Language of Physics : The Calculus and the Development of Theoretical Physics in Europe, 1750-1914

This study began as an attempt to understand mechanics in the nineteenth century. The terms mechanics and mechanical world view were being used as general descriptions of nineteenth-century physicists' assumptions and interpretations of nature. However, there were no studies of the particulars of these assumptions or the range and content of these interpretations. Rene Dugas' work on classical mechanics focused on France. The search for the particulars of these forms of "mechanics" led me to explore precisely what mechanics meant to physicists of a century and more ago. However, none of Lagrange's, Hamilton's, or Jacobi's "mechanics," while ele­ gant, fits easily within the history of physics. Lagrange reduced mechanics to an exercise in analysis; Hamilton and Jacobi used mechanics to explore solutions to partial differential equations. They were mathematicians doing mathematics. As I went deeper into the matter it became obvious that, in the nineteenth century, there were two kinds of mechanics, each containing a variety of forms, one physical, the other mathematical. There were a group of men using mechanics to understand nature and another group using the equations of mechanics to explore the calcu­ lus. However, when tracing these two traditions back into the eighteenth century, physics disappeared altogether.

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 rom the ear of Euler and Bernoulli o that of Hilbert and Einstein. At all times physicists and mathematicians retained their distinct sets of disciplinary standards and goals. Interactions within historical ears are handled using the standards of the time to define mathematics and physics. In this context, the works of Lagrange, Laplace, Fourier, Jacobi, William Thomson, Maxwell, Helmholtz, and many others are discussed, and by 1870, it is evident that the essentials of modern theoretical physics are in place. The epilogue, spanning the decades from 1870 to the First World War, deals with the decline of these interactions and the building of new connections. It is particularly significant that these new patterns of interactions became paradigmatic for the rest of the twentieth century.

The unique perspectives concerning the history of theoretical physics will undoubtedly cause some raised eyebrows, as the author convincingly demonstrates that practices, methods, and language shaped the development of the field, and are a key to understanding the mergence of the modern academic discipline. Mathematicians and physicists, as well as historians of both disciplines, will find this provocative work of great interest.