ID this Sci-Fi novel

This should be an easy one, I think it’s quite well known, and I remember a few details; however, googling didn’t turn anything up.

So, there’s an expedition to some distant planet by means of a generation ship (I think); at least, there are children born on the spaceship, which are being tutored by an intelligent computer system—if I remember correctly, the ship was sent on its path, with the children being born such that they are grown up and have the skills necessary in order to fulfill the ship’s mission by the time they arrive. The children’s names are derived from the greek alphabet in order of their birth—alpha, beth, and so on.

There is some sophisticated VR technology on the ship, kind of a bed or tube that you can lie down in, which then connects to your central nervous system and directly stimulates it to create the necessary impressions. At one point, they discover that you can create a kind of ‘hive-mind’ by wiring several of these things together, and a splinter group lives as such a mind for a while.

One scene I remember is that there is some kind of math test, but several of the children don’t finish, or finish by cheating—one reprograms her computer, another discovers a problem that’s more interesting to her, which she then spends hours trying to solve, and so on.

Any thoughts?

Is it any of these?

I Googled on “generation ship in fiction”.

Wild guess.

“Generation ship” was maybe misleading; it’s not continuously inhabited, but rather, there are children born some years before arrival at the ship’s destination (if I remember correctly).

How could it not be continuously inhabited?

Well, the children are born artificially, presumably from frozen embryos; then, they’re raised and tutored by an AI (again, if I’m not misremembering).

I know of a couple of stories like that (children raised by an AI after (or very late into) an interstellar trip) - one is Vinge’s “Long Shot” and another is Hogan’s Voyage from Yesteryear.

Wasn’t it, but it led me to the wikipedia page for embryo space colonization, where I found the 1982 East German novel Andymon; I’m pretty sure that’s it, it fits down to the kids being named Alfa, Beth, Gamma, Delth and so on.

Not quite sure about the VR beds, but maybe I’m conflating with something from a different source.

Perhaps Frederick Pohl’s story “The Gold at the Starbow’s End” or the novel-length version Starburst.

People on a long-term space mission and their children born on board become super-intelligent beings.

Was there one person who saw a whole generation grow and die because he was periodically suspended and the whole “first generation” was basically to instruct him?

If so, I’ve read it and might be able to find it but can’t remember the name of the top of my head.

Dark Beyond the Stars came to mind, but I don’t have a clear memory of it. What I am thinking of is a story with the children on the ships with robot caretakers. At some point the caretaker robots are called ‘War Mothers’ I think. There’s some kind of space battle where there’s a problem with some fighter ships being turned into their anti-matter equivalents somehow. That’s all that’s coming to mind. Not sure what or where that’s from.

If I can’t help on purpose, I can at least help accidentally…

That’s Greg Bear’s Anvil of Stars (sequel to Forge of God); this review mentions the antimatter bit