数学发现和论证的两种原型:古希腊与古中国

萨博论点认为希腊数学证明源于埃利亚学派,但没有涉及与之相关的社会文化原因。把视野扩大到社会文化背景,可以发现,古希腊重甲步兵的出现以及其社会地位的提高,创造了以对抗或竞赛为象征的民族精神,从而既摆脱了怀疑主义哲学的束缚,又使得批判思维统治社会成为可能,这才是埃利亚学派及其数学产生的社会原因。另一方面,结合中国传统社会的考察,分析《九章算术》源于日常实践的问题以及复杂的理论回答,可以发现,中国古代需要大量人力完成的农业技术发展和日常生活中的实用技术发展,都得益于其算法的实用性,中国传统数学由此而成为东方数学的最高形式。两种数学实践的原型代表着两种重要的数学价值观,即确定性与实用性。

Two Archetypes of Mathematical Discoveries and Demonstrations:Ancient Greece and Ancient China

Szabó’s argument claims that mathematical justifications of Greek mathematics originated from Eleatics,but neglects social and cultural aspects in the origin of Greek mathematics.From a broader perspective with considerations of social and cultural backgrounds,we find that the emergence of hoplite and the rising of its social status created a national spirit whose symbol was agon.The spirit not only helped Greeks get rid of the yoke of skepticism,but also made a society with a critical thinking atmosphere possible.To make a comparison with Chinese mathematics,based on the consideration of the features of traditional Chinese society and analyses of mathematical examples on problems of everyday life and their complicated solutions in Nine Chapters on the Mathematical Arts,we find that,Ancient Chinese agricultural technologies which usually required large amounts of manpower and their developments enjoyed benefits from the practicability feature of Chinese algorithm,which made Chinese traditional mathematics become the highest form of Eastern mathematics.The two archetypes of mathematical practices represent two important values in mathematics:certainty and utility.