Hilbert's twenty-fourth problem

American Mathematical Monthly

Volumn 110, Issue 1, 2003, Pages 1-24

  Thiele, Rüdiger ^a  

^a UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

[No Author keywords available]

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EID: 0037247846     PISSN: 00029890     EISSN: None     Source Type: Journal    
DOI: 10.2307/3072340     Document Type: Article

References (154)

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29. _, Über formal unentscheidbare Sätze der Principia Mathematica und verwandte Systeme I, Monatshefte für Mathematik und Physik 38 (1) (1931) 173-198; English translation, On formally undecidable propositions of Principia Mathematica and related systems, I, in The Undecidable, M. Davis, ed., Raven Press, Hewlett, NY, 1965, pp. 5-38; further English edition by R. B. Braithwaite, Dover, New York, 1992; with English translation in Collected Works, S. Feferman et al., eds., vol. 1, Oxford University Press, 1986, pp. 144-195.
30. _, Über formal unentscheidbare Sätze der Principia Mathematica und verwandte Systeme I, Monatshefte für Mathematik und Physik 38 (1) (1931) 173-198; English translation, On formally undecidable propositions of Principia Mathematica and related systems, I, in The Undecidable, M. Davis, ed., Raven Press, Hewlett, NY, 1965, pp. 5-38; further English edition by R. B. Braithwaite, Dover, New York, 1992; with English translation in Collected Works, S. Feferman et al., eds., vol. 1, Oxford University Press, 1986, pp. 144-195.
31. _, Über formal unentscheidbare Sätze der Principia Mathematica und verwandte Systeme I, Monatshefte für Mathematik und Physik 38 (1) (1931) 173-198; English translation, On formally undecidable propositions of Principia Mathematica and related systems, I, in The Undecidable, M. Davis, ed., Raven Press, Hewlett, NY, 1965, pp. 5-38; further English edition by R. B. Braithwaite, Dover, New York, 1992; with English translation in Collected Works, S. Feferman et al., eds., vol. 1, Oxford University Press, 1986, pp. 144-195.
32. _, Über die Länge von Beweisen, Erg. Math. Koll. 7 (1934) 23-24.
33. _, Letters to Constance Reid from March 22, 1966, and June 25, 1969; letters in the possession of Mrs. Reid, not yet included in Gödel's Collected Works, S. Feferman et al., eds., but partly quoted in Reid [87]. I quote with the kind permission of the Institute for Advanced Study, Princeton, NJ.
34. _, Letter to Ernst Zermelo from October 12, 1931, University of Freiburg i.Br., Universitätsarchiv, C 129/36.
35. I. Grattan-Guinness, A sideways look at Hilbert's twenty-three problems of 1900, Notices Amer. Math. Soc. 47 (2000) 752-757; corrections by G. H. Moore and response of Grattan-Guinness in Letters to the Editor, Notices 48 (2001) 167.
36. J. Gray, The Hubert Challenge, Oxford University Press, Oxford, 2000.
37. P. A. Griffith, Mathematics at the turn of the millennium, this MONTHLY 107 (2000) 1-14.
38. H. Hahn et al., Diskussion zur Grundlegung der Mathematik am Sonntag, dem 7. Sept. 1930 [Discussion on the second Meeting Erkenntnislehre in Königsberg, September 5-7, 1930], Erkenntnis 2 (1930) 135-149. Note both the Vorbemerkung of the editors on the page before the content and Gödel's supplement [25].
39. G. B. Halsted, The International Congress of Mathematicians, this MONTHLY 7 (1900) 188-189.
40. G. H. Hardy, A Mathematician's Apology, Cambridge University Press, Cambridge, 1940; reprinted with a foreword by C. P. Snow, 1967. (I quote the enlarged 1967 edition.)
41. A. Heyting, Mathematische Grundlagenforschung. Intuitionismus. Beweistheorie, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 3, Heft 4, Springer-Verlag, Berlin, 1934.
42. D. Hilbert, Mathematische Probleme, lecture held at the Paris ICM 1900, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen (1900) 253-297; revised version in Archiv der Mathematik und Physik 1 (1901) 44-63, 213-237, and [58:3, pp. 290-329]; English translation (by M. W. Newson) in Bull. Amer. Math. Soc. 8 (1901) 437-479; reprinted in the Bulletin 37 (2000) 407-436; also in Browder [8:1, pp. 1-34], Yandell [115, pp. 324-3891, and Gray [31, pp. 240-282], selected parts in Ewald [17:2, pp. [096-1105] and Reid [87, chap. 9]; French translations by L. Laugel (with corrections and additions) in Compte rendu du deuxième congrès international des mathématiciens tenu à Paris du 6 au 12 août 1900, E. Duporcq, ed., Gauthier-Villars, Paris, 1902, pp. 58-114; (fragments) L'Enseignement Mathématique 2 (1900) 349-354 and Revue Générale des Sciences Pures et Appliquées 12 (1901) 168-174; annotated Russian edition, Problemy Gilberta, P. S. Alexandrov, ed., Nauka, Moscow, 1969; its German edition Die Hilbertschen Probleme, Akademische Verlagsgesellschaft, Leipzig, 1976, 2nd ed. 1979, reprint 1998 (both the Russian and German editions give the revised version of [58:3]). (I quote Newson's translation.)
43. D. Hilbert, Mathematische Probleme, lecture held at the Paris ICM 1900, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen (1900) 253-297; revised version in Archiv der Mathematik und Physik 1 (1901) 44-63, 213-237, and [58:3, pp. 290-329]; English translation (by M. W. Newson) in Bull. Amer. Math. Soc. 8 (1901) 437-479; reprinted in the Bulletin 37 (2000) 407-436; also in Browder [8:1, pp. 1-34], Yandell [115, pp. 324-3891, and Gray [31, pp. 240-282], selected parts in Ewald [17:2, pp. [096-1105] and Reid [87, chap. 9]; French translations by L. Laugel (with corrections and additions) in Compte rendu du deuxième congrès international des mathématiciens tenu à Paris du 6 au 12 août 1900, E. Duporcq, ed., Gauthier-Villars, Paris, 1902, pp. 58-114; (fragments) L'Enseignement Mathématique 2 (1900) 349-354 and Revue Générale des Sciences Pures et Appliquées 12 (1901) 168-174; annotated Russian edition, Problemy Gilberta, P. S. Alexandrov, ed., Nauka, Moscow, 1969; its German edition Die Hilbertschen Probleme, Akademische Verlagsgesellschaft, Leipzig, 1976, 2nd ed. 1979, reprint 1998 (both the Russian and German editions give the revised version of [58:3]). (I quote Newson's translation.)
