Posted: 27.09.2014

History refuted the prediction of Poincare that the physicists will always choose the Euclidean structure, only a few years later, when Einstein used the non-Euclidean geometry of Riemann in his general theory of relativity. Thereby Einstein obtained a considerable gain in simplicity for the total system of physics in spite of the loss in simplicity of geometry.^{[1]} This is in accordance with the consensus or opinion now, which is that geometry should be regarded as a part of physics and therefore, our system of geometry should be one in which the rest of physics can be expressed as simply as possible.^{[2]} It was this consideration that ultimately led Einstein to the curved space of general relativity.

Thus, it was only through the work of Einstein that the question of physical geometry was settled. Einstein's theory of relativity predicted the non-Euclidean result which was confirmed by astronomical observations and thus gave a clear evidence of the fact that the universe was a four-dimensional continuum of space and time, and the geometry of the space was a non-Euclidean one.^{[3]}