Anxiety and abstraction in nineteenth-century mathematics

Science in Context

Volumn 17, Issue 1-2, 2004, Pages 23-47

  Gray, Jeremy J ^a  

^a OPEN UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3142757245     PISSN: 02698897     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0269889704000043     Document Type: Conference Paper

References (71)

1. Avellone, M., A. Brigaglia, and C. Zappulla. 2002. "The Foundations of Projective Geometry in Italy from De Paolis to Fieri." Archive for History of Exact Sciences 56:363-425.
2. Bliss, G. A. 1923. "The Reduction of Singularities of Plane Curves by Birational Transformation." Bulletin of the American Mathematical Society 29:161-183.
3. Boniface, J. and N. Schappacher. 2001. '"Sur le concept de nombre en mathématique'. Cours inédit de Leopold Kronecker à Berlin (1891)." Revue d'Histoire des Mathématiques 7(2)-.207-275.
4. Borel, E. et al. [1904] 1914. "Cinq lettres sur la théorie des ensembles." Bulletin de la Société mathématique de France, reprinted in Leçons sur la théorie des fonctions, 2nd ed., 150-160. Paris: Gauthier-Villars.
5. Borel, E. et al. [1904] 1914. "Cinq lettres sur la théorie des ensembles." Bulletin de la Société mathématique de France, reprinted in Leçons sur la théorie des fonctions, 2nd ed., 150-160. Paris: Gauthier-Villars.
6. Bottazzini, U. [1981] 1986. Il calcolo sublime. Storia dell' analisi matematica da Euler a Weierstrass. Turin: Editore Boringhieri. Translated as The Higher Calculus, a History of Real and Complex Analysis from Euler to Weierstrass. New York: Springer-Verlag.
7. Bottazzini, U. [1981] 1986. Il calcolo sublime. Storia dell' analisi matematica da Euler a Weierstrass. Turin: Editore Boringhieri. Translated as The Higher Calculus, a History of Real and Complex Analysis from Euler to Weierstrass. New York: Springer-Verlag.
8. Bottazzini, U. 1999. "Die Theorie der komplexen Funktionen, 1780-1900." In Jahnke 1999, 267-328.
9. Burrow, J. W 2000. The Crisis of Reason; European Thought, 1848-1914. New Haven: Yale University Press.
10. Cayley, A. 1865 "Note on Lobatchewsky's Imaginary Geometry." Philosophical Magazine 29:231-233. In Collected Mathematical Papers 5(no. 362):471-472.
11. Cayley, A. 1865 "Note on Lobatchewsky's Imaginary Geometry." Philosophical Magazine 29:231-233. In Collected Mathematical Papers 5(no. 362):471-472.
12. Coolidge, J. L. [1940] 1963. A History of Geometrical Methods. Oxford: Oxford University Press, Dover reprint.
13. Cremona, L. 1868. "Mémoire de géométrie pure sur les surfaces du troisième ordre." Journal für die reine und angewandte Mathematik 68:1-133.
14. Dalen, D. van. 1990. "The War of the Frogs and the Mice, or the Crisis of the Mathematische Annalen." Mathematical Intelligencer 12 (4): 17-31.
15. Dalen, D. van. 1999. Mystic, Geometer, and Intuitionist, The Life of L. E. J. Brouwer, vol. 1, The Dawning Revolution. Oxford: Clarendon Press.
16. Darboux, G. 1875. "Mémoire sur les fonctions discontinues." Annales Scientifiques de l'École Normale Supérieure. 4(2):58-112.
17. Dauben, J. W 1979. Georg Cantor. His Mathematics and Philosophy of the Infinite. Cambridge: Harvard University Press.
18. Dombrowski, P. 1979. "150 Years after Gauss's Disquisitiones Arithmeticae." Astérisque 62:1-153.
19. Enriques, F. 1906. Problemi della sdenza. Bologna: Zanichelli.
20. Enriques, F. 1912. II significato della critica dei principi nello sviluppo delle matematiche. Scientia 12:172-191.
21. Epple, M. 1999. "Das Ende der Grössenlehre: Grundlagen der Analysis 1860-1910." In Jahnke 1999, 371-410.
