Truly Seeing Mathematics: An Exploration of Mathematical Aspects through Ability, Skill, and Expertise

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2023
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Haverford College. Department of Philosophy
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Thesis
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Award
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eng
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Tri-College users only
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Abstract
Mathematics has been described as a form of synthetic a priori. This paper uses Wittgensteinian aspects to examine the realm of mathematics in ability, skill, and expertise. These categories show different degrees of mathematical comprehension. Aspects are meant to help us “see” meaning under the original concept of an object. This thesis aims to bring examples to light to support my claim that mathematics is not black and white. I hope to show how we can see mathematical aspects as they relate to matching identities, patterns, and constructions to gather a deeper understanding for why there are such differences between levels of mathematical knowledge. As a student continues to develop their mathematical familiarity, they take everything they have acquired from ability to skill to potentially becoming an expert one day. But rather than focusing on a linear relationship between these three categories, I hope to instead give an account of why these are distinct categories.
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