The geometrical structure of space has always fascinated people, and Gauss was perhaps the first to try to settle this experimentally. Since then it has been the big open problem in fundamental physics. In this talk we examine the hypothesis of Volovich that space time is p-adic at the Planck scale. That spacetime geometry could be based on a p-adic or even a finite field seems to have been suggested first in the 1950's. Enrico Beltrametti and his collaborators (Cassinelli and Blasi) in the late 1960's and early 1970's were among the earliest in exploring this line of thought. Igor Volovich formulated his hypothesis in 1987.