## So You Want to Write a Pop-Math Book?

In April 2003 I published a book named *Prime Obsession*, an account of the Riemann Hypothesis for
not-very-mathematical readers. My
book has been more successful than a book of that kind has any right to be, for which I am of course very grateful.
One of the editors of this
magazine asked me to write down some notes about the making and selling of the book, and about the matter of pop-math
books in general.

First I should explain how I came to write a book of this kind. I am not a professional mathematician, nor even a teacher of mathematics (though I once, briefly, was that). I am a freelance writer, journalist, and web journalist. Before that, I was a computer programmer in the financial-services industry. I had started out in life with the intention of becoming a mathematician, though, and attended University College, London for three years, graduating with a bachelor's degree in math. At that time in England, at any rate at that college, there was no nonsense about majors and minors; we just did three straight years of unadulterated math. This got us to a pretty high level — much higher than that reached by a first-degree course in a present-day American (or, probably, British) university.

In the course of rising to those rarefied mathematical altitudes I gained an item of what, according to the Ancient Greeks, is the most precious type of knowledge: self-knowledge. I discovered that I was not very good at math. I discovered this by the oft-repeated experience of watching more gifted classmates "see through" a problem in five minutes of reflection, while I myself had to spend a weekend sweating over the same problem to get the same result. There were also some areas, particularly in algebra, where I simply "hit the wall" — where I found that, with the most diligent application I was capable of, I could not understand the material.

With this precious item of self-knowledge in hand, following graduation I did the sensible thing and took up a non-mathematical career. I never lost my affection for math, though, nor my belief that it is the highest form of intellectual endeavor. My own love for the subject was unrequited — I loved math, but math didn't love me — yet it is a well-known peculiarity of human nature, illustrated for example by the career of the poet W.B. Yeats, that unrequited love can sometimes be the most enduring and inspiring kind. I continued to love math, to read math books and magazines, occasionally to work my way through a textbook, patiently completing all the exercises. (A math textbook, to my way of thinking, is useless if it doesn't have lots of exercises.) Since living in the U.S.A. I have kept up membership in both the M.A.A. and the A.M.S., and sit at the breakfast table chuckling over math periodicals, to the bafflement of my wife, who is deeply un-mathematical.

And so, in the summer of 2000, I happened to be reading Abe Shenitzer's excellent translation of the late Detlef Laugwitz's book on Bernhard Riemann. Just at this time, my literary agent was trying, without any success, to place a novel I had written. I like my agent, and wanted him to go on being my agent, so I thought I had better have a book proposal ready for him, for that inevitable day when he declared that he had done all he could do with the novel. It occurred to me that there was a book to be written about the Riemann Hypothesis, in which the math of the topic could be agreeably mixed with historical and biographical background material. I did some further reading, carried out some explorations on the Internet, and had dinner with Andrew Odlyzko, whose name had kept turning up in my Internet browsing.

Andrew is now at the University of Minnesota, but at that time he was still working for Bell Labs in New Jersey. I drove over there from my home on Long Island, and we had dinner at an Italian restaurant near the labs. Andrew was a key player in some of the events related to the Riemann Hypothesis in the 1970s and 1980s, and maintains a keen interest in the topic. That's why I had kept seeing his name on the Internet. He is also, I should add, something of a character. When you mention his name, people start to tell amusing, affectionate Odlyzko stories, along the lines of the apocrypha that often develop around colorful mathematical personalities — Paul Erdős and David Hilbert come to mind. I may at some future date make a collection of these stories and present it to Andrew. At any rate, he was extremely patient and kind in the face of my, at that point, not-very-well-informed inquiries. It was that dinner with Andrew that really got my book project off the ground. I went home with a sheaf of notes and, in less than a week, had a 20-page proposal ready.

My literary agent was at first skeptical. I introduced him to the idea over lunch in Manhattan one day.

"Howard," I announced, "I'd like to write a book about a great unsolved mathematical problem. You know, like Simon Singh's book about Fermat's Last Theorem." [Singh's book was, as everyone in the book business knows, phenomenally successful.]

He perked up. "Oh? What is this problem?"

"Well," I said, "it is the Riemann Hypothesis."

"I see. And what does it say, this Riemann Hypothesis?"

"It asserts that all the nontrivial zeros of the Zeta function have real part one-half."

My agent looked at me in silence for a minute or two. Then he looked at his food. Then he looked at me again, and said: "You know, John, there are some doors Man was never meant to open."

In spite of this discouraging start, I eventually sold him on the idea. It remained for him to sell it to some publisher. This did not go very well. Months passed, and all we were getting was rejections. I was busy changing careers, and the Riemann project slipped from my mind.

In the summer of 2001 I took my family to China for a few weeks to visit with my wife's family and allow my children to get to know something about the country of half their ancestors. A few days after arriving, I thought I had better check my e-mail, so I logged in at one of the Internet cafés that can be found everywhere in China (where they are actually called "Internet bars"). The very first e-mail message I opened up was from my agent: "I have placed the Riemann book!" The proposal I had made up was now so far in the past, and I had been so preoccupied with moving my family around China, it was a moment or two before I understood what was meant. Riemann book? What Riemann book? Once I did understand, there was very little I could do, other than authorize the agent to negotiate the best deal he could get, which I would sign off on when I came home in the fall.

