In 1900, at a time when his international prominence as a leading mathematician was just becoming firmly established, David Hilbert (1862–1943) delivered one of the central invited lectures at the Second International Congress of Mathematicians, held in Paris. The lecture bore the title “Mathematical Problems”. At this very significant opportunity, Hilbert attempted to “lift the veil” and peer into the development of mathematics in the century that was about to begin. He chose to present a list of twenty-three problems that in his opinion would and should occupy the efforts of mathematicians in the years to come. This famous list has been an object of mathematical and historical interest ever since. Mathematicians of all specialties and in all countries have taken up its challenges. Solving an item from the list came to be considered a significant achievement that could determine the fate of the academic career of any aspiring mathematician.
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- 1.Hilbert 1930 (“We must know. We will know.”)Google Scholar
- 2.This issue is discussed in greater detail below in § 2.3.2.Google Scholar
- 3.Cf. Wightman 1976, Gnedenko 1979.Google Scholar
- 4.Yandell 2002, 159.Google Scholar
- 5.A similar conclusion is implied in Cercignani 1998, 223.Google Scholar
- 6.Reid 1970.Google Scholar
- 7.Blumenthal 1922.Google Scholar
- 8.Weyl 1944, 619.Google Scholar
- 9.See Born 1978, 81–85, for retrospective account of his experience as Hilbert’s studentGoogle Scholar
- 10.Dieudonné 1962, 551 (italics in the original). This topic is discussed in greater detail in Corry 1997.Google Scholar
- 11.Reid 1970, 127. No first-hand quotation of this claim, however, seems to exist. One possible, contemporary hearsay testimony appears in a letter of Max Abraham to Tullio Levi-Civita, dated August 1, 1917, and quoted in Cattani & De Maria 1989a, 172.Google Scholar
- 12.Hilbert 1916–17, 2–3. Cf. also below Ch. 8, note 72.Google Scholar