My DS (2nd child) was incredibly aware of surroundings and showed very early signs of separation anxiety and lots of other people commented on how it looked as if he was an old man in a baby's body as even when a few months old, it looked as if he somehow knew what was going on around him.
Other than that, with an older toddler, didn't have time to teach him letters/numbers but he picked it up himself. Was astounded when, a much older child was showing off his counting in tens to his parents, when DS (still in a buggy) was able to carry on past 100! Definitely strong ability to see signs/read early, numbers and full understanding of number.
Pre-school commented on how he would actively seek out learning opportunities even when very young and sometimes away from other children. But he was still sociable but incredibly self conscious (again aware of surroundings). I did ask the question about ASD/spectrum but teacher, very experienced, said 'he's just very bright'. Generally speaking school and other adults have always commented on how bright he is, but we did notice his capability to remember things and process and draw connections at quite adult levels, made an appearance very early on. And was quite interesting as with oldest child, we didn't see these things so it was evident DC2 was different in that sense.
DS now is still an extremely chatty child, still a bit self conscious but has lots of friends and a great sense of humour (quite sarcastic and adult)! He's still gifted and has a high IQ.