In this paper, I propose that applying the methods of data science to “the problem of whether mathematical explanations occur within mathematics itself” (Mancosu 2018) might be a fruitful way to shed new light on the problem. By carefully selecting indicator words for explanation and justification, and then systematically searching for these indicators in databases of scholarly works in mathematics, we can get an idea of how mathematicians use these terms in mathematical practice and with what frequency. The results of this empirical study suggest that mathematical explanations do occur in research articles published in mathematics journals, as indicated by the occurrence of explanation indicators. When compared with the use of justification indicators, however, the data suggest that justifications occur much more frequently than explanations in scholarly mathematical practice. The results also suggest that justificatory proofs occur much more frequently than explanatory proofs, thus suggesting that proof may be playing a larger justificatory role than an explanatory role in scholarly mathematical practice.

中文翻译：

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数学实践中的证明、解释和论证

在本文中，我建议将数据科学方法应用于“数学本身是否存在数学解释的问题”（Mancosu 2018）可能是阐明该问题的一种富有成效的方式。通过仔细选择用于解释和论证的指示词，然后在数学学术著作数据库中系统地搜索这些指示词，我们可以了解数学家在数学实践中如何使用这些术语以及使用频率。这项实证研究的结果表明，数学解释确实出现在发表在数学期刊上的研究文章中，正如解释指标的出现所表明的那样。然而，与使用理由指标相比，数据表明，在学术数学实践中，理由比解释更频繁地出现。结果还表明，证明性证明比解释性证明出现得更频繁，因此表明证明在学术数学实践中可能扮演着比解释性作用更大的证明作用。