44. D. Hilbert, Mathematische Probleme, lecture held at the Paris ICM 1900, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen (1900) 253-297; revised version in Archiv der Mathematik und Physik 1 (1901) 44-63, 213-237, and [58:3, pp. 290-329]; English translation (by M. W. Newson) in Bull. Amer. Math. Soc. 8 (1901) 437-479; reprinted in the Bulletin 37 (2000) 407-436; also in Browder [8:1, pp. 1-34], Yandell [115, pp. 324-3891, and Gray [31, pp. 240-282], selected parts in Ewald [17:2, pp. [096-1105] and Reid [87, chap. 9]; French translations by L. Laugel (with corrections and additions) in Compte rendu du deuxième congrès international des mathématiciens tenu à Paris du 6 au 12 août 1900, E. Duporcq, ed., Gauthier-Villars, Paris, 1902, pp. 58-114; (fragments) L'Enseignement Mathématique 2 (1900) 349-354 and Revue Générale des Sciences Pures et Appliquées 12 (1901) 168-174; annotated Russian edition, Problemy Gilberta, P. S. Alexandrov, ed., Nauka, Moscow, 1969; its German edition Die Hilbertschen Probleme, Akademische Verlagsgesellschaft, Leipzig, 1976, 2nd ed. 1979, reprint 1998 (both the Russian and German editions give the revised version of [58:3]). (I quote Newson's translation.)
45. D. Hilbert, Mathematische Probleme, lecture held at the Paris ICM 1900, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen (1900) 253-297; revised version in Archiv der Mathematik und Physik 1 (1901) 44-63, 213-237, and [58:3, pp. 290-329]; English translation (by M. W. Newson) in Bull. Amer. Math. Soc. 8 (1901) 437-479; reprinted in the Bulletin 37 (2000) 407-436; also in Browder [8:1, pp. 1-34], Yandell [115, pp. 324-3891, and Gray [31, pp. 240-282], selected parts in Ewald [17:2, pp. [096-1105] and Reid [87, chap. 9]; French translations by L. Laugel (with corrections and additions) in Compte rendu du deuxième congrès international des mathématiciens tenu à Paris du 6 au 12 août 1900, E. Duporcq, ed., Gauthier-Villars, Paris, 1902, pp. 58-114; (fragments) L'Enseignement Mathématique 2 (1900) 349-354 and Revue Générale des Sciences Pures et Appliquées 12 (1901) 168-174; annotated Russian edition, Problemy Gilberta, P. S. Alexandrov, ed., Nauka, Moscow, 1969; its German edition Die Hilbertschen Probleme, Akademische Verlagsgesellschaft, Leipzig, 1976, 2nd ed. 1979, reprint 1998 (both the Russian and German editions give the revised version of [58:3]). (I quote Newson's translation.)
46. D. Hilbert, Mathematische Probleme, lecture held at the Paris ICM 1900, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen (1900) 253-297; revised version in Archiv der Mathematik und Physik 1 (1901) 44-63, 213-237, and [58:3, pp. 290-329]; English translation (by M. W. Newson) in Bull. Amer. Math. Soc. 8 (1901) 437-479; reprinted in the Bulletin 37 (2000) 407-436; also in Browder [8:1, pp. 1-34], Yandell [115, pp. 324-3891, and Gray [31, pp. 240-282], selected parts in Ewald [17:2, pp. [096-1105] and Reid [87, chap. 9]; French translations by L. Laugel (with corrections and additions) in Compte rendu du deuxième congrès international des mathématiciens tenu à Paris du 6 au 12 août 1900, E. Duporcq, ed., Gauthier-Villars, Paris, 1902, pp. 58-114; (fragments) L'Enseignement Mathématique 2 (1900) 349-354 and Revue Générale des Sciences Pures et Appliquées 12 (1901) 168-174; annotated Russian edition, Problemy Gilberta, P. S. Alexandrov, ed., Nauka, Moscow, 1969; its German edition Die Hilbertschen Probleme, Akademische Verlagsgesellschaft, Leipzig, 1976, 2nd ed. 1979, reprint 1998 (both the Russian and German editions give the revised version of [58:3]). (I quote Newson's translation.)
47. D. Hilbert, Mathematische Probleme, lecture held at the Paris ICM 1900, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen (1900) 253-297; revised version in Archiv der Mathematik und Physik 1 (1901) 44-63, 213-237, and [58:3, pp. 290-329]; English translation (by M. W. Newson) in Bull. Amer. Math. Soc. 8 (1901) 437-479; reprinted in the Bulletin 37 (2000) 407-436; also in Browder [8:1, pp. 1-34], Yandell [115, pp. 324-3891, and Gray [31, pp. 240-282], selected parts in Ewald [17:2, pp. [096-1105] and Reid [87, chap. 9]; French translations by L. Laugel (with corrections and additions) in Compte rendu du deuxième congrès international des mathématiciens tenu à Paris du 6 au 12 août 1900, E. Duporcq, ed., Gauthier-Villars, Paris, 1902, pp. 58-114; (fragments) L'Enseignement Mathématique 2 (1900) 349-354 and Revue Générale des Sciences Pures et Appliquées 12 (1901) 168-174; annotated Russian edition, Problemy Gilberta, P. S. Alexandrov, ed., Nauka, Moscow, 1969; its German edition Die Hilbertschen Probleme, Akademische Verlagsgesellschaft, Leipzig, 1976, 2nd ed. 1979, reprint 1998 (both the Russian and German editions give the revised version of [58:3]). (I quote Newson's translation.)
