  Allegedly, Brouwer discovered his famous fixed point theorem while stirring a
cup of coffee and noticing that there is always at least one point in the
liquid that does not move. In this paper, based on a talk in honour of Brouwer
at the University of Amsterdam, we will explore how Brouwer's ideas about this
phenomenon spilt over in a lot of different areas of mathematics and how this
eventually led to an intriguing geometrical theory we now know as mirror
symmetry.
