https://orcid.org/0000-0001-9975-6120
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Abstract
This article discusses Jonathan Borwein’s writings on some of the dynamics between experimental mathematics and mathematics education. We demonstrate that over many years Borwein, in addition to becoming a leader in the use of computers in mathematical research, persistently and passionately promoted the symbiosis of the two. We also reflect on the relationship between mathematical thinking and experimental mathematics.
Keywords:
Acknowledgments
The authors wish to thank Ms. Pam Borghardt, Dr. Ozren Jungić, and Dr. Miroslav Lovrić for their contributions to improving the text.
Notes
1 Borwein also described himself as “computer-assisted quasi-empiricist.” [Citation10]
2 See, for example, [Citation22] for a possible summary of the important related developments in the 1970s and 1980s.
3 For a first-hand testimonial about the creation and the early history of MAPLE, see history.siam.org/oralhistories/gonnet.htm.
7 Heath attributes it to Theodorus of Cyrene, Plato’s teacher of mathematics [Citation24].
8 The above-quoted paragraph was written in 2003. The modern student may choose one of many freely available online applications that have been developed since.
9 Borwein used the same example in several of his publications. See, for example, Bailey et al. [Citation6], Borwein [Citation9, Citation12], and Borwein and Devlin [Citation15].
11 In 1998 Peter Taylor and Nathalie Sinclair conducted this experiment in a Grade 12 class [Citation34].
12 The Teacher Manual advises teachers that “it’s well worth making the effort to get hold of a car tire on a rim and keep it around for future years. The same hole will serve for many years.”
13 callysto.ca/
17 The paper also contains a collection of experimental mathematics in action-type examples accessible to first-year students.
Additional information
Notes on contributors
Veselin Jungić
Veselin Jungic has a Ph.D. in Pure Mathematics from Simon Fraser University and a M.Sc. in Mathematics from the University of Zagreb. He is a recipient of several teaching awards, including the 3M National Teaching Fellowship, the Canadian Mathematical Society Teaching Award, and the Pacific Institute for Mathematical Sciences Educational Award.
Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada
Andrijana Burazin
Andrijana Burazin has a Ph.D. in Applied Mathematics from the University of Waterloo and a M.Sc. in Mathematics from McMaster University. At the University of Toronto Mississauga (UTM), she has been providing mathematics support to undergraduate students at the Robert Gillespie Academic Skills Centre (RGASC), as well as a part of the Department of Mathematical and Computational Sciences, having taught several undergraduate mathematics courses at all levels. She is an Assistant Professor, Teaching Stream, and a Numeracy Specialist.
Robert Gillespie Academic Skills Centre and the Department of Mathematical and Computational Sciences, University of Toronto Mississauga, Mississauga, ON, L5L 1C6, Canada