Abstract I focus on specific practices in twentieth- and twenty-first-century mathematics of articulating, barring, taming, and operating with what mathematicians widely call mathematical monsters. I describe how over centuries the quotidian procedures of the epitome of rational practice – mathematics – have produced beings outside the extant purified categories understood by theorems and proofs, despite, and sometimes as a consequence of, ever greater precision and rigor. However, mathematical monsters stand in a different relation to their makers than socio-economic and moral monsters who are barred from the world. Indeed, we will see how mathematicians have made plural and productive accommodation with their monsters. Although some mathematicians have been persuaded by logicians to bar monsters from the temple of mathematics by simply forbidding the operations that engender beings against nature, most mathematicians have accommodated or simply cohabited with their monsters by extending axioms, definitions, theorems, and methods of proving theorems as a part of quotidianized practice.

中文翻译：

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负数的平方根是虚数

摘要 我专注于 20 世纪和 21 世纪数学中的具体实践，即表达、禁止、驯服和使用数学家广泛称为数学怪物的东西。我描述了几个世纪以来，理性实践的缩影——数学——的日常程序如何产生了定理和证明所理解的现存纯化范畴之外的存在，尽管，有时是由于越来越精确和严格的结果。然而，数学怪物与其制造者的关系不同于被禁止进入世界的社会经济和道德怪物。事实上，我们将看到数学家如何与他们的怪物进行多元化和富有成效的适应。