Dan Rockmore's book: Stalking the Riemann Hypothesis

Stalking the Riemann Hypothesis
Pantheon Books, New York, 2005
Dan Rockmore

The Proof: an interview with Dan Rockmore
New Hampshire Public April 12. 2005
John Walters

As the stakes increase, Prime-Number theory Moves Closer to Proof]
Wall Street Journal,Science Journal. A[ro; 8. 2005
Sharon Begley

Math Monster
The Telegraph (Calcut, Indea), April 8, 2005
Pathik Guha

http://www.dartmouth.edu/~chance/wikivideos/mathmonster.jpg

In 1998 the Mathematical Sciences Research Institutein 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, and a discussion of his talk by the science writers, can be found here under "Mathematics for the Media"

Unfortuanately, Sarnak's talk was not fully appreciated by the Science writers. One of them said that she felt like she recently did when she was in Gremany and met a Gernman friend at the party. She said that at the beginning of a conversation her friend spoke English but then switched to German and she was completely lost.

The Science writers said that, to write an article based on Sartnac's talk they would have to sit down with Sarnak and have him explain what he had said in a way they could understand and then they will have to them to write an article for their readers, many of whom have at most 8th grade mathematics, with no math symbols or equations and at most an occasional graphic.

With this book Dan discusses the Prime Number Theorem and its history in a way that the Science writers proposed for the generl public. He does this by explaining the relevant mathematical concepts in terms of concepts familliar to his readers. For example the exponential function and rate of increase are discussed in terms of the spread of a rumor and the logarithm in terms of the Rickter scale. Density is described ifirst in terms of population density. remarking that the average number of people per square mile living in South Dekota is quite different from that of New Jersey. He then writes:

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

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

line with basket in hans, picking up primes, we will eventally acquaire them at a

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

.Along the way Dan gives a lively discussion of the mathematicians Euler, Gauss, Riemann and many others up to present day mathematicians working on solving the Riemann Hypothesis. He also gives the readers an understanding of what mathematics and mathematial research is all about.