In 1854, 27-year-old Riemann had to give a public lecture to qualify as a professor at Göttingen. Custom was to propose three topics; examiners almost always chose the first. His examiner was Gauss, who broke convention and picked the third - the one Riemann had barely prepared: the foundations of geometry. The audience was the philosophy faculty, so Riemann used almost no formulas. In plain prose, he argued that the geometry of space is not given in advance - space could be curved, and only measurement can decide. Gauss, famously impossible to impress, walked home praising the lecture. It was published only after Riemann's death at 39. Sixty-one years after the lecture, Einstein needed exactly that mathematics to write general relativity.