In 1864, after his lean years as a Viennese Privatdozent, Mach obtained a position in Graz as professor of mathematics. He later claimed that Graz was something of a neglected institution, but that there he was able to improve his self-acquired mathematical education and to pursue experiments in sense physiology. Mach's lectures there included a reprise of his Vienna lectures on psychophysics in the winter of 1864–65, and lectures on mechanics in the summer of 1864 in which he developed most of his views on physical space and time and on multidimensional spaces, without, as he pointly remarks, having read the famous Probevorlesung of Riemann which was published in 1867.¹