48. D. Hilbert, Mathematische Probleme, lecture held at the Paris ICM 1900, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen (1900) 253-297; revised version in Archiv der Mathematik und Physik 1 (1901) 44-63, 213-237, and [58:3, pp. 290-329]; English translation (by M. W. Newson) in Bull. Amer. Math. Soc. 8 (1901) 437-479; reprinted in the Bulletin 37 (2000) 407-436; also in Browder [8:1, pp. 1-34], Yandell [115, pp. 324-3891, and Gray [31, pp. 240-282], selected parts in Ewald [17:2, pp. [096-1105] and Reid [87, chap. 9]; French translations by L. Laugel (with corrections and additions) in Compte rendu du deuxième congrès international des mathématiciens tenu à Paris du 6 au 12 août 1900, E. Duporcq, ed., Gauthier-Villars, Paris, 1902, pp. 58-114; (fragments) L'Enseignement Mathématique 2 (1900) 349-354 and Revue Générale des Sciences Pures et Appliquées 12 (1901) 168-174; annotated Russian edition, Problemy Gilberta, P. S. Alexandrov, ed., Nauka, Moscow, 1969; its German edition Die Hilbertschen Probleme, Akademische Verlagsgesellschaft, Leipzig, 1976, 2nd ed. 1979, reprint 1998 (both the Russian and German editions give the revised version of [58:3]). (I quote Newson's translation.)
49. D. Hilbert, Mathematische Probleme, lecture held at the Paris ICM 1900, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen (1900) 253-297; revised version in Archiv der Mathematik und Physik 1 (1901) 44-63, 213-237, and [58:3, pp. 290-329]; English translation (by M. W. Newson) in Bull. Amer. Math. Soc. 8 (1901) 437-479; reprinted in the Bulletin 37 (2000) 407-436; also in Browder [8:1, pp. 1-34], Yandell [115, pp. 324-3891, and Gray [31, pp. 240-282], selected parts in Ewald [17:2, pp. [096-1105] and Reid [87, chap. 9]; French translations by L. Laugel (with corrections and additions) in Compte rendu du deuxième congrès international des mathématiciens tenu à Paris du 6 au 12 août 1900, E. Duporcq, ed., Gauthier-Villars, Paris, 1902, pp. 58-114; (fragments) L'Enseignement Mathématique 2 (1900) 349-354 and Revue Générale des Sciences Pures et Appliquées 12 (1901) 168-174; annotated Russian edition, Problemy Gilberta, P. S. Alexandrov, ed., Nauka, Moscow, 1969; its German edition Die Hilbertschen Probleme, Akademische Verlagsgesellschaft, Leipzig, 1976, 2nd ed. 1979, reprint 1998 (both the Russian and German editions give the revised version of [58:3]). (I quote Newson's translation.)
50. D. Hilbert, Mathematische Probleme, lecture held at the Paris ICM 1900, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen (1900) 253-297; revised version in Archiv der Mathematik und Physik 1 (1901) 44-63, 213-237, and [58:3, pp. 290-329]; English translation (by M. W. Newson) in Bull. Amer. Math. Soc. 8 (1901) 437-479; reprinted in the Bulletin 37 (2000) 407-436; also in Browder [8:1, pp. 1-34], Yandell [115, pp. 324-3891, and Gray [31, pp. 240-282], selected parts in Ewald [17:2, pp. [096-1105] and Reid [87, chap. 9]; French translations by L. Laugel (with corrections and additions) in Compte rendu du deuxième congrès international des mathématiciens tenu à Paris du 6 au 12 août 1900, E. Duporcq, ed., Gauthier-Villars, Paris, 1902, pp. 58-114; (fragments) L'Enseignement Mathématique 2 (1900) 349-354 and Revue Générale des Sciences Pures et Appliquées 12 (1901) 168-174; annotated Russian edition, Problemy Gilberta, P. S. Alexandrov, ed., Nauka, Moscow, 1969; its German edition Die Hilbertschen Probleme, Akademische Verlagsgesellschaft, Leipzig, 1976, 2nd ed. 1979, reprint 1998 (both the Russian and German editions give the revised version of [58:3]). (I quote Newson's translation.)
51. D. Hilbert, Mathematische Probleme, lecture held at the Paris ICM 1900, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen (1900) 253-297; revised version in Archiv der Mathematik und Physik 1 (1901) 44-63, 213-237, and [58:3, pp. 290-329]; English translation (by M. W. Newson) in Bull. Amer. Math. Soc. 8 (1901) 437-479; reprinted in the Bulletin 37 (2000) 407-436; also in Browder [8:1, pp. 1-34], Yandell [115, pp. 324-3891, and Gray [31, pp. 240-282], selected parts in Ewald [17:2, pp. [096-1105] and Reid [87, chap. 9]; French translations by L. Laugel (with corrections and additions) in Compte rendu du deuxième congrès international des mathématiciens tenu à Paris du 6 au 12 août 1900, E. Duporcq, ed., Gauthier-Villars, Paris, 1902, pp. 58-114; (fragments) L'Enseignement Mathématique 2 (1900) 349-354 and Revue Générale des Sciences Pures et Appliquées 12 (1901) 168-174; annotated Russian edition, Problemy Gilberta, P. S. Alexandrov, ed., Nauka, Moscow, 1969; its German edition Die Hilbertschen Probleme, Akademische Verlagsgesellschaft, Leipzig, 1976, 2nd ed. 1979, reprint 1998 (both the Russian and German editions give the revised version of [58:3]). (I quote Newson's translation.)
52. D. Hilbert, Mathematische Probleme, lecture held at the Paris ICM 1900, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen (1900) 253-297; revised version in Archiv der Mathematik und Physik 1 (1901) 44-63, 213-237, and [58:3, pp. 290-329]; English translation (by M. W. Newson) in Bull. Amer. Math. Soc. 8 (1901) 437-479; reprinted in the Bulletin 37 (2000) 407-436; also in Browder [8:1, pp. 1-34], Yandell [115, pp. 324-3891, and Gray [31, pp. 240-282], selected parts in Ewald [17:2, pp. [096-1105] and Reid [87, chap. 9]; French translations by L. Laugel (with corrections and additions) in Compte rendu du deuxième congrès international des mathématiciens tenu à Paris du 6 au 12 août 1900, E. Duporcq, ed., Gauthier-Villars, Paris, 1902, pp. 58-114; (fragments) L'Enseignement Mathématique 2 (1900) 349-354 and Revue Générale des Sciences Pures et Appliquées 12 (1901) 168-174; annotated Russian edition, Problemy Gilberta, P. S. Alexandrov, ed., Nauka, Moscow, 1969; its German edition Die Hilbertschen Probleme, Akademische Verlagsgesellschaft, Leipzig, 1976, 2nd ed. 1979, reprint 1998 (both the Russian and German editions give the revised version of [58:3]). (I quote Newson's translation.)
