Hopf spent his youth in his hometown. He studied at breslau University in 19 14, and was immediately enlisted because of the outbreak of World War I. During the summer vacation 19 17, he boldly went to listen to the course of set theory by E. Schmidt, among which L.E.J. Brouwer (.
1920, Schmidt became a professor at the University of Berlin, and hopf studied with him. Under the guidance of Schmidt, hopf received his doctorate from the University of Berlin on 1925. The title of this paper is "Topology and Metrics". In 2008+0925, he studied at the University of G? ttingen for one year. Under the strong influence of Norther, he met the mathematician пс Aleksandrov from the Soviet Union.
He is qualified to be a lecturer at Berlin University. In the winter semester of 1927- 1928, he and Alexanderov visited Princeton University with the support of Rockefeller Foundation. At that time, because of the work of Van Buren, Lefschetz and Alexander, Princeton had become the center of world topology. Hopf's association with them benefited him a lot. He published two papers in the United States to promote Lefschetz's stationary work. And began to study homotopy mapping. /kloc-in the summer of 0/928, he and Aleksandrov got together again in Gottingen. They each had a class and organized a discussion class on topology. At this time, R. Courant invited them to write topology for his Yellow Book series, and they accepted the invitation, but underestimated its difficulty. It took them seven years and ".
193 1 year, hopf was hired as a full professor by Zurich University of Technology. Since then, the Topology Center has been established in Switzerland, and many talents have been trained in the past 20 years. For example, E. Stiefel, B. Eckmann, W. Gysin and H. Samelson are all experts in topology and other fields. Hopf also became the most influential authority of European topology before and after World War II. During this period, he actively participated in international mathematics activities from 1932. He attended all previous international congresses of mathematicians and served as the president of the International Mathematical Union from 1955 to 1958. 1935 Attended the Moscow International Topology Conference and got to know all the people at that time. 1950, he attended an international conference to celebrate the birthday of F. Severi. This is the first large-scale gathering of international mathematicians after the war. After the vicissitudes of 15, he met his old friend Alexanderov again and had a happy time. /kloc-retired in 0/964, 1967, and his health deteriorated gradually after his wife died, 197 1 April.
Hopf has published nearly 70 papers and co-authored Topology I.. [6]) all published in 1983.