I think this goes to the heart of the issue of whether these people have exceptional mathematical talent, or are simply really good arithmetic calculation and memorization.
An insightful question: how many of Hilbert's 23 problems were solved by savants?I think this goes to the heart of the issue of whether these people have exceptional mathematical talent, or are simply really good arithmetic calculation and memorization.
Your guess is probably "zero" and I agree. It's true that Yuri Matiyasevich was a teenager when he proved that there's no universal algorithm for solving Diophantine equations (Problem 10), so one might think that perhaps he was a savant. But we have to distinguish between savants and prodigies. Plenty of great mathematicians showed their abilities at a very early age, but there's no evidence that any of them were autistic savants (although some might have had Asperger's Syndrome—see Earthdweller's post #25 on this thread).
Links for Hilbert's problems:
Mathematical Problems, a translation into English of Hilbert's lecture delivered before the International Congress of Mathematicians at Paris in 1900.
Hilbert's Problems, a status report.