No matter where you stand, the pattern in the pavement outside the student bar at Wadham College never repeats. This is because it is a Penrose tiling, named after the mathematician Roger Penrose who invented it in the 1970s. Penrose tilings not only have many interesting mathematical properties, they also explain the structure of some unusual metallic crystals, called quasicrystals, that were discovered in the 1980s and won Dan Shechtman the Nobel Prize for Chemistry in 2011.