Dan Rockmore's book: Stalking the Riemann Hypothesis
Stalking the Riemann Hypothesis
Pantheon Books, New York, 2005
The Proof: an interview with Dan Rockmore
New Hampshire Public April 12. 2005
As the stakes increase, Prime-Number theory Moves Closer to Proof
Wall Street Journal, Science Journal, April 8. 2005
The Telegraph (Calcutta, India), April 8, 2005
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, and a discussion of his talk by the science writers, can be found here under "Mathematics for the Media"
Unfortunately, Sarnak's talk was not fully appreciated by the science writers. The first writer to comment said that she felt like she did when she was in Germany and a friend took her to a party. At the party the Germans initially tried to speak to her in English, and she could understand them pretty well, but then they would drift into German and she was lost.
Another science writer said that, to write an article based on Sarnac's talk, she would have to sit down with him and have him explain what he had said in a way she could understand. Then she would have to write an article for her readers without using formulas or mathematical symbols--a few graphics would be o.k.
With his book "Stalking the Riemann Hypothesis", Dan discusses the Riemann Hypothesis and its history in a way that the science writers proposed for the general public. He does this by explaining the relevant mathematical concepts in terms of concepts familiar to his readers. For example the rate of increase is discussed first in terms of the spread of a rumor and the logarithm in terms of the Richter scale. Density is described in terms of population density noting that the average number of people per square mile living in South Dakota is quite different from that of New Jersey. Then we read
Similarly, we can ask how many prime numbers "live in the Neighborhoods" of a particular number? Gauss's estimates imply that as we traipse along the number line with basket in hand, picking up primes, we will eventually acquire them at a rate approaching the reciprocal of the logarithm of the position that we've just passed.
While there are no formulas and minimal math symbols, Dan does make good usage of great graphics made by our mutual friend Peter Kostelec.
Along the way, Dan gives a lively discussion of the great mathematicians Euler, Gauss, Riemann and many others up to present working on solving the Riemann Hypothesis. He also gives the readers an understanding of what mathematics and mathematical research is all about. In the Telegraph Dan is quoted as saying:
My overarching goal has always been to provide a window through which the public might get some sense of what mathematical research is like while showing the surprising breadth of math as a subject, I felt that the best way to achieve this was through a single story, for I believe that narrative is the key to holding a reader's interest. It seemed to me that the history of the Riemann Hypothesis - given its central place in modern mathematical history and research - would provide such an opportunity. The story of the search for its resolution would provide a structure off which I could hang a broader story of modern math.
This is not Dan's first attempt to give the general public a better understanding of what mathematicians do, what mathematics is all about and how it effects our daily life. (I once mentioned to a musician that I was a mathematician and he said, "I guess you learn how to multiply and add numbers faster than we can".)
Dan's first article for the general public was an essay in the New York Times in 1998. In this essay Dan used the movie" Good Will Hunting" to illustrate stereotypes of mathematicians. He writes:
The main messages of the movie are old and trite: You are either someone who can do math or you are not; mathematics is impossible to explain to others, even other mathematicians, and to be a mathematician and to think about mathematics is to separate yourself from most of society. After all, what could be more at odds with Will's working-class, street-wise background than a talent for mathematics?
Dan then gives examples from the arts to show the pervasiveness of mathematics in the real world. For example, the Movie "Sliding Doors" illustrates how long-term behavior of a system can be highly dependent on the initial conditions -- the butterfly effect. He remarks that identifying these connections does not need to lead to madness as it does for the hero of the movie Pi.
More recently Dan has presented on Vermont Public Radio a series of mathematical commentaries with jazzy titles such as "Math, a love story", "Halving Your Cake" and "Can you hear the shape of your date?" giving explanations of important modern mathematical results that we see in everyday life. You can hear these commentaries here.
Last year Dan and his colleagues Wendy Conquest and Bob Drake made a movie called "The Math Life" in which leading mathematicians talk about how they got into mathematics, what kind of mathematics interests them and what it is like to work on and solve a mathematical problem. This movie was shown on public television and used in numerous classrooms.
"Stalking the Riemann Hypothesis" is Dan's greatest challenge to bring mathematics to the general public. It is hard to image a better mathematical story to show the general public the beauty, the excitement, and the importance of mathematics. Dan is an engaging writer and he tells the story in a wonderful way. We can hardly wait for the movie!