惠特尼是20世纪关国最有影响的数学家之一。文章在对原始文献进行分类研究的基础上,论述他在转向拓扑学之前的图论工作:他不仅对可平面图、平面图的哈密顿回路问题、色多项式理论做出了巨大贡献,还使图论产生全新的分支——拟阵论,并在《关于线性相关性的抽象性质》(1935年)中奠定了拟阵论的基本理论。研究表明惠特尼的这些贡献均与求解四色猜想密切相关,他虽未成功解决四色猜想,但由此取得的理论成果对现代图论的发展影响深远。他开展数学研究的基本特征是寻求表象内在的原因,另一个特征是他在图论研究中的拓扑学思维方式,这对图论本身及之后的拓扑学研究都产生重大影响。
Hassler Whitney is one of the most influential mathematicians in the 20th century. With an analysis based on the classification of primary sources, this paper discusses Whitney's work on graph theory before he switched to topology. It reviews his great contributions to planar graph, Hamihonian circuits in planar graphs, chromatic polynomials and matroid theory, which was founded by Whitney in his paper entitled "On the abstract properties of linear dependence" in 1935. The results show that these contributions are closely related to the four-color conjecture. He made many theoretical achievements derived from it even though he didn't succeed. And his legacies have a great impact on the development of modern graph theory. A prime characteristic of Whitney's mathematical work is the search for inner reasons (SIR) for phenomena. And another one is the thought infiltration of topology into graph theory, which has significantly influenced graph theory and topology. It is expected to be beneficial for understanding Whitney's academic achievements in all aspects.