People seem to interpret my comments as some kind of tall-poppy syndrome or ignorance, but I actually believe that a lot of these mathematical abilities do generate at about the age that Terrence was said to display them (even if we accept he was early and prodigious).

if someone told you that they developed sight before they physically developed eyes, surely you'd pause for thought. But make similar claims concerning the neurological development or mental faculties in prodigies at a young age and suddenly everyone's critical thinking switches off.

I've actually read the study which involved Terrence before this thread, and I'll repeat it again: nothing I'm saying is trying to take away from his accomplishments or current abilities.

The far more plausible story is simply that he had two highly educated parents, one of whom was a math teacher, he has some innate ability, and his parents specifically focused on him and taught and pushed him in math from an early age, then they went about accessing opportunities for him to learn and continue his development at an abnormally early age and they additionally got him special access to educational resources, educators and equipment.

If anything, the video and further research confirms my early conclusions, but my point is really quite fundamental and has little to do with Terence's abilities or current day achievements: I don't believe a 2 year old can teach themselves to read (or at least to anything approximating what a skeptical person would call reading). I think anyone who's had dealing with kids and understands development would say that claim at least SMELLS of bullshit if it isn't actually so.

Why can't a 2 yr old start reading but a 10 yr old can solve the hardest mathematics problems posed?

well, firstly, the claim can be broken down into two parts: taught himself, and reading at two.

I won't address the first because the discussion will get too long if you think that's genuinely how children learn, even geniuses.

on the later, because the basic foundations of math can be found in (at least some) ten year old minds. what the common man believes is possible in math is mainly influenced by cultural exposure and the order in which we learn it. But there's really only 3 - 4 meta-concepts that underlie all of math, and the rest is about exposure/experimentation, syntax and terminology. Terrence himself I believe says as much and if you read through the accounts of interviews with Terrence at a young age it's apparent that's how his mind is working (and explains the concepts he understands, the mistakes he makes, and those areas he hasn't had exposure to).

  whereas the cognitive layers required for reading take time to develop in the child's brain, and you first have to wait for the verbal/aural language systems to develop the actual language structure first, then tack on some symbolic representation for letters, then understand composition for words, then attach words to their meanings, etc. You can skip some of those bits to perform party tricks (I.e rote symbolic recognition and repetition of aural sounds on cue), but this does not reading make. Reading we believe, from a cognitive science point of view, we think is a kind of a kind of kludge on top of later developed brain mechanics, whereas it's aural/verbal language that appears as an almost innate developmental ability around that age. (I say innate, but you still have to be exposed to other humans interacting and speaking for a young mind to learn the language).