22. Gauss, C. F. 1900. Werke, vol. 8. Göttingen and Leipzig: Teubner.
23. Giusti, E. 1984. "Gli 'errori' di Cauchy e i fondamenti dell'analisi." Bolettino di Storia delle Scienze matematiche 4:24-54.
24. Grabiner, J. V 1974. "Is mathematical truth time-dependent?" American Mathematical Monthly 81:354-356.
25. Grabiner, J. V 1981. The Origins of Cauchy's Rigorous Calculus. Cambridge: MIT Press.
26. Grattan-Guinness, I. 1990. Convolutions in French Mathematics. Boston and Basel: Birkhäuser.
27. Grattan-Guinness, I., ed. 1993. Companion Encyclopaedia of the History and Philosophy of the Mathematical Sciences. London: Routledge.
28. Grattan-Guinness, I. 2000. The Search for Mathematical Roots, 1870-1940. Princeton: Princeton University Press.
29. Gray J. J. and Walter Scott, eds. 1997. Henri Poincaré; Three Supplementary Essays on the Discovery of Fuchsian Functions. Berlin: Akademie Verlag and Paris: Blanchard.
30. Gray, J. J. 1989. Ideas of Space: Euclidean, non-Euclidean, and Relativistic, 2nd ed. Oxford: Oxford University Press.
31. Gray, J. J. 1991. "Did Poincaré say 'Set theory is a disease'?" The Mathematical Intelligencer 13(1):19-22.
32. Gray, J. J. 1992. "A nineteenth-century revolution in mathematical ontology." In Revolutions in Mathematics, edited by D. Gillies, 226-248. Oxford: Oxford University Press
33. Gray, J. J., ed. 1999. The Symbolic Universe: Geometry and Physics, 1890-1930. "Introduction," 1-21; and an essay "Geometry - Formalisms and Intuitions," 58-83. Oxford: Oxford University Press.
34. Gray, J. J., ed. 1999. The Symbolic Universe: Geometry and Physics, 1890-1930. "Introduction," 1-21; and an essay "Geometry - Formalisms and Intuitions," 58-83. Oxford: Oxford University Press.
35. Gray, J. J. 2000a. Linear differential equations and group theory from Riemann to Poincaré, 2nd edition. Boston and Basel: Birkhäuser.
36. Gray, J. J. 2000b. "Goursat, Pringsheim, Walsh, and the Cauchy Integral Theorem." Mathematical Intelligencer 22(4):60-66.
37. Hawkins T. 1975. Lebesgue's Theory of Integration, 2nd ed. New York: Chelsea.
38. Hawkins T. 1977. "Weierstrass and the Theory of Matrices." A. H. E. S. 17(2):119-163.
39. Hawkins T. 2000. The Emergence of the Theory of Lie Groups, An Essay in the History of Mathematics 1869-1926. New York: Springer Verlag.
40. Hermite, C. and T.-J. Stieltjes. 1905. Correspondance d'Hermite et de Stieltjes, 2 vols. Edited by B. Baillaud and H. Bourget. Paris: Gauthier-Villars.
41. Hesseling, D. Gnomes in the Fog. The Reception of Brouwer's Intuitionism in the 1920s. PhD diss. Utrecht.
42. Jahnke, H. N., ed. 1999. Geschichte der Analysis. Texte zur Didaktik der Mathematik. Heidelberg and Berlin: Spektrum Akademischer Verlag.
43. Jahnke, Hans Niels, ed. 2003. A History of Analysis. Providence: American Mathematical Society.
44. Kline, M. 1972 Mathematical Thought from Ancient to Modern Times. Oxford: Oxford University Press.
45. Kohnke, K. C. [1986] 1991. The Rise of neo-Kantianism. Cambridge: Cambridge University Press. German original, Entstehung und Aufstieg des Neukantianismus.
46. Lakatos, I. 1976. Proofs and Refutations. Cambridge: Cambridge University Press.
47. Laugwitz, D. 2000. "Comments on the paper 'Two letters by Newton Luzin to M. Ya Vigodskii'." American Mathematical Monthly 107:267-276.
48. Lützen, J. 1990. Joseph Liouville, 1809-1882, Master of Pure and Applied Mathematics. New York: Springer-Verlag.
49. Lützen, J. 1999. "Grundlagen der Analysis in 19. Jahrhundert." In Jahnke 1999, 191-244.
