At the beginning of this century, David Hilbert (1862–1943), a world-leading mathematician and logician, posed 23 classes of enormously difficult technical problems that were intended to set the logico-mathematical tone of the 20th century. He succeeded. Indeed, his so-called Tenth Problem, on the existence of an algorithm to solve an arbitrary Diophantine problem, was settled negatively only about 25 years ago. Such Diophantine problems have close connections to integer programming problems, which, in turn, are neatly linked to scheduling problems of mathematical programming. Hilbert’s name is rightly joined to numerous formal ideas, such as Hilbert space (certain linear vector spaces with many uses in quantum mechanics, among other places), Hilbert transform, and Hilbert axiom. He was the world champion of axiomatics and their uses in the sciences, in spite of the serious limitations of axiomatics shown later by Gödel and many others. Amazingly, Gödel never met nor even corresponded with Hilbert.

This valuable book spans the many activities of a complex human being deeply devoted to the world of logic and mathematics. Even at the beginning of the 20th century, he had no hesitation in supporting capable women, but he believed there were only two kinds of mathematicians--those who worked on and solved deep programs and those who did not. Among the many topics discussed in this fine book are youth, friends, problems, the scientific life, war, the infinite, and logic. Overall, the book is superb. It contains nearly 30 interesting photographs concerning Hilbert. My only (minor) complaint is that the map given in the book, surely of “old” Königsberg, is left unlabeled.

Hilbert was able to predict the course of 20th-century mathematics far more accurately than any politician was able to predict the war and terror unleashed in the 20th century. His optimism is summarized in the couplet of his epitaph: “Wir müssen wissen. Wir werden wissen.” (“We must know. We will know.”)