Twórcza rola patologii w matematyce
Keywords:
pathological object, paradox, mathematical intuition, counterexampleAbstract
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.Downloads
Metrics
References
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.
Downloads
Published
How to Cite
Issue
Section
License
Read the full statement of the license to publish PDF file.
(see English version) (see Polish version)
