By the end of his career, David Hilbert was the best known mathematician in the world, as well as the most influential. His contributions did not merely affect but decisively altered the directions taken in many fields. In some ways, however, his career ended in disappointment; he had inherited one of the great mathematical centers for research and teaching, but from his retirement he had to watch its glory disappear under the ideological onslaught from the Nazi government. Nevertheless, the heritage of the contributions he made to mathematics, as well as the students he trained, has outlasted the disruptions of World War II.

Hilbert was born in Wehlau, near Königsberg, on January 23, 1862. His family was staunchly Protestant, although Hilbert himself was later to leave the church in which he was baptized. Otto Hilbert, his father, was a lawyer of social standing in the society around K...