Mathematics is often treated as different from other disciplines, since arguments in the field rely on deductive proof rather than empirical evidence as in the natural sciences. A mathematical paper can therefore, at least in principle, be replicated simply by reading it. While this distinction is sometimes taken as the basis to claim that the results in mathematics are therefore certain, mathematicians themselves know that the published literature contains many mistakes. Reading a proof is not easy, and checking whether an argument constitutes a proof is surprisingly difficult. This article uses peer review of submissions to mathematics journals as a site where referees are explicitly concerned with checking whether a paper is correct and therefore could be published. Drawing on 95 qualitative interviews with mathematics journal editors, as well as a collection of more than 100 referee reports and other correspondence from peer review processes, this article establishes that while mathematicians acknowledge that peer review does not guarantee correctness, they still value it. For mathematicians, peer review 'adds a bit of certainty', especially in contrast to papers only submitted to preprint servers such as arXiv. Furthermore, during peer review there can be disagreements not just regarding the importance of a result, but also whether a particular argument constitutes a proof or not (in particular, whether there are substantial gaps in the proof). Finally, the mathematical community is seen as important when it comes to accepting arguments as proofs and assigning certainty to results. Publishing an argument in a peer-reviewed journal is often only the first step in having a result accepted. Results get accepted if they stand the test of time and are used by other mathematicians.

中文翻译：

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检查数学同行评审的正确性。

数学通常被视为与其他学科不同，因为该领域的论证依赖于演绎证明，而不是像自然科学中的经验证据。因此，至少在原则上，一篇数学论文可以通过阅读来复制。虽然这种区别有时被视为数学结果是确定的基础，但数学家自己也知道已发表的文献包含许多错误。阅读证明并不容易，而检查一个论证是否构成证明则出人意料地困难。本文使用对数学期刊提交的同行评审作为一个网站，审稿人明确关注检查论文是否正确并因此可以发表。本文基于对数学期刊编辑的 95 次定性访谈，以及 100 多份审稿报告和同行评审过程中的其他信件的集合，表明虽然数学家承认同行评审不能保证正确性，但他们仍然重视它。对于数学家来说，同行评审“增加了一点确定性”，特别是与仅提交给 arXiv 等预印本服务器的论文相比。此外，在同行评审期间，不仅可能会在结果的重要性方面存在分歧，而且还会在特定论点是否构成证明（特别是证明中是否存在重大差距）方面存在分歧。最后，在接受论证作为证明并为结果赋予确定性方面，数学界被认为非常重要。在同行评审期刊上发表论点通常只是结果被接受的第一步。如果结果经得起时间的考验并被其他数学家使用，那么它们就会被接受。