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This essay takes a close look at specially selected features of the Göttingen mathematical culture during the period 1895–1920. Drawing heavily on personal accounts and archival resources, it describes the changing roles played by Felix Klein and David Hilbert, as Göttingen's two senior mathematicians, within a fast-growing community that attracted an impressive number of young talents. Within the course of these twenty-five years Göttingen exerted a profound impact on mathematics and physics throughout the world. Many factors contributed to the creation of a special atmosphere that served as a model for several other important centers for mathematical research. Göttingen exemplified a dynamic new way of doing mathematics within a highly competitive community in which the spoken word often carried more weight than did information conveyed in written texts. This oral dimension of the Göttingen culture played an important, till now overlooked role in the early development of Einstein's general theory of relativity.

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One of the most famous episodes in the early history of general relativity involves the ''race between Albert Einstein and David Hilbert to uncover the ''correct'' form for the ten gravitational field equations. In light of recent archival findings, however, this story now has become a topic of renewed interest and controversy among historians of physics and mathematics. Drawing on recent studies and newly found sources, the present essay takes up this familiar tale from a new perspective, one that has seldom received due attention in the standard literature, namely, the mathematical issues at the heart of Einstein's theory. Told from this angle, the leading actors are Einstein's collaborator Marcel Grossmann, his critic Tullio Levi-Civita, his competitor David Hilbert, and several other mathematicians, many of them connected with Hilbert's Gö ttingen colleagues such as Hermann Weyl, Felix Klein, and Emmy Noether. As Einstein was the first to admit, Gö ttingen was far more important than Berlin as an active center for research in general relativity. Any account which, like this one, tries to understand both the actions and motives of the leading players must confront the problem of interpreting the rather sparse documentary evidence available. The interpretation offered herein, whatever its merits, aims first and foremost to show how mathematical issues deeply permeated the early history of general relativity.