TL;DR
This paper explores the unique nature of mathematical reasoning, emphasizing its role as a system of conventions and norms that facilitate understanding and reasoning, with insights from theorem proving and history.
Contribution
It offers a philosophical perspective on mathematics as a designed system, highlighting how its effectiveness depends on underlying conventions and norms.
Findings
Mathematical reasoning is characterized by conventions and norms.
The philosophy of mathematics helps understand principles of effective reasoning.
Mathematics can perform well or poorly depending on its design.
Abstract
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes that we view mathematics as a system of conventions and norms that is designed to help us make sense of the world and reason efficiently. Like any designed system, it can perform well or poorly, and the philosophy of mathematics has a role to play in helping us understand the general principles by which it serves its purposes well.
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Taxonomy
TopicsHistory and Theory of Mathematics