Read Ted Chiang's story "Understand," and you'll be better able to appreciate the following story:
http://www.guardian....1409903,00.html
A genius explains
Daniel Tammet is an autistic savant. He can perform mind-boggling mathematical calculations at breakneck speeds. But unlike other savants, who can perform similar feats, Tammet can describe how he does it. He speaks seven languages and is even devising his own language. Now scientists are asking whether his exceptional abilities are the key to unlock the secrets of autism.
I was specifically struck by Tammet's description of his calculating process, which sounds like something out a Golden Age science fiction story (Jommy the Slan describing his mental powers):
"When I multiply numbers together, I see two shapes. The image starts to change and evolve, and a third shape emerges. That's the answer. It's mental imagery. It's like maths without having to think."