Mathematische Probleme

Edition

Excerpt of the lecture as printed in the Nachrichten von der Königl. Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-physikalische Klasse, 1900, Heft 3, pp. 253-297. The text comes from the proofread transcription of German Wikisource (raw wikitext of the pages Seite:Hilbert_-_Mathematische_Probleme.pdf/2 to /46), compared word by word with the OCR of the Göttinger Digitalisierungszentrum (PPN252457811_1900), every difference and every formula being settled on the scan of that printing (Wikimedia Commons, File:Hilbert - Mathematische Probleme.pdf, from the GDZ). Kept, verbatim: the title block (in the header); the first six paragraphs of the lecture (pp. 253-254, “Wer von uns” to “gelungene Lösung”); the three paragraphs “Diese merkwürdige Thatsache” to “kein Ignorabimus!” (pp. 261-262); the two that open the problems, “Unermeßlich ist” and “Ueberblicken wir” (p. 262); the numbered heading of each of the 23 problems, with these paragraphs: 1, all five; 2, “Wenn es sich darum handelt” and “Vor Allem aber”; 3, its paragraph; 4, “Eine andere Problemstellung” and “In der Minkowskischen Geometrie”; 5, “Lie hat bekanntlich” and “Auch für unendliche Gruppen”; 6, “Durch die Untersuchungen”; 7, its paragraph; 8, “In der Theorie der Verteilung”, “Nach einer erschöpfenden Diskussion” and “Aber von nicht geringerem Interesse”; 9 and 10, their paragraph; 11, “Unsere jetzige Kenntnis”; 12, “Von Kronecker rührt”, “erstens”, “zweitens”, “Von der höchsten Bedeutung” and “Wie wir sehen”; 13, “Wahrscheinlich ist nun” to the end; 14, “Es seien eine Anzahl” to “zahlentheoretisch zu verfeinern”; 15, its paragraph; 16, both paragraphs; 17, “Definit heißt”; 18, “Genau die entsprechenden Thatsachen” and “Ein Fundamentalbereich”; 19, “Eine der begrifflich merkwürdigsten Thatsachen”; 20 and 21, their paragraph; 22, “Wie Poincaré zuerst”; 23, “Bisher habe ich” and “Die Variationsrechnung im weitesten Sinne”; and the last three paragraphs of the lecture (pp. 296-297). Every cut is marked […]; the rules between groups of problems fall within the cuts. Hilbert’s footnotes of the kept text are numbered 1 to 26 and listed at the end (the print numbers them page by page); the notes of Wikisource are left out. Differences from Wikisource, all back to the print: the long dashes of the print (em dashes, U+2014), which Wikisource sets as en dashes (U+2013); no comma in “Durch die Lösung von” (p. 254), “ursprünglich verlangten” (p. 262), “ein frühestes Element hat” (p. 264), “nicht mit Hülfe” (p. 281); “Nicht-Euklidischen” (p. 262); “v.” of v. Mangoldt not letterspaced (p. 274) and “Schwarz” letterspaced (p. 289); problem 14 as printed, “X1, X2, ..., Xm der n Variabeln x1, x2, ..., xn vorgelegt:”, then “X1, ..., Xm” and “x1, ..., xn”, “x1, ... xn wird”, the system (S) with its row of dots and final period; the series of ζ(s) ending in centred dots; in the notes, “Bd. 32” (p. 284, Wikisource “82”), “Berichte” (p. 276), “Napoli 1880.” (p. 285), “Vgl.” and a final period in note 1 of p. 286, whose range “2 to 3” is set with an em dash. Normalizations: the umlauts that the print drops are restored, as Wikisource does, in headings 3 (“Grundflache und Hohe”), 9 (“Reciprocitatsgesetzes”), 15 (“Abzählungskalkul”) and 23 (“Weiterfuhrung”) and in the notes (“Naturkrafte”, “Funfter”, “fur”, “uber”), and the turned letter of “zu Gruude” (p. 278) is set “Grunde”; the misspellings “Richtigtigkeit” (p. 275), “Kronekerschen” (heading 12), “Tetraeter” (p. 286) and “Differenziirbarkeit” (p. 289) are kept; words hyphenated at line ends are rejoined; running heads, page numbers and sheet signatures are dropped. Letterspaced words are letterspaced. The formulas are set with KaTeX.

Rights

David Hilbert died on 14 February 1943 (Wikidata Q41585) and the lecture was published in 1900: it is in the public domain in France, where the author died before 1 January 1956, and in the United States, where it was published before 1 January 1931. Wikimedia Commons marks the scan as public domain (PD-old).

The Wikisource transcription reproduces the public domain text; its own notes are left out.