While it is possible to imagine Mises without Hayek, it is not possible to imagine Hayek without Mises. - Alan O. Ebenstein

Hayek’s essential gist in capital theory was that capital is heterogeneous, that it cannot be put to many uses simultaneously or at different times. If these empirical assumptions as to capital’s heterogeneity are false, then his theoretical system of economic activity falls. Hayek never established that changes in interest rates primarily and predominantly influence capital production of goods of higher order and their prices.

Hayek truly did get Popper his position at the London School of Economics. “I am personally anxious to get Dr. Popper to this School,” Hayek wrote Gombrich as early as 1943. Given the later prominence that Popper achieved for the school, this was one of Hayek’s most significant contributions to its reputation, as well as the decisive career move in Popper’s life.
Hayek also genuinely influenced Popper’s political philosophy. While Popper always remained to Hayek’s left, he started out much further to Hayek’s left than he wound up, and this movement was in no small part the result of Hayek’s influence. Popper was a charter member of the Mont Pelerin Society. He suggested, however, that socialists be brought into it. Hayek wrote Popper several deeply personal letters in connection with his divorce. It is likely that their personal relationship was more important to and valued by Hayek than Popper, though Popper valued highly Hayek’s friendship.

Expressed egotism is, of course, no reason necessarily to disregard someone’s work, but it is a warning signal. If someone can evaluate his work so poorly, is the work itself likely to be better? In many of his areas of intellectual interest, Popper’s work is wanting.
Hayek did more to advance Popper professionally early in his career than anyone else, and Popper remembered his personal debt to Hayek. Over the years, he wrote him a number of appreciative letters.