Big Mathematics? The Classification of Finite Simple Groups, 1950s to 1980.

大数学？

• 批准号: 528127386
• 负责人: Professor Dr. Volker Remmert
• 金额: --
• 依托单位: Institut für Mathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/528127386?language=en
• 关键词: Big; Mathematics; Classification; Finite; Simple

The Classification of Finite Simple Groups (CFSG), also known as the enormous theorem, is a highlight of 20th-century mathematics, both with respect to its mathematical content and to the complex process of proving the result. From a historical perspective, it offers an excellent opportunity to focus on more general developments in the history of 20th-century mathematics, such as: changing perceptions of what a mathematical proof is, the character and the many contexts of mathematics as an intergenerational and international collaborative enterprise, the roles that trust and consensus play within this enterprise, and the impact of Cold War research policies on CFSG/pure mathematics. We consider the CFSG as (possibly) the first instant of what we tentatively call big mathematics in this project (a concept to be critically discussed within the framework of the project). The existing proof of the CFSG is estimated to be spread on somewhere between 10,000 and 15,000 journal pages in ca. 500 separate articles written by more than 100 mathematicians. The unprecedented nature of this enterprise from the 1950s until the 1980s is quite tangible: the extraordinarily large number of mathematicians involved internationally (working as a team), the difficulty and complexity of the problem, the use of computers within the proof, the repercussions for the mathematical community, the effect of the Cold War on CFSG/pure mathematics (e.g. via new funding possibilities by both civil and military agencies). Our overall long-term goal is to thoroughly analyze the history of the CFSG and use it as a magnifying glass allowing to draw general conclusions not only about the history of mathematics and the mathematical community in the context of the Cold War. In particular the history of CFSG has to be studied as a key example of the impact of politics on research in pure mathematics in the Cold War, namely via new possibilities of funding research in general and of mathematical research in particular, a largely unexplored territory, but crucial for CFSG. The historical analysis will be guided by three themes: suitability of big mathematics as an analytical concept, the role of self-historicization in CFSG, and the changing nature of proof in mathematics in the second half of the 20th century.

有限单群的分类（CFSG），也被称为巨大定理，是20世纪数学的一个亮点，无论是在其数学内容还是证明结果的复杂过程方面。从历史的角度来看，它提供了一个很好的机会，专注于20世纪数学史上更普遍的发展，例如：改变对数学证明是什么的看法，数学作为一个代际和国际合作企业的特点和许多背景，信任和共识在这个企业中发挥的作用，以及冷战研究政策对CFSG/纯数学的影响。我们认为CFSG（可能）是我们在这个项目中暂时称为大数学的第一个瞬间（这个概念将在项目框架内进行批判性讨论）。据估计，CFSG的现有证据大约分布在10，000到15，000页的期刊上。500多篇文章，由100多位数学家撰写。从1950年代到1980年代，这项事业的空前性质是相当明显的：大量的数学家在国际上（作为团队工作）、问题的难度和复杂性、证明中计算机的使用、对数学界的影响，冷战对CFSG/纯数学的影响（例如，通过民事和军事机构的新资助可能性）。我们的总体长期目标是彻底分析CFSG的历史，并将其作为放大镜，不仅可以得出关于数学史和冷战背景下数学界的一般结论。特别是CFSG的历史必须作为冷战时期政治对纯数学研究的影响的一个重要例子来研究，即通过新的可能性来资助一般的研究，特别是数学研究，这是一个基本上未探索的领域，但对CFSG至关重要。历史分析将以三个主题为指导：大数学作为分析概念的适用性，CFSG中自我历史化的作用，以及世纪后半叶数学证明的变化性质。