How are autistic savants able to perform certain mathematical computations so quickly?

• How do autistic savants (or other people with these abilities) compute equations like $81^{100}$ in 2.5 minutes?
• Which algorithms do they use? Is it an efficient one, or do they just have a lot of memory?
• Can non-autistic savants use these algorithms to solve equations just as quickly?
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Not $81^{100}$ but have a look at Arthur Benjamin does "Mathemagic" in TED where he tries to show his thought processes. –  lhf Jun 26 '12 at 1:06
Due to the number $81^{100}$ involved, I think he's referring question: Mathematical Discoveries that were made or supported by Savants –  draks ... Jun 26 '12 at 10:12
Related question about child prodigies and math. –  Josh Gitlin Jun 26 '12 at 11:49

migrated from math.stackexchange.comJun 26 '12 at 10:01

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Savant syndrome is poorly understood. No widely accepted cognitive theory explains the combination of talent and deficit found in savants. It has been suggested that individuals with autism are biased towards detail-focused processing and that this cognitive style predisposes both individuals with and without autism to savant talents.

Another hypothesis is that hyper-systemizing predisposes people to show talent, where hyper-systemizing is an extreme state in the empathizing–systemizing theory that classifies people based on their skills in empathizing with others versus systemizing facts about the external world, and that the attention to detail shown by many savants is a consequence of enhanced perception or sensory hypersensitivity in individuals with autism.

It has also been suggested that savants operate by directly accessing low-level, less-processed information that exists in all human brains but is normally not available to conscious awareness.

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