We could perhaps modify the theory, thinking of the mechanics of research. Progress is made by an individual in the niches where others have not managed yet. Therefore the advantage in geometry for a blind mathematician may be in a different mental model of spaces.
It is not surprising at all that almost all blind mathematicians are geometers. The spatial intuition that sighted people have is based on the image of the world that is projected on their retinas; thus it is a two (and not three) dimensional image that is analysed in the brain of a sighted person. A blind person’s spatial intuition on the other hand, is primarily the result of tile and operational experience. It is also deeper – in the literal as well as the metaphorical sense. […]
recent biomathematical studies have shown that the deepest mathematical structures, such as topological structures, are innate, whereas finer structures, such as linear structures are acquired. Thus, at first, the blind person who regains his sight does not distinguish a square from a circle: He only sees their topological equivalence. In contrast, he immediately sees that a torus is not a sphere […]
I'm not convinced that blind mathematicians count as their own species, nor that they echolocate, and so it doesn't seem to say much about his theory one way or the other.
