D O C U M E N T 3 9 9 K Y O T O L E C T U R E 6 3 9 When I returned to Zurich from Prague, my close friend, the mathematician Grossmann, was there.[12] During my days at the Patent Office in Bern, it had been difficult for me to obtain mathematical literature and he had been the one who would help me. This time, he taught me Ricci and, after that, Riemann. So I asked my friend whether my problem could really be solved through Riemannian theory, i.e., whether the invariance of the curved line element completely determines its co- efficients, which I had been trying to find. In 1913 we wrote a paper together.[13] We were unable, however, in that paper, to obtain the correct equation for universal gravitation. Although I continued my research into Riemann’s equation, trying va- rious different approaches, I only found many different reasons that made me be- lieve that it could not give me the results I wanted at all. Two years of hard work followed. Then I finally realized there was a mistake in my previous calculations. I therefore returned to invariance theory and tried to find the correct equation for universal gravitation. Two weeks later, the correct equation finally emerged before my eyes for the first time.[14] Of the work I did after 1915, I only want to mention the problem of cosmology. This concerned the geometry of the universe and time, and was based, on the one hand, on the treatment of boundary conditions in the general theory of relativity and, on the other hand, on Mach’s observations about inertia. Of course, I do not know specifically what Mach’s opinions were about the relative nature of inertia, but at least on me he definitely exerted an extremely important influence. At any rate, after trying to find invariant boundary conditions for the equation for universal gravitation, I was finally able to solve the problem of cosmology by regarding the world as a closed space and removing the boundary. From this I de- rived the following: inertia emerges purely as a property shared by a number of bo- dies. If there are no other bodies in the vicinity of a particular body, its inertia must vanish. I believe that this made the general theory of relativity epistemologically satisfactory. The above, I think, gives a brief historical outline of how the essential elements of the theory of relativity were created. [1]The English translation presented here was prepared for this volume by the editors in coopera- tion with Masako Ohnuki on the basis of a draft translation by Ryoichi Itagaki and Michel Janssen. For a discussion of the problem of translation, see the editorial note, “Einstein’s Lecture at the Uni- versity of Kyoto,” pp. 624–627 above. [2]For earlier accounts by Einstein on the development of the theory of relativity, see Einstein 1921d (Vol. 7, Doc. 53), and Vol. 12, Appendix D, especially p. 519. [3]Einstein 1905r (Vol. 2, Doc. 23) was received by the Annalen der Physik on 30 June 1905, some seventeen and a half years before the lecture. [4]In Itagaki 1999, it is pointed out that the earlier translations of Ogawa and Ono differ in their rendering of this sentence. They have the following versions: “This idea was as similar as the one in the Michelson experiment, but I had not carried out the experiment yet to obtain any definite result”