This essay was written by upper-sixth former Ben Watkins, and a finalist for the 2020 Independent Learning Assignment. The following provides a short abstract to the full essay, which can be found at the bottom.
Estimated read time of abstract: 1 minute
Estimated read time of essay: 15 minutes
Is it possible that there are always two places on earth with the same temperature and pressure? How does the game show Blockbusters have any implications on algebraic topology? Can a general equilibrium ever be reached in an economy? Perhaps most crucially of all, can you ever truly mix a cup of tea?
My ILA provides insight into Brouwer’s fixed point theorem, a theorem found in the field of algebraic topology. It uncovers how a remarkable and seemingly counterintuitive result in what is often considered to be an abstract field of mathematics can have such broad and pertinent results in the real world. However, this isn’t to say that this ILA doesn’t uncover the result of this theorem for the sake of the beauty of it as much as uncovering it for the sake of its applications. Indeed, Luitzen Egbertus Jan Brouwer himself (the discoverer of this theorem as well as often being called ‘the Father of Topology’) was very much an upholder of this mentality: that maths has great importance for the sake of maths itself. Philosophically, Brouwer was a neo-intuitionist, which means that he thought of mathematics as purely a mental phenomenon, the result of constructive mental activity rather than uncovering any principles of an objective reality. He is often quoted in saying that “The construction itself is an art, its application to the world an evil parasite.”
To view Ben’s full article, follow this link below.