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The Experimental Mathematician: the Pleasure of Discovery and the Role of Proof

  • Jonathan M. BorweinEmail author
Article

Abstract

The emergence of powerful mathematical computing environments, the growing availability of correspondingly powerful (multi-processor) computers and the pervasive presence of the internet allow for mathematicians, students and teachers, to proceed heuristically and ‘quasi-inductively’. We may increasingly use symbolic and numeric computation, visualization tools, simulation and data mining. The unique features of our discipline make this both more problematic and more challenging. For example, there is still no truly satisfactory way of displaying mathematical notation on the web; and we care more about the reliability of our literature than does any other science. The traditional role of proof in mathematics is arguably under siege – for reasons both good and bad.

Keywords

aesthetics constructivism experimental mathematics humanist philosophy insight integer relations proof 

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References

  1. Bailey D.H., Borwein J.M., (2000). Experimental mathematics: Recent developments and future outlook. In: Engquist B., Schmid W., (eds) Mathematics Unlimited – 2∞1 and Beyond (Vol. 1, pp. 51–66). Springer-Verlag. [CECM Preprint 99:143].36.Google Scholar
  2. Borwein J.M., Bailey D.H., (2003). Mathematics by Experiment: Plausible Reasoning in the 21st Century. AK Peters Ltd.Google Scholar
  3. Borwein J.M., Bailey D.H., Girgensohn R., (2004). Experimentation in Mathematics: Computational Paths to Discovery. AK Peters Ltd.Google Scholar
  4. Borwein, J. M., (2004). “Aesthetics for the Working Mathematician,” in Beauty and the Mathematical Beast, in press (2004). [CECM Preprint 01:165].Google Scholar
  5. Borwein, J.M., Borwein, P.B. 2001Challenges for mathematical computingComputing in Science and Engineering34853[CECM Preprint 00:160]Google Scholar
  6. Borwein, J.M., Borwein, P.B., Girgensohn, R., Parnes, S. 1996Making sense of experimental mathematicsMathematical Intelligencer181218[CECM Preprint 95:032]MathSciNetGoogle Scholar
  7. Borwein, J.M., Bradley, D.M. 1997Empirically determined Apéry-like formulae for Zeta(4n+3)Experimental Mathematics6181194[CECM 96:069]Google Scholar
  8. Borwein, M.J., Corless, R. 1999Emerging tools for experimental mathematicsAmerican Mathematical Monthly106889909[CECM Peprint 98:110]Google Scholar
  9. Borwein, J.M., Lisonek, P. 2000Applications of integer relation algorithmsDiscrete Mathematics (Special issue for FPSAC19976582[CECM Preprint 97:104]CrossRefGoogle Scholar
  10. Dongarra, J., Sullivan, F. 2000The top 10 algorithmsComputing in Science and Engineering22223(See www.cecm.sfu.ca/personal/jborwein/algorithms.html)CrossRefGoogle Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Canada Research ChairDirector Dalhousie DRIVE Dalhousie UniversityHalifaxCanada

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