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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 Jungi?.

  • The illustrations were created by Lila Mohammed

  • The Bahasa Indonesia translation was completed by Listiarini Listiarini.

  • The Chinese translation was completed by Stephen Choi.

  • The French translation was completed by Julie Plante.

  • The Italian translation was completed by Cecilia Mundenge.

  • The Punjabi translation was completed by Tripatjit Kaur.

  • The Romanian translation was completed by Maria Vasiliu.

  • The Russian translation was completed by Liudmila Guseva.

  • The Serbian translation was completed by Zoran Jungi?.

  • The Spanish translation was completed by Elizabeth and Enrique Hern¨¢ndez-Zavaleta.

  • The Tamil translation was completed by Pamini Thangarajah.

  • The Tla'amin translation was completed by Ochele.

  • ¡°Small Number Around the World¡± was compiled by Veselin Jungi?.

The ¡°Small Number and the Red Kangaroo¡± story is inspired by a story that the author heard in 1974 from Dr. Fikret Vajzovi?, a professor of mathematics at the University of Sarajevo. In Dr. Vajzovi?'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:

  1. Gaining insight and intuition;
  2. Visualizing mathematical principles;
  3. Discovering new relationships;
  4. Testing and especially falsifying conjectures;
  5. Exploring a possible result to see if it merits formal proof;
  6. Suggesting approaches for formal proof;
  7. Replacing lengthy and error-prone hand derivations; and
  8. Confirming analytically derived results.