The history of mathematics is punctuated by important contributions from artists, while the history of art includes significant innovations by mathematicians. In this illustrated talk we will discover exemplary cases from each of the main periods of cultural history (and prehistory). Ice age music, Megalithic geometry, Islamic patterns, Kepler's music, Fractal paintings before computers. Is mathematics invented by humans, revealed from heaven, imported from space? What will be the next major advance on mathematical or artistic style?