In a 2022 paper, Hamami claimed that the orthodox view in mathematics is that a proof is rigorous if it can be translated into a derivation. Hamami then developed a descriptive account that explains how mathematicians check proofs for rigor in this sense and how they develop the capacity to do so. By exploring introductory texts in computability theory, we demonstrate that Hamami’s descriptive account does not accord with actual mathematical practice with respect to computability theory. We argue instead for an alternative account in which imagination, anticipation, and interpretations of natural language play roles in establishing mathematical rigor.

中文翻译：

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想象力和预期在接受可计算性证明中的作用：对严格标准帐户的挑战

在 2022 年的一篇论文中，Hamami 声称，数学中的正统观点是，如果可以将证明转化为推导，则证明是严格的。Hamami 随后开发了一个描述性说明，解释了数学家如何在这个意义上检查证明的严谨性，以及他们如何培养这样做的能力。通过探索可计算性理论的介绍性文本，我们证明了 Hamami 的描述性说明在可计算性理论方面不符合实际的数学实践。相反，我们主张另一种解释，其中自然语言的想象、预期和解释在建立数学严谨性方面发挥作用。