I duly came home and signed the agreement, which was for a healthy advance from a respectable publisher, with the manuscript to be delivered in January 2003. That gave me fifteen months to write the book, which I thought was not as long as I would have liked, but manageable.

At that point the Fickle Finger of Fate decided to point my way. The publisher had assigned an editor to me, and this editor went off on a tour of some European countries. One of his duties now was to sell translation rights to my book in those countries. Attempting to do so, he discovered an unhappy fact: Two other authors were already at work on Riemann Hypothesis books, one of them with over a year's lead time on us. This kind of thing often happens in book publishing. A certain idea is "in the air," and two or more authors will decide to tackle it. This may not necessarily be bad news. Depending on the timing, one book, if successful, might awaken enough interest to make the others successful too. However, my publisher took the view that we needed to speed up my particular project dramatically. At their insistence, though with some concessions on my advance to soften the blow, we had to re-negotiate the contract. Delivery of the manuscript was now set for June 30, 2002 — a mere eight months ahead. This was a horribly tight schedule.

I dropped everything but some casual web journalism and threw myself into the project, reading everything I could find. Fortunately I live in an area well-supplied with first-class university math libraries, none of which raised any objection to my walking in and browsing their stacks. I read Euler in Latin and half a dozen authors in German — languages I had learned at school but had mostly forgotten. I badgered Andrew Odlyzko, and any other mathematicians willing to be badgered. (And one or two who were not at first very willing … But all were extraordinarily generous with their time and trouble, and I finished the project with a warm regard for mathematicians in general.) I spent hours fiddling with Mathematica, a tool I had hardly used before. I attended a scholarly conference on the Hypothesis, much of which went right over my head.

At last, somehow, it all got done. The book came out, and I started consuming my way through the publisher's marketing budget. Though not large, the budget covered several trips to "events" at bookstores and radio stations around the country. I quickly learned some necessary precautions for getting through these events. For example, I learned to make it clear at the very beginning of the proceedings that I am not a mathematician, only a writer who likes math. This allowed me to shrug off with proper insouciance questions like "Don't you think that Connes' noncommutative formulation of Poincaré duality in K-homologies offers a promising approach?" I developed a set of stock responses to commonly-asked questions, especially: "What use is the Riemann Hypothesis?" I accumulated a repertoire of small jokes and minor theatrical stunts to enliven my talks. I began, in fact, to enjoy myself … just as the marketing budget ran out.

The relative success of *Prime Obsession* — by the end of 2003 we had sold somewhat over
25,000 hardcover copies, whereas
the "expected" hardback sales for a book of that type would be in the range from five to ten
thousand — caused me much
reflection. The book has, after all, a lot of heavy math in it. I had decided from the start that there is no point
in writing a book about the
Riemann Hypothesis if you don't tell your readers what the Hypothesis is, and why mathematicians want to resolve it.
To do that, I needed to give
my readers a lot of math, so I buckled down to it and gave them that math, making it as palatable as I could, and
scattering it among the historical
and biographical material as thinly as possible. *Prime Obsession* is still, though, I think, a hard book for
anyone who left math behind in
high school, and I am not at all sure I understand why so many people have bought it.

Interest in mathematical topics among non-mathematical but well-educated readers is not entirely a new thing.
Kasner and Newman's
*Mathematics and the Imagination*, first published in 1940, was a great success. (And was an inspiration to me
in my teen years.) There are
certainly more pop-math books around today than there have ever been, though. In part I think that this is a
consequence of the spread of personal
computers. Not that there is much of a direct connection between using a computer and doing math; but widespread
acquaintance with, for example,
spreadsheet programs, has helped break down the wall of anxiety that left a lot of people repelled by anything to do
with math. The rise of
experimental math, and the availability of picturesque pop-math artifacts like the Mandelbrot set, are also part of
this phenomenon.

There is also, I think, a deeper issue, to do with the yearning for certainty in a society of relativistic morality, declining religious faith, economic insecurity and fast-changing technology. College-educated people of all disciplines have internalized Aristotle's observation that only mathematical knowledge is certain, all other kinds being merely probable. (Whether this is true or not is beside the point; I am only saying that most educated Americans are nowadays acquainted with the notion.) Thoughtful people would like to know more about this realm of absolute certainty, as in the world around them they see standards blurring, old verities questioned, new job classifications coming up as long-established old ones fall into oblivion. It is possible that the public appetite for math books is related in some distant sense to the forces that, in less happy lands, drive intelligent young people into religious fundamentalism.

I cherish the private fancy that in the particular case of *Prime Obsession*, part of the reason for the
book's success has been
Bernhard Riemann himself. Every book worth reading cloaks a human personality, if only the author's. I was drawn to
my topic at first by the
personality of Riemann, by the curious contrast between his outer and inner lives: between the shy, timid, sickly,
unsocial, poverty-stricken body,
and the blazing fire of imaginative genius within. I had all that in mind from the beginning; I dedicated my book, in
my prologue, to Riemann's
memory; and I like to think that if he is anywhere right now, he is smiling down fondly on my brief, hurried
efforts.