Celebrating our mathematical thinking

The Way Mathematicians Bend Space

This song was written by George Gadanidis (Univ. of Western Ontario) from a transcript by Richard Barwell (Univ. of Ottawa) of Marcus du Sautoy (Univ. of Oxford) and Ian Stewart (Univ. of Warwick) speaking on BBC program In Our Time about the Poincare Conjecture
see a live performance of this song, with grades 3-6 students

we live in a three dimensional space
a particular three dimensional space
in a fairly small bit of it
we don’t explore huge amounts
we don’t explore huge amounts

so how is our universe wrapped up?
it might be a flat universe
where it just sort of goes on forever
that’s what most people think

or it’s closed up in some way
such that if I keep on looking
I’ll actually eventually see the back of my head
see the back of my head

Poincaré was interested in what possible shapes
the universe could be wrapped up in
could it be a big hyper football?
or bend like a hyper bagel?

we live in a three dimensional space
a particular three dimensional space
in a fairly small bit of it
we don’t explore huge amounts
we don’t explore huge amounts

now the way mathematicians bend
three dimensional space
actually they don’t bend it at all
they slice it into bits

then they tell you
how conceptually you glue
the pieces together again

you work out how all the pieces
fit together edge to edge
do a massive mathematical simplification
and you end up discovering
you can simplify the structure

we live in a three dimensional space
a particular three dimensional space
in a fairly small bit of it
we don’t explore huge amounts
we don’t explore huge amounts