《数学: 确定性的丧失》是美国数学史家莫里斯·克莱因 (Morris Kline) 的经典著作, 从哲学与历史视角系统梳理了数学从“绝对真理”到“不确定性”的演变历程。克莱因通过分析数学基础危机 (如哥德尔不完备定理、罗素悖论) 、非欧几何的冲击以及现代数学的抽象化转向, 揭示了数学作为人类理性工具的内在矛盾与局限性。本书不仅是一部数学思想史, 更是一场对数学本质的深刻哲学反思, 挑战了数学“永恒真理”的传统观念, 为理解科学与人文的关系提供了独特视角。

“Mathematics: The Loss of Certainty” is a classical work by American historian of mathematics Morris Kline, offering a systematic exploration of mathematics'  evolution from “absolute truth” to “uncertainty” through philosophical and historical lenses. Kline reveals the inherent contradictions and limitations of mathematics as a human rational tool by analyzing foundational crises (such as Gödel' s incompleteness theorems and Russell' s paradox) , the impact of non-Euclidean geometry, and modern mathematics'  abstract shift. This book not only chronicles the intellectual history of mathematics but also provides profound philosophical reflections on its nature, challenging the traditional notion of mathematics as “eternal truth” while offering unique perspectives on the interplay between scientific and humanistic thought.