Reflections in a cup of coffee

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 honor of Brouwer at the University of Amsterdam, we will explore how Brouwer's ideas about this phenomenon spilled 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.