Doctoral Dissertation Research: Mathematics, Aesthetics, and Modernism in America

该奖项是一个博士论文改进补助金。它支持数学史上的一个项目，特别关注二十世纪的前几十年，这是数学发生深刻变化的时期。这一时期被定义为“数学现代主义”的概念，标志着一种正式的、抽象的数学方法的开始，这种方法导致了这门学科越来越多的自主性和专业化。它告知传统的观点，即数学现代主义的轨迹与这一时期艺术和建筑的平行转型发展是分开的。相比之下，这个项目将揭示数学现代主义和艺术中其他现代主义变革之间的一系列相互联系。它将提供一个新的视角，从中了解数学实践发生的各种背景。这个项目的结果将感兴趣STS学者，数学和科学的历史学家，以及现代美国的其他学者知识和文化史，包括艺术历史学家。它们将作为学术书籍和研究文章分发。更广泛地说，该项目将通过研究鲜为人知的数学教育方法，为正在进行的关于教育政策和科学传播的讨论做出贡献。它还将促进数学家和艺术家之间的研究基础设施的发展，重点是艺术家和数学家之间的富有成效的交流。1920年至1960年之间的现代主义和美学概念，以了解什么构成了数学实践，以及数学家如何理解他们的职业，艺术家它将历史化的自然主义概念的“数学现代主义”，数学家和历史学家经常利用从事数学史与以前被忽视的学术，特别是艺术史和美国的思想史。它还将通过质疑纯数学与应用数学以及艺术与科学等二元关系来质疑现代学科的历史。它将揭示数学家，艺术家和其他实践社区如何保持不断和不可预测的相互交流，从而导致对现代主义，学科形成和数学史的既定叙述的重新思考。现代主义将被视为试图超越形式和制度结构，并消除学科界限。恢复这段历史对于改变我们如何看待数学实践，美国科学院学科的知识组织以及数学知识本身的分类具有至关重要的意义。

General Audience Summary This award is a doctoral dissertation improvement grant. It supports a project in the history of mathematics specifically focusing on the first few decades of the twentieth century, a period of deep change in mathematics. That period has come to be defined by the concept of "mathematical modernism," designating the beginning of a formal, abstract approach to mathematics, an approach that led to the discipline's increasing autonomy and professionalization. It informs the conventional view that the trajectory of mathematical modernism is separate from parallel transformational developments in the arts and architecture during this time. By contrast, this project will bring to light a set of interconnections between mathematical modernism and other modernist transformations in the arts. It will provide a new perspective from which to understand the varied contexts in which mathematical practice takes place. The results of this project will interest STS scholars, historians of mathematics and science, and other scholars of modern U.S. intellectual and cultural history, including art historians. They will be disseminated as a scholarly book and research articles. More broadly, the project will contribute to on-going discussions about education policy and science communication by examining little-known approaches to mathematical education. It will also promote the development of research infrastructure among mathematicians and artists by focusing on productive exchanges between artists and mathematicians, Technical Summary This project examines the exchanges American mathematicians had with philosophical, artistic, and aesthetic notions of modernism between 1920 and 1960 in order to understand what constituted mathematical practice and how mathematicians understood their vocation in relation to artists. It will historicize the naturalistic conception of "mathematical modernism" that mathematicians and historians often draw upon by engaging the history of mathematics with previously neglected scholarship, particularly the history of art and US intellectual history. It will also problematize histories of modern disciplines by calling into question such binaries as pure vs. applied mathematics and the arts vs. sciences. It will reveal how mathematicians, artists, and other communities of practice remained in constant and unpredictable communication with each other, and thereby lead to a rethinking of established narratives of modernism, disciplinary formation, and the history of mathematics. Modernism then will be regarded as the attempt to move beyond formal and institutional structures and dissolve disciplinary boundaries. Recovering this history has crucial implications for changing how we view mathematical practice, the intellectual organization of disciplines in the American Academy, and the classification of mathematical knowledge itself.