If we think of Dyscalculia as one end of a spectrum, math savants can be thought of a being at the opposite end of the spectrum.
A small group of persons have been identified by psychologists as having “exceptional” math abilities without necessarily having gone through a regular math education. Intriguingly many of these savants also seem to have other brain related disabilities and also possess a prodigious memory. There are many cases of people in the autistic spectrum having such abilities.
A few researchers have studied this phenomenon. But the root case for such a conditions have not been found. This condition is being called Hypercalculia.
Some savants say that they are able to visualise numbers as having unique shapes & colours which helps them in memorising them. This condition, where an object or event is perceived simultaneously through several different senses, is called Synesthesia. Savants are mostly found in five major areas: art, memory, arithmetic, musical abilities, and spatial skills. A commonly found math skill in savants is the ability to tell the day of the week for any calendar date.
One such savant is Daniel Tammet who has been examined by experts. Tammet is also able to explain some of the mental images that he has while thinking of numbers. Several youtube videos about him are available in the Net. Tammet recited the value of π to 22,514 decimal places under laboratory conditions. He said it took him a week to memorise it.
Some people refer to savants as math geniuses, which may not be strictly correct. They can perform computations involving huge numbers, but there is no evidence of their having other mathematical insights and abilities. But is certainly is a superhuman gift!
When such skills where, detected about a century ago the term “idiot savants” came into use. The current terminology is “savant syndrome”.
Shakuntala Devi from India could perform such mental calculations and she did not have any disabilities. In fact, she has written books on many non-mathematical topics.
What is intriguing is that the brain seems to have an innate ability to perform mathematical computations, while at the macroscale mathematics is able to explain the workings of the universe. One mathematician has called it the “uncanny ability of mathematics” to explain the laws of the universe to several decimals of accuracy. Is there a link between these two?