TL;DR
This paper explores the historical and mathematical development of Brouwer's fixed point theorem, illustrating its influence on various fields including the emergence of mirror symmetry in geometry.
Contribution
It traces the evolution of Brouwer's ideas from a coffee cup analogy to their impact on modern mathematical theories like mirror symmetry.
Findings
Brouwer's fixed point theorem originated from a coffee cup analogy.
The theorem influenced multiple areas of mathematics.
Mirror symmetry emerged as a geometric theory related to Brouwer's ideas.
Abstract
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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematics and Applications · Homotopy and Cohomology in Algebraic Topology