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

本奖项为博士学位论文改进奖。它支持数学史上的一个项目，专门关注20世纪的头几十年，这是数学的深刻变革时期。这一时期已经被“数学现代主义”的概念所定义，它标志着一种正式的、抽象的数学方法的开始，这种方法导致了该学科日益增强的自主性和职业化。它告诉传统观点，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，这个项目将揭示出数学现代主义和艺术中其他现代主义转变之间的一系列相互联系。它将提供一个新的视角，从这个角度来理解数学实践发生的各种背景。这一项目的结果将引起STS学者、数学和科学历史学家以及包括艺术历史学家在内的其他美国现代知识分子和文化史学者的兴趣。它们将以学术书籍和研究文章的形式传播。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交流的讨论做出贡献。它还将通过关注艺术家和数学家之间的富有成效的交流，促进数学家和艺术家之间研究基础设施的发展。这个项目考察了1920至1960年间美国数学家与现代主义哲学、艺术和美学概念的交流，以了解什么是数学实践，以及数学家如何理解他们与艺术家有关的职业。数学家和历史学家通过将数学史与以前被忽视的学术联系起来，特别是艺术史和美国思想史，将把数学家和历史学家经常利用的自然主义的“数学现代主义”概念历史化。它还将通过质疑纯数学与应用数学、艺术与科学等二元论来使现代学科的历史产生问题。它将揭示数学家、艺术家和其他实践社区如何保持着持续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事的重新思考。到那时，现代主义将被视为试图超越正式和体制结构，消除学科界限。恢复这段历史对于改变我们看待数学实践的方式、美国科学院学科的智力组织以及数学知识本身的分类具有至关重要的影响。

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.