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 comments of the science writers is best illustrated by the writer who said she felt the way she did when she was in Germany and went to a party of her German friends. When she began a confersation she could understand them but once they got going they spoke much to fast for her to understand.

The fact that news writers almost never include formulas in discussing mathematics suggests that they feel that the public will not understand them. As our forsooth shows, even news writers do not always uderstand formulas. The famous Physicist Stephen Hawkins said : "Equations are just the boring part of mathematics.I attempt to see things in terms of geometry.Hawkins was adviced that for every equation in the book the readership will be halved, so included only a equation: E=m{c^2}.

With this book Dan attempts to describe the Prime Number Theorem and its history to the general public without using formulas. He does this by explaining the relevant mathematical concepts in terms of concepts famililer 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. 

Of course