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

Question

• 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?

Answer 1

Here's the Wikipedia page on that:

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.

Answer 2

How one performs quick mental calculations through tricks and shortcuts can easily be looked up on the internet. How some Savant's do it cannot because we don't know. There is some argument that some do those same tricks but others seem not to do so.

Consider that a substantial amount of computational power goes into immediately recognizing that your friend is deeply unhappy when you first see them but puts on a brave face for you and is avoiding talking about something deeply troubling them. You see that immediately while the typical savant sees nothing, or confusion. That same Savant can do amazing mathematical, or spatial computations with tremendous facility. So, perhaps the reason we don't understand it is because it's actually a different kind of a mind.