从恩格斯关于数学公理之定义谈起

Make Mention from Engels' Definition of Mathematical Axioms

F.恩格斯(1820-1895)于1873至1883年间写成一本世界名著《自然辩证法》,在该书中对于数学公理给出一个简洁的定义。在现代数学公理化方法研究的历史长河中,D.格高尼和M.巴许是先驱者,而G.皮亚诺和D.希尔伯特则是独立地发现者。1899年,希尔伯特的名著《几何基础》出版;1901年,著名数学家B.罗素又提出创建纯粹数学理论的新思维。从此而后,纯粹数学蓬勃发展,蒸蒸日上。

Friedrich Engels（1820--1895） has written a world famous book--＂Dialectics of Nature＂ duing 1873--1883 and provided a simple definition of mathematical axioms. For the method of axiomatization of modern mathematics in the long process of history, D. Gergonne and M. Pasch are ancestors, but G. Peano and D. Hilbert are original discoverers. In 1899, David Hilber＇s famous book ＂Grundlagen der Geometrie＂ was published; In 1901,the famous mathematician Bertrand Bussell put forward a new method to find theory of pure mathematics. After this hereafter, the pure mathematics are springing up energetically.