Chapter 13 Small Number and the Red Kangaroo
A Tribute to Jonathan Borwein, 1951-2016, one of the founders of Experimental Mathematics
Presented at as part of the keynote presentation “Why do I think of Jonathan Borwein whenever I hear the words “mathematical thinking”?” at the AMSI/AustMS Workshop on Mathematical Thinking, University of Newcastle, Newcastle, NSW, Australia, 2018
This story was written by Veselin Jungic (SFU) and Mark MacLean (UBC)
The illustrations were created by Lila Mohammed
The “Small Number and the Red Kangaroo” story is inspired by a story that the first author heard from Dr. Fikret Vajzović, a professor of mathematics at the University of Sarajevo, in 1974. In Dr. Vajzović’s story the three characters were a physicist, a mathematician, and a mathematician-logician. A version of the same story, with the characters of an economist, a logician, and a mathematician, appears in the novel The Curious Incident of the Dog in the Night-Time written by Mark Haddon and published by Doubleday Canada, Toronto, in 2002. Christopher, the main character of the novel, observes that “economists are not real scientists” and that “logicians think more clearly, but mathematicians are best.”
In a 2015 article entitled “Experimental Mathematics in the Society of the Future”, David H. Bailey and Jonathan Borwein described experimental mathematics in the following way: By experimental mathematics we mean the following computationally assisted approach to mathematical research:
- Gaining insight and intuition;
- Visualizing mathematical principles;
- Discovering new relationships;
- Testing and especially falsifying conjectures;
- Exploring a possible result to see if it merits formal proof;
- Suggesting approaches for formal proof;
- Replacing lengthy and error-prone hand derivations; and
- Confirming analytically derived results.
Click here to learn more about the mathematical concepts, cultural themes, and Indigenous languages explored in the Small Number stories. Discover teaching resources to help incorporate Small Number into your classroom.