53. D. Hilbert, Mathematische Probleme, lecture held at the Paris ICM 1900, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen (1900) 253-297; revised version in Archiv der Mathematik und Physik 1 (1901) 44-63, 213-237, and [58:3, pp. 290-329]; English translation (by M. W. Newson) in Bull. Amer. Math. Soc. 8 (1901) 437-479; reprinted in the Bulletin 37 (2000) 407-436; also in Browder [8:1, pp. 1-34], Yandell [115, pp. 324-3891, and Gray [31, pp. 240-282], selected parts in Ewald [17:2, pp. [096-1105] and Reid [87, chap. 9]; French translations by L. Laugel (with corrections and additions) in Compte rendu du deuxième congrès international des mathématiciens tenu à Paris du 6 au 12 août 1900, E. Duporcq, ed., Gauthier-Villars, Paris, 1902, pp. 58-114; (fragments) L'Enseignement Mathématique 2 (1900) 349-354 and Revue Générale des Sciences Pures et Appliquées 12 (1901) 168-174; annotated Russian edition, Problemy Gilberta, P. S. Alexandrov, ed., Nauka, Moscow, 1969; its German edition Die Hilbertschen Probleme, Akademische Verlagsgesellschaft, Leipzig, 1976, 2nd ed. 1979, reprint 1998 (both the Russian and German editions give the revised version of [58:3]). (I quote Newson's translation.)
54. D. Hilbert, Mathematische Probleme, lecture held at the Paris ICM 1900, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen (1900) 253-297; revised version in Archiv der Mathematik und Physik 1 (1901) 44-63, 213-237, and [58:3, pp. 290-329]; English translation (by M. W. Newson) in Bull. Amer. Math. Soc. 8 (1901) 437-479; reprinted in the Bulletin 37 (2000) 407-436; also in Browder [8:1, pp. 1-34], Yandell [115, pp. 324-3891, and Gray [31, pp. 240-282], selected parts in Ewald [17:2, pp. [096-1105] and Reid [87, chap. 9]; French translations by L. Laugel (with corrections and additions) in Compte rendu du deuxième congrès international des mathématiciens tenu à Paris du 6 au 12 août 1900, E. Duporcq, ed., Gauthier-Villars, Paris, 1902, pp. 58-114; (fragments) L'Enseignement Mathématique 2 (1900) 349-354 and Revue Générale des Sciences Pures et Appliquées 12 (1901) 168-174; annotated Russian edition, Problemy Gilberta, P. S. Alexandrov, ed., Nauka, Moscow, 1969; its German edition Die Hilbertschen Probleme, Akademische Verlagsgesellschaft, Leipzig, 1976, 2nd ed. 1979, reprint 1998 (both the Russian and German editions give the revised version of [58:3]). (I quote Newson's translation.)
55. D. Hilbert, Mathematische Probleme, lecture held at the Paris ICM 1900, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen (1900) 253-297; revised version in Archiv der Mathematik und Physik 1 (1901) 44-63, 213-237, and [58:3, pp. 290-329]; English translation (by M. W. Newson) in Bull. Amer. Math. Soc. 8 (1901) 437-479; reprinted in the Bulletin 37 (2000) 407-436; also in Browder [8:1, pp. 1-34], Yandell [115, pp. 324-3891, and Gray [31, pp. 240-282], selected parts in Ewald [17:2, pp. [096-1105] and Reid [87, chap. 9]; French translations by L. Laugel (with corrections and additions) in Compte rendu du deuxième congrès international des mathématiciens tenu à Paris du 6 au 12 août 1900, E. Duporcq, ed., Gauthier-Villars, Paris, 1902, pp. 58-114; (fragments) L'Enseignement Mathématique 2 (1900) 349-354 and Revue Générale des Sciences Pures et Appliquées 12 (1901) 168-174; annotated Russian edition, Problemy Gilberta, P. S. Alexandrov, ed., Nauka, Moscow, 1969; its German edition Die Hilbertschen Probleme, Akademische Verlagsgesellschaft, Leipzig, 1976, 2nd ed. 1979, reprint 1998 (both the Russian and German editions give the revised version of [58:3]). (I quote Newson's translation.)
56. D. Hilbert, Mathematische Probleme, lecture held at the Paris ICM 1900, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen (1900) 253-297; revised version in Archiv der Mathematik und Physik 1 (1901) 44-63, 213-237, and [58:3, pp. 290-329]; English translation (by M. W. Newson) in Bull. Amer. Math. Soc. 8 (1901) 437-479; reprinted in the Bulletin 37 (2000) 407-436; also in Browder [8:1, pp. 1-34], Yandell [115, pp. 324-3891, and Gray [31, pp. 240-282], selected parts in Ewald [17:2, pp. [096-1105] and Reid [87, chap. 9]; French translations by L. Laugel (with corrections and additions) in Compte rendu du deuxième congrès international des mathématiciens tenu à Paris du 6 au 12 août 1900, E. Duporcq, ed., Gauthier-Villars, Paris, 1902, pp. 58-114; (fragments) L'Enseignement Mathématique 2 (1900) 349-354 and Revue Générale des Sciences Pures et Appliquées 12 (1901) 168-174; annotated Russian edition, Problemy Gilberta, P. S. Alexandrov, ed., Nauka, Moscow, 1969; its German edition Die Hilbertschen Probleme, Akademische Verlagsgesellschaft, Leipzig, 1976, 2nd ed. 1979, reprint 1998 (both the Russian and German editions give the revised version of [58:3]). (I quote Newson's translation.)
57. _, Mathematische Notizbücher, 3 notebooks, Niedersächsische Staats- und Universitätsbibliothek Göttingen, Handschriftenabteilung, Cod. Ms. D. Hilbert 600:1-3.
58. _, Invariantentheorie, lecture notes from Winter 1886 by Hilbert, Niedersächsische Staats- und Universitätsbibliothek Göttingen, Handschriftenabteilung, Cod. Ms. D. Hilbert 521.
