On the Background to Hilbert’s Paris Lecture “Mathematical Problems”

Much has been written about the famous lecture on “Mathematical Problems” (Hilbert 1901) that David Hilbert delivered at the Second International Congress of Mathematicians, which took place in Paris during the summer of 1900 (Alexandrov 1979; Browder 1976). Not that the event itself evoked such great interest, nor have many writers paid particularly close attention to what Hilbert had to say on that occasion. What mattered – both for the text and the larger context – came afterward. Mathematicians remember ICM II and Hilbert’s role in it for just one reason: this was the occasion when he unveiled a famous list of 23 problems, a challenge to those who wished to make names for themselves in the coming century (Gray 2000). These “Hilbert Problems” and “their solvers” have long served as a central theme around which numerous stories have been written (Yandell 2002; Rowe 2004a). They have also served as a convenient peg for describing important mathematical developments of the twentieth century (Struik 1987). Yet relatively little has been written about the events that led up to Hilbert’s lecture or the larger themes he set forth in the main body of his text. With this in mind, the present essay aims to address these less familiar parts of the story by sketching some of the relevant historical and mathematical background.