Lakatos’ (Lakatos, 1976) model of mathematical conceptual change has been criticized for neglecting the diversity of dynamics exhibited by mathematical concepts. In this work, I will propose a pluralist approach to mathematical change that re-conceptualizes Lakatos’ model of proofs and refutations as an ideal dynamic that mathematical concepts can exhibit to different degrees with respect to multiple dimensions. Drawing inspiration from Godfrey-Smith’s (Godfrey-Smith, 2009) population-based Darwinism, my proposal will be structured around the notion of a conceptual population, the opposition between Lakatosian and Euclidean populations, and the spatial tools of the Lakatosian space. I will show how my approach is able to account for the variety of dynamics exhibited by mathematical concepts with the help of three case studies.

拉卡托斯（Lakatos，1976）的数学概念变化模型因忽视数学概念所表现出的动态多样性而受到批评。在这项工作中，我将提出一种数学变革的多元方法，将拉卡托斯的证明和反驳模型重新概念化为一种理想的动态，数学概念可以在多个维度上以不同程度展现。受到戈弗雷-史密斯（Godfrey-Smith，2009）基于人口的达尔文主义的启发，我的提案将围绕概念人口的概念、拉卡托斯人口与欧几里得人口之间的对立以及拉卡托空间的空间工具来构建。我将借助三个案例研究来展示我的方法如何能够解释数学概念所表现出的各种动态。