, Volume 21, Issue 1, pp 28–35 | Cite as

Aspects of the pluralistic nature of mathematics

  • I. Kleiner
  • N. Movshovitz-Hadar


Pluralistic Nature 
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  1. Bottazini, U. (1986).The higher calculus: A history of real and complex analysis from Euler to Weierstrass. New York: Springer-Verlag.Google Scholar
  2. Boyer, C. B. (1954). Analysis: Notes on the evolution of a subject and a name.Mathematics Teacher,47, 450–462.Google Scholar
  3. Boyer, C. B. (1989).A history of mathematics (2nd ed., revised by U. Merzbach). New York: John Wiley & Sons.Google Scholar
  4. Cipra, B. (1988, December). Computer search solves an old math problem.Science,242(16), 1507–1508.Google Scholar
  5. Davis, P. J. (1965).The mathematics of matrices. Waltham, MA: Blaisdell.Google Scholar
  6. Davis, P. J., & Hersh, R. (1981).The mathematical experience. Boston: Birkhäuser.Google Scholar
  7. Dedekind, R. (1963). The nature and meaning of numbers. In hisEssays on the theory of numbers (pp. 31–115). New York: Dover.Google Scholar
  8. Dieudonn'e, J. (1973, Jan./Feb.). Should we teach “modern” mathematics?.American Scientist,61, 16–19.Google Scholar
  9. Edwards, C. H. (1979).The historical development of the calculus. New York: Springer-Verlag.Google Scholar
  10. Edwards, H. M. (1987). Dedekind's invention of ideals. In E. R. Phillips (Ed.),Studies in the history of mathematics (pp. 8–20). Mathematical Association of America.Google Scholar
  11. Fraser, C. G. (1989). The calculus as algebraic analysis: Some observations on mathematical analysis in the 18th century.Archive for History of Exact Sciences,39, 317–335.Google Scholar
  12. Hacking, I. (1980). Proof and eternal truths: Descartes and Leibniz. In S. Gaukroger (Ed.),Descartes: Philosophy, mathematics and physics (pp. 169–180). Totowa, N.J.: Barnes & Noble.Google Scholar
  13. Hankins, T. L. (1980).Sir William Rowan Hamilton. Baltimore: The Johns Hopkins University Press.Google Scholar
  14. Kleiner, I. (1989). Evolution of the function concept: A brief survey.Colleges Mathematics Journal,20, 282–300.Google Scholar
  15. Kline, M. (1972).Mathematical thought from ancient to modern times. New York: Oxford University Press.Google Scholar
  16. Kolata, G. B. (1976, June). Mathematical proofs: The genesis of reasonable doubt.Science,192, 989–990.Google Scholar
  17. Langer, R. E. (1947). Fourier's series: The genesis and evolution of a theory. The first Herbert Ellsworth Slaught memorial paper, Mathematical Association of America. (Supplement to vol. 54 of theAmerican Mathematical Monthly, pp. 1–86.)Google Scholar
  18. Lützen, J. (1978). The development of the concept of function from Euler to Dirichlet (in Danish).Nordisk. Mat. Tidskr. 25/26, 5–32.Google Scholar
  19. Mahoney, M. S. (1981). Descartes: Mathematics and physics. In C. C. Gillispie (Ed.),Dictionary of scientific biography (vol. 4) (pp. 55–61). New York: Charles Scribner's Sons.Google Scholar
  20. Moore, G. H. (1982).Zermelo's axiom of choice: Its origins, development, and influence. New York: Springer-Verlag.Google Scholar
  21. Neuenschwander, E. (1981). Studies in the history of complex function theory II: Interactions among the French School, Riemann, and Weierstrass.Bulletin of the American Mathematical Society,5(2), 87–105.Google Scholar
  22. Neugebauer, O. (1969).The exact sciences in antiquity (2nd ed.). New York: Dover.Google Scholar
  23. Pederson, O. (1974). Logistics and the theory of functions: An essay in the history of Greek mathematics.Arch. Intern. d'Hist. des Sci.,24, 29–50.Google Scholar
  24. Peterson, I. (1988).The mathematical tourist: Snapshots of modern mathematics. New York: W. H. Freeman.Google Scholar
  25. Poincaré, H. (1952). The future of mathematics. In hisScience and Method (pp. 25–45). New York: Dover.Google Scholar
  26. Pycior, H. M. (1981). George Peacock and the British origins of symbolical algebra.Historia Mathematica,8, 23–45.Google Scholar
  27. Ravetz, J. R. (1961). Vibrating strings and arbitrary functions. InThe logic of personal knowledge: Essays presented to M. Polanyi on his seventieth birthday (pp. 71–88). New York: The Free Press.Google Scholar
  28. Rosenfeld, B. A. (1988).A history of non-Euclidean geometry (A. Shenitzer, Trans.). New York: Springer-Verlag.Google Scholar
  29. Seidenberg, A. (1962).Lectures in projective geometry. New York: Van Nostrand.Google Scholar
  30. Shenitzer, A. (in press). The Cinderella career of projective geometry.The Mathematical Intelligencer.Google Scholar
  31. Steen, L. A. (1986). Living with a new mathematical species.The Mathematical Intelligencer,8(2), 33–40.Google Scholar
  32. Steen, L. A. (1988, Apr. 29). The science of pattern.Science,240, 611–616.Google Scholar
  33. Stewart, I. (1986). Frog and mouse revisited: A review of....The Mathematical Intelligencer,8(4), 78–82.Google Scholar
  34. Struik, D. J. (1987).A concise history of mathematics (4th revised edition). New York: Dover.Google Scholar
  35. Thom, R. (1971, Nov./Dec.). Modern mathematics: An educational and philosophical error?American Scientist,59, 695–699.Google Scholar
  36. von Neumann, J. (1963). The role of mathematics in the sciences and in society. In A. H. Taub (Ed.),Collected works (vol. 6) (pp. 477–490). New York: Macmillan.Google Scholar
  37. Weyl, H. (1946). Mathematics and logic.American Mathematical Monthly,53, 2–13.Google Scholar
  38. Wilder, R. L. (1967). The role of the axiomatic method.American Mathematical Monthly,74, 115–127.Google Scholar

Copyright information

© The Ontario Institute for Studies in Education 1990

Authors and Affiliations

  • I. Kleiner
    • 1
    • 2
  • N. Movshovitz-Hadar
    • 1
    • 2
  1. 1.York UniversityToronto
  2. 2.Israel Institute of TechnologyHaifa

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