59. _, Über die Theorie der algebraischen Invarianten, submitted to the International Mathematical Congress in Chicago 1893, in Mathematical Papers Published by the American Mathematical Society, vol. 1, E. H. Moore et al., eds., Macmillan, New York, 1896, pp. 116-124.
60. _, Gewöhnliche Differentialgleichungen, lecture notes from Summer 1896, Niedersächsische Staats- und Universitätsbibliothek Göttingen, Handschriftenabteilung, Cod. Ms. D. Hilbert 546.
61. _, Theorie der algebraischen Invarianten nebst Anwendungen auf Geometrie, lecture notes from Summer 1897 prepared by Sophus Marxsen, Library of the Mathematical Institute of the University of Göttingen; English translation Theory of Algebraic Invariants, R. C. Laubenbacher and B. Sturmfels, eds. [using a different copy from the Mathematics Library of Cornell University], Cambridge University Press, Cambridge, 1993. (1 quote Laubenbacher's translation.)
62. _, Theorie der algebraischen Invarianten nebst Anwendungen auf Geometrie, lecture notes from Summer 1897 prepared by Sophus Marxsen, Library of the Mathematical Institute of the University of Göttingen; English translation Theory of Algebraic Invariants, R. C. Laubenbacher and B. Sturmfels, eds. [using a different copy from the Mathematics Library of Cornell University], Cambridge University Press, Cambridge, 1993. (1 quote Laubenbacher's translation.)
63. _, Über den Zahlbegriff, Jahresber. Deutsch. Math. Verein. 8 (1900) 180-184; also in [57] from the 3rd to 7th editions, pp. 256-262 (3rd. ed., 1909), pp. 237-242 (4th to 6th ed., 1913, 1922, and 1923), pp. 241-246 (7th ed., 1930); English translation (by W. Ewald) [17:2, pp. 1089-1095].
64. _, Über die Grundlagen der Logik und der Arithmetik, in Verhandlungen des 3. Internationalen Mathematiker-Kongresses in Heidelberg 1904, A. Krazer, ed., Teubner-Verlag, Leipzig, 1905, pp. 174-185; also in [57] from the 3rd to the 7th editions, pp. 263-279 (3rd ed., 1909), pp. 243-258 (4th to 6th ed., 1913, 1922, and 1923), pp. 247-261 (7th ed. 1930); English translations (by G. B. Halsted) The Monist 15 (1905) 338-352 and (by W. Woodward) in From Frege to Gödel. A Source Book in Mathematical Logic 1879-1931, J. van Heijenoort, ed., Harvard University Press, Cambridge, 1967, pp. 130-138; 2nd ed., 1971; French translation L'Enseignement Mathematique 7 (1905) 89-103.
65. _, Über die Grundlagen der Logik und der Arithmetik, in Verhandlungen des 3. Internationalen Mathematiker-Kongresses in Heidelberg 1904, A. Krazer, ed., Teubner-Verlag, Leipzig, 1905, pp. 174-185; also in [57] from the 3rd to the 7th editions, pp. 263-279 (3rd ed., 1909), pp. 243-258 (4th to 6th ed., 1913, 1922, and 1923), pp. 247-261 (7th ed. 1930); English translations (by G. B. Halsted) The Monist 15 (1905) 338-352 and (by W. Woodward) in From Frege to Gödel. A Source Book in Mathematical Logic 1879-1931, J. van Heijenoort, ed., Harvard University Press, Cambridge, 1967, pp. 130-138; 2nd ed., 1971; French translation L'Enseignement Mathematique 7 (1905) 89-103.
66. _, Über die Grundlagen der Logik und der Arithmetik, in Verhandlungen des 3. Internationalen Mathematiker-Kongresses in Heidelberg 1904, A. Krazer, ed., Teubner-Verlag, Leipzig, 1905, pp. 174-185; also in [57] from the 3rd to the 7th editions, pp. 263-279 (3rd ed., 1909), pp. 243-258 (4th to 6th ed., 1913, 1922, and 1923), pp. 247-261 (7th ed. 1930); English translations (by G. B. Halsted) The Monist 15 (1905) 338-352 and (by W. Woodward) in From Frege to Gödel. A Source Book in Mathematical Logic 1879-1931, J. van Heijenoort, ed., Harvard University Press, Cambridge, 1967, pp. 130-138; 2nd ed., 1971; French translation L'Enseignement Mathematique 7 (1905) 89-103.
67. _, Über die Grundlagen der Logik und der Arithmetik, in Verhandlungen des 3. Internationalen Mathematiker-Kongresses in Heidelberg 1904, A. Krazer, ed., Teubner-Verlag, Leipzig, 1905, pp. 174-185; also in [57] from the 3rd to the 7th editions, pp. 263-279 (3rd ed., 1909), pp. 243-258 (4th to 6th ed., 1913, 1922, and 1923), pp. 247-261 (7th ed. 1930); English translations (by G. B. Halsted) The Monist 15 (1905) 338-352 and (by W. Woodward) in From Frege to Gödel. A Source Book in Mathematical Logic 1879-1931, J. van Heijenoort, ed., Harvard University Press, Cambridge, 1967, pp. 130-138; 2nd ed., 1971; French translation L'Enseignement Mathematique 7 (1905) 89-103.
68. _, Loglsche Prinzipien des mathematischen Denkens, lecture notes from Summer 1905 prepared by E. Hellinger, Library of the Mathematical Institute of the University of Göttingen.
69. _, Logische Prinzipien des mathematischen Denkens, lecture notes from Summer 1905 prepared by M. Born, Niedersächsische Staats- und Universitätsbibliothek Göttingen, Handschriftenabteilung, Cod. Ms. D. Hilbert 558a.
70. _, Principien der Mathematik, lecture notes from Winter 1917 prepared by P. Bernays, Library of the Mathematical Institute of the University of Göttingen.
71. _, Axiomatisches Denken, Math. Annal. 78 (1918) 405-415; also in [58:3, pp. 146-156]; English translations (by Ewald) [17:2, pp. 1105-1115] and (by Fang) [18, pp. 187-198]; French translation L'Enseignement Mathématique 20 (1918) 122-136.
