惠特尼1934～1936年微分流形工作的历史分析

An Analysis of Hassler Whitney's Work on Differentiable Mannifolds from 1934 to 1936

惠特尼是20世纪美国最有影响的数学家之一,也是微分拓扑的奠基人。他在《微分流形》(1936)中给出的微分流形的概念是20世纪数学有代表性的基本概念,是描述无数自然现象的一种空间形式。但惠特尼早期从事的是图论,大约从1933年才转向拓扑。在对原始文献进行分类研究的基础上,文章探讨了惠特尼从图论转向拓扑的原因,分析了1934～1936年间他对微分流形的具体工作和历史意义以及对中国数学的影响。

Hassler Whitney is one of the most influential mathematicians in America during the 20th century, as well as the founder of differential topology. The concept of manifold in his Manifold （1936） is a representative basic mathematical concept in the 20th century, which is described as a space form for numerous natural phenomena. But Whitney worked on graph theory early until he switched to topology in 1933. Basing on the classified researches of primary sources,this paper dis- cusses the reason why Whitney shifted to topology from graph theory, analyses his work on differential manifolds from 1934 to 1936 and reviews the historical significance of his specific work as well as its impact on Chinese mathematics.