十九世纪早期,数学内部矛盾的发展酝酿着一场意义深刻的变革,其结果导致了罗巴切夫斯基非欧几何的诞生。罗氏非欧几何从根本上改变了人们对数学性质的理解,引出关于几何基础和数学基础的一系列重大课题,迫使数学家们对欧几里得以来根据经验而建立起的现 In the early nineteenth century, the development of contradictions within mathematics brewed a profound change, the result of which led to the birth of the non-Euclidean geometry of Lobachevsky. Roche non-Euclidean fundamentally changed people’s understanding of the nature of mathematics, leading to a series of major issues concerning the basis of geometry and mathematics, forcing mathematicians to establish empirically based on Euclidean