中国传统数学与数学机械化

中国传统数学在三代萌芽,经过春秋的发展,到战国至西汉以《九章算术》的编纂为代表,进入第一个高潮,在许多领域跃居世界前列.魏晋南北朝是第二个高潮,刘徽以演绎逻辑为主要方法全面证明了《九章算术》的公式、解法,奠定了中国传统数学的理论基础,并在世界数学史上首次将无穷小分割方法引入数学证明.第三个高潮发生在宋元,贾宪、秦九韶、李冶、朱世杰等创造了欧洲数学大师17-19世纪才得出的许多重大成就.上世纪70年代吴文俊指出,中国古代数学的算法具有构造性、机械化的特点,并出现几何问题代数化的思想.西方数学史家一直将中国排除在世界数学发展的主流之外.吴文俊提出“在历史的长河中,数学机械化算法体系与数学公理化演绎体系曾多次反复互为消长交替成为数学发展中的主流”,从而从理论上解决了中国传统数学是世界数学发展主流的一部分的问题.微积分的产生也证明中国传统数学属于世界数学发展的主流.微积分产生时的推理模式不是希腊式的,而是接近中国式的.吴文俊受到中国传统数学的构造性、机械化特色以及几何问题代数化思想的启发,产生了数学机械化思想,发展了笛卡儿、莱布尼茨、希尔伯特等的设想,创立了数学机械化理论.他首先在初等几何定理的机器证明方面取得突破.接着,提出了一个将问题化为代数方程组求解的数学机械化方案.他从朱世杰的四元消法得到启示,发现了三角化整序法,是目前唯一完整求解代数方程组的方法.吴文俊指出,继续发扬中国古代传统数学的机械化特色,实现数学各个不同领域的机械化,是绵亘整个21世纪才能大体趋于完善的事.

Traditional Mathematics of China and Mathematics Mechanization

Based on the development in the three ancient dynasties and the Spring and Autumn Period,mathematics in China reached its first climax in the period from the Warring States Period to the Western Han Dynasty.The compilation of the Nine chapters of mathematical procedure was a representative achievement of this period of time.The second climax was reached in the third century AD.Liu Hui presented comprehensive proofs for the formulas and algorithms of the Nine Chapters of mathematical procedures.This established the theoretic base of mathematics in China.He introduced the method of infinite division into mathematical proof.The third climax was reached during the 10th to 14th century.During this period,Jia Xian,Qin Jiushao,Li Ye and Zhu Shijie achieved important accomplishments,some of them were attained later in Europe during 17th to 19th century.Western historians of mathematics always regarded the development of mathematics in China was outside of the mainstream of mathematics.From 1970s,Wu Wenjun pointed out repeatedly that mathematics developed in ancient China had the character of constructivity and mechanization.He pointed out,in the long flow of history,the systems of mathematical mechanization and axiomatization had been the mainstream of the development of mathematics alternately.This ascertains that the mathematics development in ancient China belongs to the mainstream of mathematics world widely.Inspired by ancient mathematics in China,Wu Wenjun developed the thought of mathematics mechanization,and establishes the theory of mathematics mechanization.After attained his achievement in the mechanical proof of the theories in elementary geometry,he presented a plan of mathematics mechanization based on transferring the problems to systems of algebraic equations.Inspired by the methods of Siyuan shu of Zhu Shijie,he achieved new accomplishments.