算术公理化的发明人—格拉斯曼

    中国人“打算盘”需要用组多“口诀”（公理）。 

    打算盘的“口诀”，比如：三加五除二（一条公理）。

1860年，德国数学家格拉斯曼发明了自然数“后继数”（successor）的概念，借助“后继数”，只要几条公理即可推导算术的所有定理。

由此可见，算术公理化的发明人是格拉斯曼，皮亚诺是“后来人”。

请参阅本文明附件。

袁萌  陈启清  1月19日

附件：

Hermann Grassmann（1809-1877，格拉斯曼）, who showed in the 1860s that many facts in arithmetic could be derived from more basic facts about the successor operation and induction. In 1881, Charles Sanders Peirce provided an axiomatization of natural-number arithmetic. In 1888, Richard Dedekind proposed another axiomatization of natural-number arithmetic, and in 1889, Peano published a simplified version of them as a collection of axioms in his book, The principles of arithmetic presented by a new method (Latin: Arithmetices principia, nova methodo exposita).