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 鈥淲hy do I think of Jonathan Borwein whenever I hear the words 鈥渕athematical thinking鈥�?鈥� at the AMSI/AustMS Workshop on Mathematical Thinking, University of Newcastle, Newcastle, NSW, Australia, 2018.
This story was written by Veselin Jungi膰.
The illustrations were created by Lila Mohammed
The French translation was completed by Julie Plante.
The 鈥淪mall Number and the Red Kangaroo鈥� story is inspired by a story that the author heard in 1974 from Dr. Fikret Vajzovi膰, a professor of mathematics at the University of Sarajevo. In Dr. Vajzovi膰'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 鈥渆conomists are not real scientists鈥� and that 鈥渓ogicians think more clearly, but mathematicians are best.鈥�
In a 2015 article entitled 鈥淓xperimental Mathematics in the Society of the Future鈥�, 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.