Genuinely asking the question in the title.
If it is more gifted-looking, any suggestions as to what to do? We live somewhere with no specialist programmes for G&T kids. So anything I do will be me supplementing a mediocre local private school education.
DS (21 months) has been speaking in sentences since about age 17 months, and able to read a few favourite words for a while. He was pointing out the relevant letters in the alphabet up on his wall, referring back to Peepo (a favourite book, read every night) at about 16-17 months. He has books with alphabets in and sometimes will go on a hunt for a favourite letter "where's my little q". At 18-19 months ish I realised that if I wrote out the main words from his favourite books, he knew what they were (Gruffalo, Stick Man, Mr Frumble, Lowly, etc.). He points out words where there is no obvious context - eg "music shop" written on an otherwise blank wall.
At 19 months he demonstrated he knows digits by walking round the street reading the (digits of) house numbers on the letterboxes, though he'd probably known them a lot longer. He knew colours at about 15 months.
He gets concepts like vertical vs. horizontal straight away (they were today's favourite new thing to point out) and re-applies them correctly in other contexts.
He can tell you the story of each of his favourite books, in his own way - eg Gruffalo's Child (mix of book and film) "Squirrel footprints. Mummy squirrel says No, too small. Little Gruffalo hedgehog squeaky. Daddy gruffalo grumpy, why not why not, big bad mouse after you. [etc.]". Favourite books are things like the Julia Donaldsons, Where the wild things are, Peter Rabbit, Benjamin Bunny, Jeremy Fisher, Mrs Tiggywinkle, and anything and everything by Richard Scarry. He loves the Usborne First Thousand Words book - knows everything in there and will spend ages pointing things out. He was intrigued when I got out the French one, and French Beatrix Potters, last week.
He recognizes tunes when they're played or sung out of context. He only sings one tune, but it's correct. He used to sing a D when I tuned my violin (it hasn't been out of its case in months - I should get it out). He knows the songs of about 20 birds (wren, chaffinch, etc) and will correct us if we give the wrong name - this is from those books that have the recordings and pictures of the birds - he can also identify about 10 of these in real life (haven't ever seen the other ones).
He absolutely loves things that spin, and different notes - so his favourite youtube material ever is watching change ringing filmed in a belfry with bells turning round on wheels, and making nice patterns of notes. Favourite thing at the local museum is the anemometer on the roof, which he spontaneously remembered at 19 months after a 3 month gap, and ran over to the correct window saying "where's my hammer motor?"
We haven't actively taught him any of this - I half-heartedly started with a few flashcards around 18 months but was too lazy/sleep deprived to do it consistently. The only things we've done consistently are read with him, many books per day; and play lots of music (classical and jazz), recordings and on piano/recorders/guitar/violin. As of the past week I am trying to read one book in French per day as well.
He's also an absolutely terrible sleeper (seems to not need to sleep after about 1am), throws the most spectacular screeching tantrums (often because he's really tired by the time we're at playgroup at 10am), and is terrible at task switching. He walked at 13 months but only learnt to crawl and get up off the floor last week at 21 months, so is a long way behind his peers in climbing, running and jumping.
Opinions very welcome, and particularly suggestions of resources.