Mathematical Theory Development in America

该奖项支持数学史的博士论文研究项目。它使用假设理论，一种数学基础的方法，寻找并建立支配特定数学领域的基本假设（或原理），作为了解 20 世纪上半叶数学与美国社会之间关系的窗口。目的是展示二十世纪初期数学与社会之间的关系如何帮助建立今天参与数学界的障碍。与文化和多样性问题密切相关的是关于数学教育和公众参与挑战的持续辩论。这项研究对 20 世纪初数学教育辩论的分析将突出这些辩论中的许多重要因素，这些因素在起草和审议当前政策时需要考虑。该项目解决了三个主要研究问题：对数学基础的探索如何影响 1900 年代初美国数学的意义和价值？在那段时期，美国是如何重新定义专业数学的边界的？美国数学家的文化认同和公众形象如何随着进步时代的等级和差异概念而变化？这些问题将通过对机构和公共媒体档案以及从事假设研究的个别数学家的工作的分析来回答。总体目的是通过将美国数学在二十世纪初的发展置于美国社会的背景下，进一步了解美国数学的发展。通过探索美国进步时代专业数学家的形象和地位，以及对谁被认为能够对数学知识做出贡献的历史看法，这项研究将揭示美国科学中包容性和文化认同的动态。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

This award supports a doctoral dissertation research project in the history of mathematics. It uses postulate theory, an approach to the foundations of mathematics that searches for and establishes the basic postulates (or principles) that govern a particular mathematical field, as a window into the relationship between mathematics and American society during the first half of the 20th Century. The goal is to show how the relationship between mathematics and society in the early twentieth century helped erect barriers to participation in the mathematics community today. Closely tied to culture and diversity issues are ongoing debates about math education and the challenge of public engagement. This study's analysis of math education debates in the early twentieth century will highlight the many factors that are at stake in such debates, which are important to consider when drafting and deliberating current policy.The project addresses three primary research questions: How did the exploration of the foundations of mathematics inform the meaning and value of American mathematics in the early 1900s? How were the boundaries of professional mathematics redefined in the US during that time? How did the cultural identity and public image of American mathematicians change alongside Progressive Era conceptions of hierarchy and difference? These questions will be answered through the analysis of institutional and public media archives as well as the work of individual mathematicians engaged in the study of postulates. The overall purpose is to further understand the development of American mathematics by situating its early-twentieth-century growth within the context of American society. By exploring the image and status of professional mathematicians in the Progressive Era United States alongside historical perceptions of who was thought capable of contributing to mathematical knowledge, this study will shed light on the dynamics of inclusivity and cultural identity in American science.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.