 This diminished the role of experience that Herbart had emphasised. Riemann was making conscious what Herbart had said occurred naturally: if intellectual reflection generates concepts with which we frame the world, in reaction to our experiences, then, said Riemann, let mathematics generate more precise and flexible concepts with which to conduct science. At the end of his lecture he explored possibilities for the application of the new geometries, especially at an atomic level, and he argued that his task had been to expand the range of theoretical options, eliminating prejudices.