72. _, Axiomatisches Denken, Math. Annal. 78 (1918) 405-415; also in [58:3, pp. 146-156]; English translations (by Ewald) [17:2, pp. 1105-1115] and (by Fang) [18, pp. 187-198]; French translation L'Enseignement Mathématique 20 (1918) 122-136.
73. _, Neubegründung der Mathematik, Erste Mitteilung, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 (1922) 157-177; also in [58:3, pp. 157-177]; English translation (by W. Ewald) [17:2, pp. 1115-1134].
74. _, Wissen und mathematisches Denken, lecture notes from Winter 1922 prepared by W. Ackermann; revised reprint, C.-F. Bödigheimer, ed., Mathematisches Institut Göttingen, 1988.
75. _, Die logischen Grundlagen der Mathematik, Math. Annal. 88 (1923) 151-165; also in [58:3, pp. 178-191]; English translation (by W. Ewald) [17:2, pp. 1134-1148].
76. _, Über das Unendliche, Math. Annal. 95 (1926) 161-190; also in [57, 7th ed., pp. 262-288], shortened version in Jahresber. Deutsch. Math. Verein. 36 (1927) 201-215; English translation (by S. Bauer-Mengelberg) in From Frege to Gödel. A Source Book in Mathematical Logic 1879-1931, J. van Heijenoort, ed., Harvard University Press, Cambridge, 1967, pp. 367-392; 2nd ed., 1971; French translation (by A. Weil), Sur l'infinie, Acta Math. 48 (1926) 91-122.
77. _, Über das Unendliche, Math. Annal. 95 (1926) 161-190; also in [57, 7th ed., pp. 262-288], shortened version in Jahresber. Deutsch. Math. Verein. 36 (1927) 201-215; English translation (by S. Bauer-Mengelberg) in From Frege to Gödel. A Source Book in Mathematical Logic 1879-1931, J. van Heijenoort, ed., Harvard University Press, Cambridge, 1967, pp. 367-392; 2nd ed., 1971; French translation (by A. Weil), Sur l'infinie, Acta Math. 48 (1926) 91-122.
78. _, Über das Unendliche, Math. Annal. 95 (1926) 161-190; also in [57, 7th ed., pp. 262-288], shortened version in Jahresber. Deutsch. Math. Verein. 36 (1927) 201-215; English translation (by S. Bauer-Mengelberg) in From Frege to Gödel. A Source Book in Mathematical Logic 1879-1931, J. van Heijenoort, ed., Harvard University Press, Cambridge, 1967, pp. 367-392; 2nd ed., 1971; French translation (by A. Weil), Sur l'infinie, Acta Math. 48 (1926) 91-122.
79. _, Die Grundlagen der Mathematik, [Zweite Mitteilung], Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 6 (1928) 65-85; followed by Diskussionsbemerkungen zu dem zweiten Hilbertschen Vortrag by H. Weyl, pp. 86-88, and Zusatz zu Huberts Vortrag by P. Bernays, pp. 89-95; shortened version in [57, 7th ed., pp. 289-312]; English translation (by S. Bauer-Mengelberg and D. Føllesdal) in From Frege to Gödel. A Source Book in Mathematical Logic 1879-1931, J. van Heijenoort, ed., Harvard University Press, Cambridge, 1967, pp. 464-479; 2nd ed., 1971.
80. _, Die Grundlagen der Mathematik, [Zweite Mitteilung], Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 6 (1928) 65-85; followed by Diskussionsbemerkungen zu dem zweiten Hilbertschen Vortrag by H. Weyl, pp. 86-88, and Zusatz zu Huberts Vortrag by P. Bernays, pp. 89-95; shortened version in [57, 7th ed., pp. 289-312]; English translation (by S. Bauer-Mengelberg and D. Føllesdal) in From Frege to Gödel. A Source Book in Mathematical Logic 1879-1931, J. van Heijenoort, ed., Harvard University Press, Cambridge, 1967, pp. 464-479; 2nd ed., 1971.
81. _, Probleme der Grundlegung der Mathematik, in Atti del Congresso Internazionale del Matematici, Bologna 1928, Tomo I, Zanichelli, Bologna, 1929, pp. 135-141; also in Math. Ann. 102 (1930) 1-9, [57, 7th ed., pp. 313-323], and Hilbert. Gedenkband, K. Reidemeister, ed., Springer-Verlag, Berlin 1971, pp. 9-19.
82. _, Probleme der Grundlegung der Mathematik, in Atti del Congresso Internazionale del Matematici, Bologna 1928, Tomo I, Zanichelli, Bologna, 1929, pp. 135-141; also in Math. Ann. 102 (1930) 1-9, [57, 7th ed., pp. 313-323], and Hilbert. Gedenkband, K. Reidemeister, ed., Springer-Verlag, Berlin 1971, pp. 9-19.
83. _, Probleme der Grundlegung der Mathematik, in Atti del Congresso Internazionale del Matematici, Bologna 1928, Tomo I, Zanichelli, Bologna, 1929, pp. 135-141; also in Math. Ann. 102 (1930) 1-9, [57, 7th ed., pp. 313-323], and Hilbert. Gedenkband, K. Reidemeister, ed., Springer-Verlag, Berlin 1971, pp. 9-19.
84. _, Naturerkennen und Logik, Naturwissenschaften (1930), 959-963; also in Gesammelte Abhandlungen [58:3, pp. 378-387]; English translations (by W. Ewald) in [17:2, pp. 1157-1165]; selected parts in Reid [87, chap. 12]; English translation of the corresponding radio broadcast in Vinnikov [102].
85. _, Naturerkennen und Logik, Naturwissenschaften (1930), 959-963; also in Gesammelte Abhandlungen [58:3, pp. 378-387]; English translations (by W. Ewald) in [17:2, pp. 1157-1165]; selected parts in Reid [87, chap. 12]; English translation of the corresponding radio broadcast in Vinnikov [102].
86. _, Die Grundlegung der elementaren Zahlenlehre, Math. Annal. 104 (1931) 485-494; shortened version in the Gesammelte Abhandlungen [58:3, pp. 192-195]; English translation (by W. Ewald) in [17:2, pp. 1148-1157].
