ABC Ockham’s Razor: Endnotes

I was on the radio this morning, talking about the power of mathematical stories.

Ockham’s Razor is a ~10 minute program, broadcast each Sunday on ABC Radio National—and webcast around the world—to provide “a soapbox for all things scientific: stories, insights, arguments or tributes”. I was one of eight speakers recorded at a live event in November 2022, and my story was broadcast on Sunday 4 December.

The talk is quite different to my recent blog post, despite being on the same theme. You can listen to the episode here, and download the script of the talk here.

Naturally, I couldn’t give due credit to all my sources during the talk, so here they are. I encourage you to follow them up.

Paragraphs 3-5, “I want to put you in a mathematical story now. Imagine you have a large pile of treasure …”
All credit to Sam Shah who wrote a blog post detailing this wonderful approach for building intuition around infinite geometric stories. I love to do this activity with students. For the radio, I just turned the paper gift into a large pile of treasure. The rest of the story closely follows Sam’s narrative.

Paragraphs 6-7, “In his wonderful book ‘The Mathematics of Human Flourishing’, the American mathematician and college professor Francis Su …”
Francis’ book will expand your view of what mathematics is, who it is for and why an inclusive approach is important. In Chapter 3 on ‘Meaning’, Francis frames mathematical explanations as stories (e.g. geometric, significance, historical, explanatory, physical, experiential), which has shaped the way I think about developing student understanding and sense making.

Paragraph 8, “One of our greatest mathematicians, Adelaide-born Terry Tao, tells an anecdote in which his aunt walked into her living room to find him rolling around on the floor with his eyes closed. …”
I included this anecdote at the last moment, and I’m so glad I did as the audience was visibly surprised that a prominent mathematician would use an informal and impromptu approach to building intuition. You can read more of the story in the Sydney Morning Herald article; the entire profile of Terry Tao is delightful reading.

Paragraph 9, “Being able to move flexibly between representations deepens understanding. […] It’s like the parable of the blindfolded men encountering an elephant.”
Preety Tripathi wrote an excellent article about developing mathematical understanding through multiple representations (link to JSTOR) that I have used for years in my teaching. I borrowed Tripathi’s analogy of the parable of the blindfolded men encountering an elephant. That story is also on Wikipedia.

Paragraph 10, “In the West this is known as Pascal’s triangle, named after French mathematician Blaise Pascal. However the same triangular arrangement of numbers is found in the texts of many other cultures, including Indian, Persian, and Chinese—hundreds of years before being published by Pascal.” 
For years, I have been encountering mentions on Twitter of the book ‘The Crest of the Peacock: Non-European Roots of Mathematics’ by JG Gheverghese (link to JSTOR). Chapter 7 is dedicated to Special Topics in Chinese Mathematics, with the invention of the ‘arithmetical triangle’ in different cultures discussed on page 270. The Wikipedia entry has some wonderful depictions of the triangle from different cultures.

Paragraph 11, “In 2014, a survey found that a quarter of people in Europe were unable to name a single female scientist— living or dead.”
The survey is mentioned in the article ‘Could you name more than one female scientist?’ by Chris Green in The Independent on Sunday 17 May 2014.

Paragraph 11, “The t-shirt I am wearing is an Australian version of the MathGals project, designed to raise awareness of past and present women in mathematics.”
The #MathGals project is the brainchild of Chrissy and Cora Newell. An Australian version of the t-shirt was launched to raise funds for the 2019-2020 Australian bushfire season, which devastated communities, farmland and bushland, and in which 33 people and countless animals lost their lives. The twitter thread below introduces the eight Australian women featured on the t-shirt.

Paragraph 12, “I will make special mention of Alison Doig Harcourt AO, now 92 and still active at The University of Melbourne.”
There are multiple excellent sources to find out more about Alison.
Short: Wikipedia article
Medium: ABC News article
Long: A public lecture, given for Ada Lovelace Day in 2021 by Alison Harcourt and Professor Kate Smith-Miles. Kate and Alison talk about the development of optimisation methods, and of Alison’s work.

I also encourage you to go to Google Videos and type in Alison’s name. There are many good, short videos featuring Alison.

Paragraph 14, “And finally we come to perhaps the most important mathematical story—our own. How would you characterise yours? As a mystery? A foreign language? A romance? Or perhaps it feels more like a horror story.”
Thanks to everyone who gave me ideas for literary genres for mathematics, including in person and on this Twitter thread. I wanted to weave in ‘Choose Your Own Adventure’ (thanks Rachael and Jo-ann!), but it didn’t make the final version.

What mathematical stories are important to you? I’d love for you to share!

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