Abstract
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.
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Notes
- 1.
A complete list of the lectures delivered between 1843 and 1890 can be found in Tobies and Volkert (1998, 227–248).
- 2.
Klein’s list of 13 December, 1894 can be found in the Personalakten Hilbert, Universitätsarchiv Göttingen.
- 3.
- 4.
For an interesting discussion of how Klein and Hilbert put new twists on the term “arithmetization,” see Petri and Schappacher (2007, 362–366).
- 5.
The information that follows is based on the report in Jahresbericht der Deutschen Mathematiker-Vereinigung, 8(1900): 3–5.
- 6.
The ICMs offered a large-scale stage for such jousting. At the 1908 ICM in Rome, Poincaré presented his own views on the future of mathematics, about which see Gray (2012).
- 7.
He even mentioned two earlier lectures that he thought might prove useful for Hilbert to read, one a speech delivered by Hermite in 1890, another by H. J. S. Smith entitled, “On the Present State and Prospects of some Branches of Pure Mathematics.”
- 8.
His private notes, however, make clear that he also saw this as a major unsolved meta-problem, about which see Thiele (2003).
- 9.
Jahresbericht der Deutschen Mathematiker-Vereinigung, 9 (1901), S. 3.
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Rowe, D.E. (2018). On the Background to Hilbert’s Paris Lecture “Mathematical Problems”. In: A Richer Picture of Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-67819-1_15
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