In the 1870s William Kingdon Clifford became the first mathematician who accepted and propagated the idea of Non-Euclidean Geometry in Britain. He translated Riemann’s famous lecture into English and proposed his own opinions on foundation of geometry and curved space. Klein was inspired by Clifford’s 1873 lecture and his hypothesis that changing curvature of space manifests itself as the motion of matter, anticipating later geometrical interpretations of matter. Klein’s advocacy made Clifford an important figure in the reception of Non-Euclidean Geometry. Historians have attributed Clifford’s courage in accepting the new geometry in the context of the British conservative attitude towards geometry and space in the 19th century to his radical personality or the rise of naturalism, and also mentioned that Clifford was influenced by Riemann and Helmholtz. It is still necessary to dig more deeply to identify in detail the influences that Clifford got from the two mathematicians and what innovation he therefore made in the theory of space and geometry.
In this talk, I will compare the geometric ideas and work of Riemann, Helmholtz and Clifford, and then investigate the sources of Clifford’s thoughts on the concept of space.

Almost every textbook on general relativity tells us that the main lesson of the theory is that gravity is not a force but that it can be reduced to space-time geometry, that gravity *is* the curvature of spacetime. Unbeknownst to most, Einstein himself actively opposed this interpretation of his theory. He thought that instead general relativity should be seen as a unification of gravity and inertia, analogous to the unification of electricity and magnetism in special relativistic electrodynamics. In this talk I am going to outline how this interpretation of general relativity originated in Einstein’s work on a relativistic theory of gravity before he first embarked on a metric theory in 1913, and how it led him to see GR as a continuation of the 19th century field theoretic programme, overcoming the duality between fields and particles as the most important task in the further development of the programme.