intensive investigation by some of the best minds on our planet for a hundred years. In the space available to me, and by the methods of exposition I have decided on, it has proved necessary to omit entire large regions of inquiry relevant to the Riemann Hypothesis. You will find not one word here about the Density Hypothesis, the approximate functional equation, or the whole fascinating issue—just recently come to life after long dormancy—of the moments of the zeta function. Nor is there any mention of the Generalized Riemann Hypothesis, the Modified Generalized Riemann Hypothesis, the Extended Riemann Hypothesis, the Grand Riemann Hypothesis, the Modified Grand Riemann Hypothesis, or the Quasi-Riemann Hypothesis.

Even more distressing, there are many workers who have toiled away valiantly in these vineyards for decades, but whose names are absent from my text: Enrico Bombieri, Amit Ghosh, Steve Gonek, Henryk Iwaniec (half of whose mail comes to him addressed as “Henry K. Iwaniec”), Nina Snaith, and many others. My sincere apologies. I did not realize, when starting out, what a vast subject I was taking on. This book could easily have been three times, or thirty times, longer, but my editor was already reaching for his chainsaw.

And one more acknowledgment. I hold the superstitious belief that any book above the level of hired drudge work—any book written with care and affection—has a presiding spirit. By that, I only mean to say that a book is about some one particular human being, who is in the author’s mind while he works, and whose personality colors the book. (In the case of fiction, I am afraid that all too often that human being is the author himself.)

The presiding spirit of this book, who seemed often to be glancing over my shoulder as I wrote, whom I sometimes imagined I heard clearing his throat shyly in an adjoining room, or moving around discreetly behind the scenes in both my mathematical and historical chapters, has been Bernhard Riemann. Reading him, and reading about him, I developed an odd mixture of feelings for the man: great sympathy for his social awkwardness, wretched health, repeated be-