In 2013, it was pointed out that the equations on the Oxford blackboard had been taken directly from a key paper on relativistic cosmology written by Einstein in April 1931 and published in the Proceedings of the Royal Prussian Academy of Science on 9 May that year. The paper, known as the Friedmann–Einstein universe, is of historic significance because it constituted the first scientific publication in which Einstein embraced the possibility of a cosmos of time-varying radius. In the paper, Einstein adopts Alexander Friedmann 's 1922 analysis of relativistic models of a universe of time-varying radius and positive curvature, but sets the cosmological constant to zero, declaring it redundant, predicting a universe that expands and contracts over time. With the use of Edwin Hubble 's observations of a linear redshift/distance relation for the spiral nebulae, Einstein extracts from his model estimates of ρ ~ 10 g/cm, P ~ 10 light-years and t ~ 10 years for the density of matter, the radius of the cosmos and the timespan of the cosmic expansion respectively. These values are displayed in the last three lines on the Oxford blackboard (although the units of measurement are not specifically stated for the density estimate, cgs units are implied by the other calculations).