简要介绍数学大师陈省身先生关于高维高斯-博内特公式的内蕴证明和由此展开的现代微分几何的一个重要篇章——阿蒂亚-辛格指标理论的发展，以及中国数学家在此领域的贡献．%This article presents a brief outline of Shiing-shen Chern＇s intrinsic proof of the higher dimensional Gauss-Bonnet formula and the consequent development of one of the most influential chapters of modern differential geometry, the Atiyah-Singer index theorem. The contributions of Chinese mathematicians in this important subject are also briefly described.
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