 Riemann was clear that the epistemological implications of this way of doing geometry were immense. His lecture was a happy combination of mathematics, philosophy and physics (Ferreirós 2006). Mathematicians should no longer need to abstract some fundamental intuitions from what they believe about physical space, such as the nature and properties of straight lines or circles, and seek to build a true geometry on the basis of some axiomatic expression of those intuitions. Rather, the direction of thought should go in the opposite direction: mathematicians were free to consider infinitely many geometries. Riemann speculated about the validity of the hypotheses of geometry "in the infinitely small" being possibly bound up with the physical forces. Scientists could now freely investigate which geometry is best for the mathematical explanation of empirical facts. He envisioned the abandonment of the Newtonian conception of phenomena, "by making in this conception the successive changes required by facts which it cannot explain." His purely conceptual (mathematical) research would be useful "in preventing this work from being hampered by too narrow views, and progress in knowledge of the interdependence of things from being checked by traditional prejudices." In this connection, it was soon shown that it is possible to do theoretical mechanics in the setting of non-Euclidean geometry.