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2014 | 6 | 101-121
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Twórcza rola patologii w matematyce

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We discuss the creative role of objects called pathologies by mathematicians.Pathologies may become “domesticated” and give rise to newmathematical domains. Thus they influence changes in mathematical intuition.
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Bibliografia
  • Błaszczyk, P.: 2007, Analiza filozoficzna rozprawy Richarda Dedekinda Stetigkeit und irrationale Zahlen, Wydawnictwo Naukowe AP w Krakowie, Kraków.
  • Corry, L.: 2004, Modern Algebra and the Rise of Mathematical Structures, Birkhäuser, Basel-Boston-Berlin.
  • Dehn, M.: 1902, Űber den Rauminhalt, Mathematische Annalen 55, 465-478.
  • Feferman, S., Friedman, H. M., Maddy, P., Steel, J. R.: 2000, Does mathematics need new axioms?, The Bulletin of Symbolic Logic 6, 401-446.
  • Friedman, H. M.: 1992, The Incompleteness Phenomena, w: F. E. Bowder (ed.), Mathematics into the Twenty-first Century. 1988 Centennial Symposium, August 8-12, American Mathematical Society, Providence, Rhode Island, 49-84.
  • Gelbaum, B. R., Olmsted, J. M. H.: 1990, Theorems and Counterexamples in Mathematics, Springer-Verlag, New York.
  • Gelbaum, B. R., Olmsted, J. M. H.: 2003, Counterexamples in Analysis, Dover Publications, Inc., Mineola, New York.
  • Hahn, H.: 1956, The crisis of intuition, w: J. R. Newman (ed.), The World of Mathematics, vol. 3, Dover Publications, Inc., Mineola, New York, 1957-1976.
  • Havil, J.: 2007, Nonplussed! Mathematical Proof of Implausible Ideas, Princeton University Press, Princeton and Oxford.
  • Havil, J.: 2008, Impossible? Surprising Solutions to Counterintuitive Conundrums, Princeton University Press, Princeton and Oxford.
  • Kanamori, A.: 1994, The Higher Infinite. Large Cardinals in Set Theory from Their Beginnings, Oxford University Press, New York, Oxford.
  • Kline, M.: 1994, Mathematical Thought from Ancient to Modern Times, Springer-Verlag, Berlin.
  • Laczkovich, M.: 1990, Equidecomposability and discrepancy: a solution to Tarski’s circle squaring problem, Journal für die Reine und Angewandte Mathematik 404, 77-117.
  • Lakatos, I.: 1976, Proofs and Refutations. The Logic of Mathematical Discovery, Cmbridge University Press, Cambridge.
  • Lakoff, G., Johnson, M.: 1980, Metaphors we live by, University of Chicago Press, Chicago.
  • Lakoff, G., Núñez, R.: 2000, Where Mathematics Comes From. How the Embodied Mind Brings Mathematics into Being, Basic Books, New York.
  • Levitin, A., Levitin, M.: 2011, Algorithmic Puzzles, Oxford University Press, New York.
  • Norwid, C. K.: 1964, Fatum, Poeci polscy. Cyprian Norwid, Czytelnik, 89.
  • Petković, M. S.: 2009, Famous Puzzles of Great Mathematicians, The American Mathematical Society, Providence, Rhode Island.
  • Pogonowski, J.: 2011, Geneza matematyki wedle kognitywistów, Investigationes Linguisticae 23, 106-147. http://inveling.amu.edu.pl/, http://www.logic.amu.edu.pl/images/3/3c/Littlejill01.pdf.
  • Pogonowski, J..: 2012, Matematyczne metafory kognitywistów. http://www.logic.amu.edu.pl/images/0/0e/Mmk2012.pdf.
  • Posamentier, A. S., Lehmann, I.: 2013, Magnificent Mistakes in Mathematics, Prometheus Books, Amherst, New York.
  • Scorpan, A.: 2005, The Wild World of 4-Manifolds, American Mathematical Society, Providence, Rhode Island.
  • Steen, L. A., Seebach, J. A., Jr.: 1995, Counterexamples in Topology, Dover Publications, Inc., New York.
  • Tarski, A.: 1925, Probléme 38, Fundamentha Mathematicae 7, 381.
  • Thurston, W.: 1997, Three-Dimensional Geometry and Topology. Volume 1 (edited by Silvio Levy), Princeton University Press, Princeton, New Jersey.
  • Winkler, P.: 2004, Mathematical Puzzles. A Connoisseur’s Collection, A K Peters, Natick, Massachusetts.
  • Winkler, P.: 2007, Mathematical Mind-Benders, A K Peters, Ltd., Wellesley, MA.
  • Wise, G. L., Hall, E. B.: 1993, Counterexamples in Probability and Real Analysis, Oxford University Press, Oxford University Press.
  • Wojtylak, P.: 1979, An example of a finite though finitely non-axiomatizable matrix, Fundamentha Mathematicae 17, 39-46.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-issn-2450-341X-year-2014-volume-6-article-3663
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