They describe how Yang went to Simons to try and find out about fiber bundles and what they might have to do with gauge theory. Simons started by referring Yang to Steenrod’s The Topology of Fibre Bundles, which Yang couldn’t make any sense of (Simons admits he never made it all the way through the book himself). This did in the end lead Simons and Yang to some real understanding of how vector potentials in gauge theory and connections on bundles were the same thing, with monopoles examples of topologically non-trivial bundles. Simons lectured at Stony Brook in 1975 on this, and a paper later that year by Wu and Yang included what became known as the “Wu-Yang dictionary” relating terminology in gauge theory and geometry. Singer learned about this soon thereafter when he visited Stony Brook, and went on to spread the news to Oxford, MIT and elsewhere （Woit）.

It gradually became clear that field theorists must learn the mathematical concept of fibre bundles. In early 1975, I invited Jim Simons to give my colleages and me a series of luncheon lectures on differential forms and fibre bundles. He kindly accepted the invitation, and we learned about the Stoke's theorem, the de Rham theorem, and so on. What we learned allowed us to understand the mathematical meaning of the Bohm-Aharonov experiment and the Dirac quantization rule of electric and magnetic monopoles. T.T.Wu and I later also understood the profound and very general Chern-Weil theorem. We appreciated that gauge fields have global geometrical connections (not to be confused with physicists' global phase factors) that are naturally formulated in terms of fibre bundle concepts. 

七十年代我了解了规范场与数学家的纤维丛的密切关系，了解了美妙的陈氏级，写了一首诗《赞陈氏级》：“天衣岂无缝，匠心剪接成。浑然归一体，广邃妙绝伦。造化爱几何，四力纤维能。千古寸心事，欧高黎嘉陈。”