Being that high of an intellectual and advanced academically so far, at such a young age - does this affect how he socializes and is able to relate to his peers? And in what ways?
Extremely so.
When it became clear that Pavel was leaps and bounds ahead of his peers as a child, it was the start of the rift that would only continuously widen between him and the people around him.
He had a lot of difficulty socialising with the younger kids around him whose interests and focus were fleeting and incredibly short-lived. At six, Pavel had already decided where his life goal ultimately lay: Starfleet. Elizaveta approved, maybe knowing this was inevitable. And if he was going to go to space, become one of the greats like the cosmonauts of the Twentieth Century who paved the way for humanity or like Zefram Cochrane, then he had to dedicate himself to that, and he would. He did.
Pavel loved to play, sure, but he loved to read and learn and explore, and the other kids thought he was weird for always knowing something about everything, for always reading, for talking the way that he did about the future. Pavel knows too much! Pavel's a freak, a monster, a weirdo—we don't like him.
So he made a couple of friends, another group of strange kids who thought he was cool and accepted him easily: Irina A. Galiulina and Anton B. Zakharov.
It bothered him, of course, this estrangement from his peers, but he couldn't really do much about it. His advancing through his education so fast never gave him the chance to really try, either. He'd be in one year, attempt to make friends, and then rocket through it and propel himself to the next one, having to leave those classmates behind. Friendships, if any, were fleeting and short-lived. He was poorly socialised during this time and the education system failed him in that regard, ill-equipped to deal with someone of his calibre.
When he made it to undergrad and ultimately Starfleet Academy, the differences had never been more apparent. At ten years old, kids have no real idea what the world around them is like, how it works, or have any real semblance of self, not in the way you realise when you're in your late twenties, your thirties, and really get a sense of who you are and what you want. They're young, still figuring things out, still being protected and guided by their parents. They're exploring, learning, growing, but far from being anything resembling an adult.
And then here's Pavel, ten, starting undergrad with students in their mid-late teens, thinking he's going to have more in common with them than anyone else. These people want to be here and learn, right? They'll have similar interests, they'll be people he can really form lasting friendships with.
Well, no.
He's a baby in their eyes. Smart, undeniably; so smart that it's almost an insult to everyone else to be shown up by a fucking child and there's some resentment for that. But on top of that, what teenager wants to be babysitting the damn kid who isn't old enough to drink, to go out, to do anything?
But Pavel doesn't see it that way and he goes to great lengths to try and prove it. He takes some silly risks while in undergrad hoping he'll be able to show them that yeah he might be younger but so what? It doesn't matter. He experiments with alcohol young when he's more-or-less dared to to make a point. He learns to talk like the older kids, swear like a sailor, sass them back when they deserve it.
Pavel does everything he can to eliminate the age gap between them, to make himself seem older, like one of their peers, but it's much harder than he realises, and to many of the older students, it's a game. It's funny, watching the kid try and play at being an adult like them.
Only, it's not all an act. He's incredibly mature for his age, something that was forced upon him by circumstance. And I think the reality of that also makes him weird not only to older kids, but especially to his peers in age and those younger than him.
A good amount of his professors like him though, because despite his attempts, he's still kind, respectful, and very involved in his research. The professors look at him strangely, but he's capable and dedicated and they like him. Respect his abilities. Challenge him, even. Socialising with them is easy enough. He likes it.
Socialising with people much older than him just becomes easier than trying to figure out things in common with his peers. It's part of why Starfleet Academy works so well for him. The structure, the atmosphere—some of his colleagues are still difficult, still come after him for his age—do well for someone who has been in academia all their lives and are mostly used to similar environments. When he's not irritating the professors, they like him more than well enough. Why his youngest friend on the ship is still at least four years older than him.
Pavel has barely any friends his own age and most kids his age think he's weird because his interests and personality have pushed him so far away from his own peers that it's hard to find a lot of common ground between them.
