In Cambridge Hopf worked on many mathematical and astronomical subjects. His paper "On the Time Average Theorem in Dynamics", which appeared in the "Proceedings of the National Academy of Sciences", is considered by many to be the first readable paper in modern ergodic theory. His book "Mathematical problems of radiative equilibrium" first appeared in 1934 and was reprinted in 1964. Another important contribution from this period is the theory of Wiener-Hopf equations, which he developed in collaboration with Norbert Wiener. By 1960, a discrete version of these equations was being extensively used in electrical engineering and geophysics, their use continuing until the present day. During this time, Hopf gained a reputation for his ability to illuminate the most complex subjects for his colleagues and even for non-specialists. Because of this talent, many discoveries and proofs of other mathematicians became easier to understand after they had been described by Hopf.