50. Mehrtens, Herbert. 1990. Moderne-Sprache-Mathematik. Frankfurt: Suhrkamp.
51. Nagel, E. 1939. "The Formation of Modern Concepts of Formal Logic in the Development of Geometry." Osiris 7:142-224.
52. Parshall, K. and D. E. Rowe. 1994. The Emergence of the American Mathematical Research Community; J. J. Sylvester, Felix Klein, and E. H. Moore. Providence, Rhode Island: American and London Mathematical Societies, History of Mathematics, vol. 8
53. Pasch, M. 1882. Vorlesungen über neuere Geometrie. Leipzig: Teubner.
54. Perron, O.1911. "Über Wahrheit und Irrtum in der Mathematik." Jahresbericht der Deutschen Mathematiker-Vereinigung 20:196-211.
55. Pieper, H. 1980. "Gegen die Schmach des Belagerungszustands." Spectrum Monatsbericht der Akademie der Wissenschaften der DDR, Heft 1:22-24.
56. Plücker, J. 1839. Theorie der algebraischen Curven. Berlin.
57. Poincaré, H. 1908. "L'Avenir des mathématiques." Rendiconti del Circolo Matematico di Palermo 26:152-168, address to the International Congress of Mathematicians, Rome. Reprinted 1916 in Science et Méthode, 19-42. Paris:Flammarion. English translation in Science and Method. New York: Dover Books.
58. Poincaré, H. 1908. "L'Avenir des mathématiques." Rendiconti del Circolo Matematico di Palermo 26:152-168, address to the International Congress of Mathematicians, Rome. Reprinted 1916 in Science et Méthode, 19-42. Paris:Flammarion. English translation in Science and Method. New York: Dover Books.
59. Poincaré, H. 1908. "L'Avenir des mathématiques." Rendiconti del Circolo Matematico di Palermo 26:152-168, address to the International Congress of Mathematicians, Rome. Reprinted 1916 in Science et Méthode, 19-42. Paris:Flammarion. English translation in Science and Method. New York: Dover Books.
60. Pringsheim, A. 1896. "Ueber Vereinfachungen in der elementaren Theorie der analytischen Functionen." Mathematische Annalen 47:121-154.
61. Richards, J. L. 1979. "The Reception of a Mathematical Theory: Non-Euclidean Geometry in England 1865-1883." In Natural Order: Historical Studies of Scientific Culture, edited by B. Barnes and S. Shapin, 143-166. Beverley Hills: Sage Publications.
62. Richards, J. L. 1988. Mathematical Visions: the Pursuit of Geometry in Victorian England. San Diego: Academic Press.
63. Samuel, P. 1988. Protective Geometry. New York: Springer Verlag.
64. Scharlau, W and H. Opolka. 1985. From Fermat to Minkowski. Heidelberg: Springer Verlag.
65. Torretti, R. 1984. Philosophy of Geometry from Riemann to Poincaré. Dordrecht: Reidel.
66. Vailati, G. 1911. Scritti. Firenze-Lipsia.
67. Voss, A. 1914. "Über die mathematische Erkenntnis." In Die Kultur der Gegenwart, edited by P. Hiinneberg. Leipzig: Teubner.
68. Wilson, E. B. 1905. "The Foundations of Science," review of Wissenschaft und Hypothese von H. Poincaré, translated by F. and L. Lindemann. Bulletin of the American Mathematical Society 12:187-193.
69. Wilson, E. B. 1905. "The Foundations of Science," review of Wissenschaft und Hypothese von H. Poincaré, translated by F. and L. Lindemann. Bulletin of the American Mathematical Society 12:187-193.
70. Wussing, H. [1969] [1979] 1984. Die Genesis des abstrakten Gruppenbegriffes. Berlin: C. F. Gauss; Leipzig: Teubner. The Genesis of the Abstract Group Concept, translated by A. Shenitzer. Cambridge: MIT Press.
71. Wussing, H. [1969] [1979] 1984. Die Genesis des abstrakten Gruppenbegriffes. Berlin: C. F. Gauss; Leipzig: Teubner. The Genesis of the Abstract Group Concept, translated by A. Shenitzer. Cambridge: MIT Press.