Abstract

It is well known that Felix Klein took a decisive step in investigating the invariants of transformation groups. However, less attention has been given to Klein’s considerations on the epistemological implications of his work on geometry. This paper proposes an interpretation of Klein’s view as a form of mathematical structuralism, according to which the study of mathematical structures provides the basis for a better understanding of how mathematical research and practice develop.

中文翻译：

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费利克斯·克莱因（Felix Klein）关于非欧几里得几何的工作中的结构主义和数学实践†

摘要

众所周知，费利克斯·克莱因（Felix Klein）在研究转化组的不变量方面迈出了决定性的一步。但是，对于克莱因对几何学的认识论影响的思考，却很少受到关注。本文提出了对克莱因作为一种数学结构主义形式的观点的解释，据此，对数学结构的研究为更好地理解数学研究和实践的发展提供了基础。