ABSTRACT Mathematics is becoming increasingly specialized, divided into a vast and growing number of subfields. While this division of cognitive labor has important benefits, it also has a significant drawback: it can sometimes impede mathematical progress by making it difficult for mathematicians to make connections to subfields other than their own. Mathematicians can address this by making their own subfield more accessible to researchers working in other areas. One way they can do this is by engaging in exposition, as I illustrate with the User’s Guide Project in algebraic topology. However, the current reward structure of mathematics does not appropriately credit mathematicians who make their subfields more accessible via exposition. I thus conclude that the reward structure of mathematics should be changed to more highly value such work, with changes being adopted at the level of departments, professional societies and funding agencies.

中文翻译：

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日益专业化：为什么我们需要让数学更容易理解

摘要 数学正变得越来越专业化，被划分为越来越多的子领域。虽然这种认知劳动的分工有重要的好处，但它也有一个明显的缺点：它有时会阻碍数学进步，因为它使数学家难以与自己的子领域建立联系。数学家可以通过让其他领域的研究人员更容易接触到他们自己的子领域来解决这个问题。他们可以做到这一点的一种方法是参与说明，正如我在代数拓扑中的用户指南项目中所说明的那样。然而，当前的数学奖励结构并没有适当地归功于数学家，他们通过阐述使他们的子领域更容易接近。因此，我得出结论，数学的奖励结构应该改变为更加重视此类工作，