please please don't send him to school early!
mine is 'advanced' (or 'fast forward' as a polish friend of mine calls it!), and so was his dad. when his dad was 3 he was assessed by a psychologist and sent to school a year early. whilst he might have been super bright, he WASN't emotionally ready for it. his parents regret it too. also, it seemed a horrendous punishment for being clever: he dind't get to leave school a year early, just had to do a year extra. thats so unfair!
he never related to anyone at his school, and says he was depressed from 3 til 16 when he got to leave. our little one is 2 but already my partner is anxious about the whole school thing.
with my son i too get a bit embarassed at him being so good at talking. somewhere between embarassed and proud. for example, when he overheard a woman in a museum telling her child a grasshopper was 'a creepy crawly', he said "actually, its a grasshopper'....he hasn't yet developed those social skills about eavesdropping and interrupting! and when people compare their child to mine i struggle not to say something dismissive of him cos i don't want to seem too boastful.
school is NOT necessarily more mentally stimulating, unless its a particularly amazing school. you could argue it narrows rather than expands the interests of children. i would suggest that one to one attention from you or other adults, plus learning to play with children his own age, is far more important than learning maths quickly. we do a lot of natural history stuff, go for walks, birdwatching, museums, libraries, that sort of thing.
don't be bullied or flattered into sending him into the highly flawed schools system yet! give him the joy and freedom of the far superior real world first!