Skip to main content
Springer Nature Link
Log in

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

  • Published:
International Journal of Computers for Mathematical Learning Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  • 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.

  • Borwein J.M., Bailey D.H., (2003). Mathematics by Experiment: Plausible Reasoning in the 21st Century. AK Peters Ltd.

  • Borwein J.M., Bailey D.H., Girgensohn R., (2004). Experimentation in Mathematics: Computational Paths to Discovery. AK Peters Ltd.

  • Borwein, J. M., (2004). “Aesthetics for the Working Mathematician,” in Beauty and the Mathematical Beast, in press (2004). [CECM Preprint 01:165].

  • J.M. Borwein P.B. Borwein (2001) ArticleTitleChallenges for mathematical computing Computing in Science and Engineering 3 48–53

    Google Scholar 

  • J.M. Borwein P.B. Borwein R. Girgensohn S. Parnes (1996) ArticleTitleMaking sense of experimental mathematics Mathematical Intelligencer 18 IssueID4 12–18 Occurrence HandleMR1413248

    MathSciNet  Google Scholar 

  • J.M. Borwein D.M. Bradley (1997) ArticleTitleEmpirically determined Apéry-like formulae for Zeta(4n+3) Experimental Mathematics 6 181–194

    Google Scholar 

  • M.J. Borwein R. Corless (1999) ArticleTitleEmerging tools for experimental mathematics American Mathematical Monthly 106 889–909

    Google Scholar 

  • J.M. Borwein P. Lisonek (2000) ArticleTitleApplications of integer relation algorithms Discrete Mathematics (Special issue for FPSAC 1997 IssueID217 65–82 Occurrence Handle10.1016/S0012-365X(99)00256-3

    Article  Google Scholar 

  • J. Dongarra F. Sullivan (2000) ArticleTitleThe top 10 algorithms Computing in Science and Engineering 2 22–23 Occurrence Handle10.1109/MCISE.2000.814652

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Canada Research Chair, Director Dalhousie DRIVE Dalhousie University, Halifax, NS, Canada

    Jonathan M. Borwein

Authors
  1. Jonathan M. Borwein
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Jonathan M. Borwein.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Borwein, J.M. The Experimental Mathematician: the Pleasure of Discovery and the Role of Proof. Int J Comput Math Learning 10, 75–108 (2005). https://doi.org/10.1007/s10758-005-5216-x

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10758-005-5216-x

Keywords