I’m not sure if math savant is even the correct term, but I’m thinking people who can do the incredible feats of mental calculations. This came about due to random thoughts of Malcolm in the Middle, where Malcolm gets a string of credit card numbers and does all sorts of crazy things with it in his head. Anyway, are people who can do these constrained to one base system (in most cases, decimal)? Or can they just as easily do it in base6, or base2, or whatever, obviously allowing time for them to become familiar with the numbering conventions? I also wondered about dividing - do they come up with answers in fractions or decimals? 322/411 vs 0.78345…
According to The Number Sense, the idiot savants, such as “Rain Man,” actually are autistics with very rich internal lives; numbers are friends, with whom they spend a lot of time. So, their abilities that seem so amazing to us (yes, they are amazing), are a product of a fairly normal intelligence cloistered inside the mind. In other words, because they’re autistic, we think they’re idiots, when in fact, they’re smart but cannot connect with other people, and even some aspects of the outside world. They’ve been working on math for a long time, and can produce within the normal limits of human ability.
Malcom’s tricks are doable to anybody who chooses to take the time to learn them; I’m skeptical (see above reference) that it’s a native ability in anybody. One can learn to calculate quickly, it’s just not worth the effort for most people. The author of this book calculated a 100-digit square root in something like one minute. But for savants and regular people, it’s a matter of being a learned skill.
I honestly don’t know the answer, but just to add what I believe africanus was trying to say: They probably aren’t going to be very good at it unless they’ve practiced it as well.