Is it obvious that a network of neurons can explain how we see? There is an apocryphal story about the mathematician Hardy, who wrote an equation on the blackboard and said "The proof of this is obvious". After a little while he murmured "At least I think it is", and left to check the proof in the library, only returning just before the end of the lecture to announce "Yes, it is obvious". Sometimes, mathematical techniques are necessary to be sure that a network with a given set of properties will generate a particular visual phenomenon. The geometrical concepts of vectors and manifolds are introduced in the context of the visual system and used to provide a framework for explaining the behaviour of the visual system.