87. _, Grundlagen der Geometrie, Teubner-Verlag, Leipzig, 1899; from the 8th amended ed. by P. Bernays with supplements, Stuttgart, 1956-1987; 14th ed., with contributions by H. Kiechle et al., M. Toepell, ed., Stuttgart, 1999; first English translation The Foundations of Geometry by E. J. Townsend, Open Court, Chicago, 1902; new translation by L. Unger, Open Court, La Salle, 1972. [The first German edition of the Grundlagen was a contribution to the Festschrift zur Enthüllung des Gauss-Weber Denkmals in Göttingen, later editions were published separately.]
88. _, Grundlagen der Geometrie, Teubner-Verlag, Leipzig, 1899; from the 8th amended ed. by P. Bernays with supplements, Stuttgart, 1956-1987; 14th ed., with contributions by H. Kiechle et al., M. Toepell, ed., Stuttgart, 1999; first English translation The Foundations of Geometry by E. J. Townsend, Open Court, Chicago, 1902; new translation by L. Unger, Open Court, La Salle, 1972. [The first German edition of the Grundlagen was a contribution to the Festschrift zur Enthüllung des Gauss-Weber Denkmals in Göttingen, later editions were published separately.]
89. _, Gesammelte Abhandlungen, 3 vols., Springer-Verlag, Berlin, 1932-1935; 2nd ed., 1970.
90. D. Hilbert and W. Ackermann, Grundzüge der theoretischen Logik, Springer-Verlag, Berlin, 1928; 6th ed., 1972; English translation of the second edition Principles of Mathematical Logic, by L. M. Hammond et al., Chelsea, New York, 1950; Chinese translation Science Press, Beijing, 1950; Russian translation Nauka, Moscow, 1979.
91. D. Hilbert and W. Ackermann, Grundzüge der theoretischen Logik, Springer-Verlag, Berlin, 1928; 6th ed., 1972; English translation of the second edition Principles of Mathematical Logic, by L. M. Hammond et al., Chelsea, New York, 1950; Chinese translation Science Press, Beijing, 1950; Russian translation Nauka, Moscow, 1979.
92. D. Hilbert and P. Bernays, Grundlagen der Mathematik, 2 vols., Springer-Verlag, Berlin, 1934-1939; 2nd ed., 1968-70; Russian translation Nauka, Moscow, 1979-1982.
93. T. Hungerford, Algebra, 8th ed., Springer-Verlag, New York, 1974.
94. H. N. Jahnke, Hilbert, Weyl und die Philosophie der Mathematik, Math. Semesterberichte 37 (1990) 157-179.
95. T. Koetsier, Hilberts 24ste probleem, Nleuw Archief voor Wiskunde 5 (2) (2001) 65-67. [The canceled 24th problem is reproduced in facsimile.]
96. T. Koetsier and J. van Mill, General topology, in particular dimension theory, in the Netherlands, in Handbook of the History of General Topology, vol. 1, C. E. Aull and R. Lowen, eds., Kluwer, Dordrecht, 1997, pp. 135-180.
97. G. Kreisel and J.-L. Krivine, Éléments de logique mathématique. Théorie des modèles, Dunond, Paris, 1967; English translation Elements of Mathematical Logic (Model Theory), North Holland, Amsterdam, 1967.
98. G. Kreisel, What have we learnt from Hubert's second problem?, in Browder [8:1, pp. 93-130].
99. C. W. H. Lam, How reliable Is a Computer-Based Proof?, Math. Intelligencer 12 (1) (1990) 8-12.
100. É. M. H. Lemoine, La Géométrographie ou l'Art des Constructions Géométriques, Naud, Paris, 1902.
101. U. Majer, Hilbert's program to axiomatize physics (in analogy to geometry), in History of Philosophy and Science, M. Heidelberger and F. Stadler, eds., Kluwer, Dordrecht, 2002, pp. 213-224.
102. Yu. Matiyasevich, Diophantine enumerable sets, Doklady Akademii Nauk SSSR 191 (1970) 279-282 [Russian]; English translation in Sov. Math Doklady 11 (1970) 354-357.
103. Yu. Matiyasevich, Diophantine enumerable sets, Doklady Akademii Nauk SSSR 191 (1970) 279-282 [Russian]; English translation in Sov. Math Doklady 11 (1970) 354-357.
104. H. Minkowski, Briefe an David Hilbert, L. Rüdenberg, ed., Springer-Verlag, Berlin, 1973. [The 105 letters are preserved in the Niedersächsische Staats- und Universitätsbibliothek Göttingen, Handschriftenabteilung, Nachlass Hilbert, Cod. Ms. D. Hilbert 258.]
105. E. Menzler-Trott, Gentzens Problem (including an essay on Gentzen's proof theory by J. von Plato), Birkhäuser-Verlag, Basel, 2001. [A shortened English translation is in preparation.]
106. H. Meschkowski, Richtigkeit und Wahrheit, Bibliographisches Institut, Mannheim, 1978.
107. F. Meyer, Bericht über den gegenwärtigen Stand der Invariantentheorie, Jahresber. Deutsch. Math. Verein. 1 (1890-91) 81-292.
108. G. H. Müller, Ω-Bibliography of Mathematical Logic, 6 vols., Springer-Verlag, Berlin, 1987.
109. R. Murawski, Recursive Functions and Metamathematics. Problems of Completeness and Decidability, Göel's Theorems, Kluwer, Dordrecht, 1999.
110. J. von Neumann, Zur Hilbertschen Beweistheorie, Math. Zeitschrift 26 (1927) 1-46.
111. J. D. Norton, 'Nature is the realisation of the simplest conceivable mathematical ideas': Einstein and the canon of mathematical simplicity, Studies in the History of Modem Physics 31 (2000) 135-170.
112. K. V. H. Parshall, The one-hundredth anniversary of the death of invariant theory?, Math. Intelligencer 12 (4) (1990) 10-16.
113. V. Peckhaus, Hilbertprogramm und Kritische Philosophie, Vandenhoeck & Ruprecht, Göttingen, 1990.
114. _, Hilbert's axiomatic programme and philosophy, in The History of Modern Mathematics, vol. 3, E. Knobloch and D. Rowe, eds., Academic Press, Boston, 1994, pp. 90-112.
115. J.-P. Pier, ed., Development of Mathematics, 1900-1950 and 1950-2000, 2 vols., Birkhäuser, Basel, 1994 and 2000.
116. P. Pudlák, The lengths of proofs, in Handbook of Proof Theory, S. R. Buss, ed., Elsevier, Amsterdam, 1998, pp. 547-637.
