This work is the first explicit examination of the key role that mathematics has played in the development of theoretical physics and will undoubtedly challenge the more conventional accounts of its historical development. Although mathematics has long been regarded as the "language" of physics, the connections between these independent disciplines have been far more complex and intimate than previous narratives have shown. This study encompasses engagements across discipline boundaries and many nations from the era of Euler and Bernoulli to that of Hilbert and Einstein. Mathematicians and physicists, as well as historians of both disciplines, will find this provocative work of great interest.