Mathematical proof is the primary form of justification for mathematical knowledge, but in order to count as a proper justification for a piece of mathematical knowledge, a mathematical proof must be rigorous. What does it mean then for a mathematical proof to be rigorous? According to what I shall call the standard view, a mathematical proof is rigorous if and only if it can be routinely translated into a formal proof. The standard view is almost an orthodoxy among contemporary mathematicians, and is endorsed by many logicians and philosophers, but it has also been heavily criticized in the philosophy of mathematics literature. Progress on the debate between the proponents and opponents of the standard view is, however, currently blocked by a major obstacle, namely, the absence of a precise formulation of it. To remedy this deficiency, I undertake in this paper to provide a precise formulation and a thorough evaluation of the standard view of mathematical rigor. The upshot of this study is that the standard view is more robust to criticisms than it transpires from the various arguments advanced against it, but that it also requires a certain conception of how mathematical proofs are judged to be rigorous in mathematical practice, a conception that can be challenged on empirical grounds by exhibiting rigor judgments of mathematical proofs in mathematical practice conflicting with it.

数学证明是证明数学知识的主要形式，但是为了算作对一项数学知识的适当证明，数学证明必须是严格的。那么，严格的数学证明意味着什么？根据我称之为标准的观点，一个数学证明是严格的当且仅当它可以被常规翻译。成正式证明。标准观点在当代数学家中几乎是一种正统观点，得到了许多逻辑学家和哲学家的认可，但在数学哲学哲学中也受到了严厉的批评。然而，标准观点的支持者和反对者之间的辩论目前受到一个主要障碍的阻碍，即缺乏对标准观点的精确表述。为了弥补这一缺陷，我承诺在本文中提供一个精确的公式和对数学严谨性的标准观点的彻底评估。这项研究的结果是，标准观点比从各种反对它的论点中得到的批评更强大，但它还需要对如何在数学实践中判断数学证明是严格的有一定的概念，