What counts as mathematics?

In 2003-6 we hosted 4 symposia at UWO, sponsored by the Fields Institute, exploring the connections between mathematics and narrative.
One of our keynote speakers was Apostolos Doxiadis, a math prodigy who became an author and filmaker. His most recent book is Logicomix.
Doxiadis said that mathematics education will not change unless what counts as mathematics first changes.
What needs to also count as mathematics, he suggested, are the stories of mathematics. 
In January, Richard Barwell (University of Ottawa) did an interesting presentation at the Fields Institute on "How mathematicians talk about mathematics." One thing he shared was part of a transcript he created  of  Marcus du Sautoy (University of Oxford) and Ian Stewart (University of Warwick) speaking on BBC program In Our Time about the Poincare Conjecture.
Richard was kind enough to share the transcript with me, and I used it to create the song below.
Whis is this song? Is it a story? Is it mathematics? Is it both? What do you think?

We actually had three different versions of this song before we settled on this one - which is now one of my favourire Joy of X songs!