117. S. Rebsdorf and H. Kragh, eds., Edward Arthur Milne-The relations of mathematics to science, Studies in History and Philosophy of Modem Physics 33 (2002) 51-64.
118. M. Rédei, "Unsolved Problems in Mathematics": John von Neumann's address to the ICM Amsterdam, 1954, Math. Intelligencer 21 (4) (1999) 7-12.
119. K. Reich, The American contribution to the theory of differential invariants, 1900-1916, in The Attraction of Gravitation, J. Barman et al., eds., Birkhäuser, Boston, 1993, pp. 225-247.
120. C. Reid, Hilbert, Springer-Verlag, New York, 1970; reprinted Copernicus, New York, 1996.
121. M. von Renteln, Zur Situation der Analysis um die Jahrhundertwende, in Vorlesungen zum Gedenken an Felix Hausdorff, E. Eichhorn and E. J. Thiele, eds., Heldermann, Berlin, 1994, pp. 107-130.
122. G.-C. Rota, Two turning points in invariant theory, Math. Intelligencer 21 (1) (1999) 20-27.
123. B. Scarpellini, Komplexitätstheorie, Wissenschaftsmagazin der Universität Basel "uni nova" 87 (6) (2000) 51-52.
124. C. A. Scott, The International Congress of Mathematicians in Paris, Bull. Amer. Math. Soc. 7 (1900) 57-79.
125. J.-P. Serre, Algèbre Locale, Ultilicités, Lecture Notes in Mathematics, no. 11, Springer-Verlag, Berlin, 1965.
126. K. Sigmund, Hans Hahn and the foundational debate, in The Foundational Debate, W. Depauli-Schimanovic et al., eds., Kluwer, Dordrecht, 1995, pp. 235-245.
127. S. G. Simpson, Partial realizations of Hilbert's program, J. Symb. Logic 53 (1988) 349-363.
128. B. Sobociński, On well constructed axiom systems, in Polskie Towarzystwo Naukowe na Obcźyznie [Polish Society of Art and Sciences, Abroad], Yearbookfor 1955-56, London, 1956, pp. 1-12.
129. M. Stöltzner, How metaphysical is "Deepening the foundations"? Hahn and Frank on Hilbert's axiomatic method, in History of Philosophy of Science, F. Stadier, ed., Kluwer, Dordrecht, 2002, pp. 245-262.
130. R. Taylor and A. Wiles, Ring-theoretic properties of certain Hecke algebras, Ann. Math. 141 (1995) 532-572.
131. R. Thiele, Hubert and his twenty-four problems, in Mathematics at the Dawn of a Millennium, Proceedings of the Canadian Society for History and Philosophy of Mathematics, Hamilton, Ont., 2000, vol. 13, M. Kinyon, ed., pp. 1-22. [Some documents including the canceled twenty-fourth problem are reproduced in facsimile.]
132. _, Von der Bernoullischen Brachistochrone zum Kallbratorkonzepl. Untersuchungen zur Geschichte der Feldtheorie bei einfachen Variationsproblemen, Habilitationsschrift, Universität Hamburg, Fachbereich Mathematik, 2001; Brepols, Turnhout, 2003 (to appear).
133. _, David Hubert and French Mathematics, in Proceedings of the XXXI. International Congress of History of Science, Mexico City, Mexico, 2001 (to appear).
134. D. Velleman, Fermat's last theorem and Hilbert's program, Math. Intelligencer 19 (1) (1997) 64-67.
135. V. Vinnikov, We shall know: Hubert's apology, Math. Intelligencer 21 (1) (1999) 42-46.
136. G. Vollmer, Gelöste, ungelöste und unlösbare Probleme, in Fortschrift und Gesellschaft, E.-L. Winnacker, ed., Hirzel-Verlag Stuttgart, 1993, pp. 79-97; also in G. Vollmer, Wissenschaftstheorie im Einsatz, Stuttgart, Hirzel-Verlag, 1993, pp. 183-210.
137. G. Vollmer, Gelöste, ungelöste und unlösbare Probleme, in Fortschrift und Gesellschaft, E.-L. Winnacker, ed., Hirzel-Verlag Stuttgart, 1993, pp. 79-97; also in G. Vollmer, Wissenschaftstheorie im Einsatz, Stuttgart, Hirzel-Verlag, 1993, pp. 183-210.
138. _, Denkzeuge, in Mannheimer Forum 90/91, E. P. Fischer, ed., Piper, München, 1991, pp. 15-78.
139. A. Weil, The future of mathematics, in Great Currents of Mathematical Thought, vol. 1, F. Le Lionnais, ed. (translated from the French by A. Dresden), Dover, New York, 1971, pp. 320-336.
140. S. Weinberg, Dreams of a Final Theory, Vintage, London, 1993.
141. H. Weyl, Randbemerkungen zu Hauptproblemen der Mathematik, Math. Zeitschrift 20 (1924) 131-150.
142. _, David Hubert and his mathematical work, Bull. Amer. Math. Soc. 50 (1944) 612-654.
143. _, Obituary: D. Hubert 1862-1943, American Philosophical Society Year Book (1944) 387-395; also in Gesammelle Abhandlungen, Springer-Verlag, Berlin, 1968, pp. 121-129.
144. _, Obituary: D. Hubert 1862-1943, American Philosophical Society Year Book (1944) 387-395; also in Gesammelle Abhandlungen, Springer-Verlag, Berlin, 1968, pp. 121-129.
145. _, A half-century of mathematics, this MONTHLY 58 (1951) 523-553; also in Gesammelte Abhandlungen, Springer-Verlag, Berlin, 1968, pp. 464-494.
146. _, A half-century of mathematics, this MONTHLY 58 (1951) 523-553; also in Gesammelte Abhandlungen, Springer-Verlag, Berlin, 1968, pp. 464-494.
147. _, The Classical Groups. Their Invariants and Representations, 2nd. ed., Princeton University Press, Princeton, 1946.
148. A. Wiles, Modular elliptic curves and Fermat's last theorem, Ann. Math. 141 (1995) 443-531.
149. L. Wos, Automating the search for elegant proofs, J. Automated Reasoning 21 (g) (1998) 135-175.
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