"What I don't understand, with his extraordinary memory, is why he is (as you say) "unteachable."
Answer is: 99 per cent of people learn through the process of interaction with other people. You will find most people need someone to "personally" transmit knowledge. Mother, father, teacher, friends.
Asperger children had a complete emotional blockade. They don't react to praise or rebuke by changing their resonse or conduct. The part of communication based on emotional imput is blanked out. That leads to all around failure to respond to usual educational mechanisms. That's why the Asperger children were removed from regular school.
However, a percentage of these children were all the same intelligent. Some went deep into their own world and learned what interested them. Not what others dictated but what they had an interest in. Being cut off from the world around them, the children evolved highly individual thought mechanisms. As if when you have myopia, your hearing compensates.
Asperger realised part of this could be of value. It regulates excessive rote-learning and sticking to one path. We need deviation from normality.
What's been lost though is the fact these children were still highly problematic. Asperger believed only a minority could stand a chance of having any future.