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."

He mentions,

"...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"?