighboood" of a

particular numb er. Gauss's estimates imply that as we traipse along the number

line with basket in hadn, picking up primes we will eventally acquaire them aat a

rate apporaching the reciprocal of the logarithm of the position that weve just passed.