Understanding, formal verification, and the philosophy of mathematics

zbMATH Open1273.00032arXiv1505.07238MaRDI QIDQ2851818

Jeremy Avigad

Publication date: 4 October 2013

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.

Full work available at URL: https://arxiv.org/abs/1505.07238

Mathematics Subject Classification ID

Philosophy of mathematics (00A30) Mechanization of proofs and logical operations (03B35)

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