The Culture of Abstract Algebra: Conceptual Languages and Working Styles in Representation Theory in the Second Half of the 20th Century

抽象代数文化：20世纪下半叶表示论的概念语言和工作方式

• 批准号: 1020169
• 负责人: Vyacheslav Gerovitch
• 金额: $ 15.89万
• 依托单位: Gerovitch Vyacheslav
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-15 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1020169&HistoricalAwards=false
• 关键词: Culture; Abstract; Algebra; Conceptual; Languages

IntroductionThis collaborative project will examine the social and cultural factors affecting the direction, scope, and priorities of recent research in representation theory, one of the most actively developing and technically difficult areas of abstract algebra.Intellectual MeritUsing oral history interviews, discourse analysis, and the study of primary sources, this study will address cultural practices of the mathematical community in two major aspects: The role of algebraic theories as conceptual languages, and the interaction of different mathematical styles in representation theory. This project will examine whether patterns in actual research practice correspond to the following stylistic oppositions: Problem-solving and conceptualism; abstraction and tangibility; conceptualization and computation; minimalism and freedom of choice; and speculation and rigor. Using the Gelfand seminar at Moscow State University as a case study, this project will examine the role of a national context in shaping mathematical practice and will explore the ramifications of cross-cultural contacts between the descendants of different research schools.Potential Broader ImpactsThe project results are likely to be useful to historians and philosophers of science interested in connections between communication modes and research styles, or in the cross-disciplinary contacts between pure mathematics and theoretical physics, or in the role of local and national contexts in shaping mathematical practice. The project will also serve to facilitate opening the esoteric practice of abstract mathematics to a wider audience, fostering better understanding and appreciation of advanced mathematics in broader culture, and helping attract talented high school students to the field of mathematics. The proposed analysis of mathematical practices that render highly abstract concepts "tangible" would help devise new educational techniques to help student?s master advanced mathematical constructions. By providing an accessible account of recent mathematical practice from the perspective of cultural history of science, this project will also facilitate a broader cultural dialogue between mathematicians and humanists.

简介这个合作项目将研究影响表示论近期研究方向、范围和优先事项的社会和文化因素，表示论是抽象代数最活跃发展和技术上最困难的领域之一。智力价值本研究将通过口述历史访谈、话语分析和原始资料研究，从两个主要方面解决数学界的文化实践：代数理论作为概念语言的作用以及相互作用。 表示论中不同数学风格的研究。该项目将检验实际研究实践中的模式是否符合以下风格上的对立：解决问题和概念主义；抽象性和有形性；概念化和计算；极简主义和选择自由；以及猜测和严谨。以莫斯科国立大学格尔凡德研讨会为案例研究，该项目将研究国家背景在塑造数学实践中的作用，并将探讨不同研究流派后代之间跨文化接触的影响。潜在的更广泛的影响该项目的结果可能对对交流模式和研究风格之间的联系感兴趣的历史学家和科学哲学家有用，或者对纯数学和数学之间的跨学科接触感兴趣。 理论物理学，或地方和国家背景在塑造数学实践中的作用。该项目还将有助于向更广泛的受众开放抽象数学的深奥实践，促进更广泛文化中对高等数学的更好理解和欣​​赏，并帮​​助吸引有才华的高中生进入数学领域。所提出的对使高度抽象的概念变得“有形”的数学实践的分析将有助于设计新的教育技术来帮助学生掌握高级数学结构。通过从科学文化史的角度提供对最近数学实践的易于理解的描述，该项目还将促进数学家和人文主义者之间更广泛的文化对话。