I heard about Shakuntala Devi for the first time today, an Indian Savant who allegedly performed such feats as finding the 23rd root of a 201 digit number in 50 seconds, unaided.
There seems to be some documentation of these feats, but there also exists plenty of documentation for the tricks of psychics and others (i.e. plenty of people, and maybe even experts, will witness the power in action and be unable to detect the trick). Given that her father was a travelling magician, and she was a practising astrologer, I'm more inclined to believe that there's a trick at work than that this woman could factor 200 digit numbers in her head.
My question is:
- Could Shakuntala Devi actually perform these feats? If so, are there other living people who can do this? If not, what sort of tricks were (or might have been) used to make people think she could?
Some additional information for comparison: A little more poking around turns up the Mental_Calculation_World_Cup, a modern, international event. Multiplication events consist of finding the product of two 8-digit numbers, which takes about 30 seconds per problem for the winners. Shakuntala Devi is claimed to have found the product of two 13-digit numbers in the same time period, which seems to be a super-linearly harder task. Similarly, the competition for root finding is to find the square root of a 6-digit number, a task which takes the world record holder about 42 seconds. Shakuntala Devi is claimed to have found a 23rd root of a random 201-digit number in 50 seconds, again, a task that seems much harder.