Officially inaugurated in 1925, the Hebrew University of Jerusalem was designed to serve the academic needs of the Jewish people and the Zionist enterprise in British Mandatory Palestine, as well as to help fulfill the economic and social requirements of the Middle East. It is intriguing that a university with such practical goals should have as one of its central pillars an institute for pure mathematics that purposely dismissed any of the varied fields of applied mathematics. This paper tells of the preparations for the inauguration of the Hebrew University during the years 1920–1925 and analyzes the founding phase of the Einstein Institute of Mathematics that was established there during the years 1924–1928. Special emphasis is given to the first terms in which this Institute operated, starting from the winter of 1927 with the activities of the director and one of the founders, the German mathematician Edmund Landau, and onward from 1928 when his successors, particularly Adolf Abraham Halevi Fraenkel and Mihály-Michael Fekete, continued Landau's heritage of pure mathematics. The paper shows why and how the Institute succeeded in rejecting applied mathematics from its court and also explores the controversial issue of center and periphery in the development of science, a topic that is briefly analyzed in the concluding section.