In his "Men
of Mathematics", Eric Temple Bell says of "the Prince of Mathematicians",
Karl Friedrich Gauss, .
" ...but Gauss had a photographic memory which retained the impressions of his infancy and childhood until his dying day."
"...the 'wonder child' of two, whose astounding intelligence impressed all who knew him as something not of this earth..."
Later, he says,
"In all the history of mathematics, there is nothing even approaching the precocity of Gauss as a child. It is not known when Archimedes first gave evidence of genius. Newton's earliest manifestations of the highest mathematical talent may have passed unnoticed. Though it seems incredible, Gauss showed his caliber before he was three years old.
"One Saturday, Gerhard Gauss was making out the weekly payroll for the laborers under his charge, unaware that his young son was following the proceedings with critical attention. Coming to the end of his long computations, Gerhard was startled to hear the little boy pipe up, "Father, the reckoning is wrong. It should be . . ." A check of the account showed that the figure named by Gauss was correct.
"Before this, the boy had teased the pronunciations of the letters of the alphabet out of his parents and their friends and had taught himself to read. Nobody had shown him anything about arithmetic. In later life, he loved to joke that he knew how to reckon before he could talk. A prodigious power for mental calculations remained with him all his life."
"When Gauss was ten years old, his brutish school teacher gave his class the job of calculating the sum of the 100 numbers from 81297 + 81495 + 81693 + ... + 100899. "Büttner had barely finished stating the problem when Gauss flung his slate on the table." For the rest of an hour, the other students toiled away. None of them got it right except Gauss."
"This opened the door through which Gauss passed on to immortality. Büttner was so astonished at what the boy of ten had done without instruction that he promptly redeemed himself, and to at least one of his pupils became a humane teacher. Out of his own pocket, he paid for the best textbook on arithmetic and presented it to Gauss. The boy flashed through the book. 'He is beyond me,' Büttner said. 'I can teach him nothing more.'"
"Gauss' lightning mastery of the classics astonished teachers and students alike. Gauss himself was strongly attracted to philological studies, but fortunately for science, he was to find a more compelling attraction in mathematics."
Ellen Winner, in her book, "Gifted Children: Myths and Realities", observes that it is especially difficult for a child to teach themselves how to read. Offhand, I guess it would suggest to me powers of induction beyond the ability to recall and relate... pure "g"?