"The First Men" aka "The Trap", a novelette by Howard Fast; first published in The Magazine of Fantasy and Science Fiction, February 1960, available at the Internet Archive; full text available also at Trussel's EclectiCity. It was also the answer to the old questions Short story - Genius children raised in institution, invent many things and isolate themselves in time bubble and I'm looking for a short story about super intelligent/ Telepathic children. The story has its own Wikipedia page. You may have read it in one of these compilations.
Starts off with narration or presentation by a man discussing "wolf/ape children" raised by animals and how beyond point X in nurturing their potential becomes truncated at less than human average.
Professor Gojee has examined records of eighteen similar cases recorded in India over the past hundred years, and in every case, he says, the recovered child was an idiot in our terms — or a wolf in objective terms. He points out that it would be incorrect to call this child an idiot or an imbecile — any more than we would call a wolf an idiot or an imbecile. The child is a wolf, perhaps a very superior wolf,
but a wolf nevertheless.
[. . . .]
So goes my childhood hero, Tarzan of the Apes, and all the noble beasts along with him. But the most terrifying thought is this — what is the substance of man himself, if this can happen to him? The learned folk here have been trying to explain to me that man is a creature of his thought and that his thought is to a very large extent shaped by his environment; and that this thought process — or
mentation as they call it — is based on words. Without words, thought becomes a process of pictures, which is on the animal level and rules out all, even the most primitive, abstract concepts. In other words, man cannot become man by himself: he is the result of other men and of the totality of human society and experience.
The man raised by the wolves is a wolf, by the baboons a baboon — and this is implacable, isn't it?
Suggests that all humanity has always suffered from default of "apes raising apes surrounded by apes",
Now dovn to the theory, which is not entirely untested, as you know. Briefly — but with two decades of practical work as a background — it is this: Mark and I have come to the conclusion that within the rank and file of Homo Sapiens is the leavening of a new race. Call them man-plus — call them what you will. They are not
of recent arrival; they have been cropping up for hundreds, perhaps thousands of years. But they are trapped in and moulded by human environment as certainly and implacably as your Assamese girl was trapped among the wolves or your Bantu boy among the baboons.
[. . . .]
Our own work adds up to the parallel conclusion : the child reared by a man is a man. If man-plus exists, he is trapped and caged as certainly as any human child reared by animals. Our proposition is that he exists.
suggests experiment of infants determined to have high potential (with willing parents, etc) be raised in environment surrounded by and educated by geniuses.
Briefly, here is what we are up to. We have been allocated a tract of eight thousand acres in Northern California. We intend to establish an environment there — under military guard and security. In die beginning, the outside world will be entirely excluded. The environment will be controlled and exclusive.
Within this environment, we intend to bring forty children to maturity — to a maturity that will result in man-plus.
[. . . .]
Now understand this — no cops and robbers stufiE, no OSS, no kidnapping. Unfortunately, the world abounds in war orphans — and in parents poor and desperate enough to sell their children. When you want a child and such a situation arises, buy! Price is no object. I will have no maudlin sentimentality or scruples. These children will be loved and cherished — and if you should acquire any by purchase, you will be giving a child
life and hope.
End of story, adult protagonist is standing over hole where academy was reading "Dear John/Progenitors" note explaining that the kids are grateful, but the rest of the species is just too painfully stupid to endure any longer so they are taking the academy and leaving to explore a dimension one of them had discovered.
We got the three years we needed, and as for the gray barrier that surrounds us, the children tell me that it is a simple device indeed. As nearly as I can understand, they altered the time sequence of the entire reservation. Not much — by less than one ten thousandth of a second. But the result is that your world outside exists this tiny fraction of a second in the future. The same sun shines on us, the same winds blow, and from inside the barrier, we see your world unaltered. But you cannot see us. When you look at us, the present of our existence has not yet come into being — and instead there is nothing, no space, no heat, no light, only the impenetrable wall of nonexistence.