"Discontinuity", a novelette by Raymond F. Jones, first published in Astounding Science Fiction, October 1950, available at the Internet Archive. You may have read it in the paperback anthology Seven Come Infinity edited by Groff Conklin.
The student, David Mantell, became Dr. Mantell, and in so doing provided the medical world with its most brilliant technique in thirty centuries of its history. He developed the Mantell Analysis, by which it was possible to probe the human
brain and determine the exact molecule bearing any given piece of information.
That alone would have given him an immortal name, but he was not content with only half a step. The full pace consisted of being able to duplicate or repair such a molecule and insert it into the vast mechanism of the mind if need be.
With one sweep he eliminated the centuries old butchery of lobotomy and topectomy which had maimed hundreds of thousands in its long fad.
Or would have—
To date, his experiments had resulted only in intensifying the very conditions they were designed to heal.
In a hundred cases of extensive brain damage, his process had restored life, but only in varying degrees of hopeless aphasia.
[. . . .]
And now David Mantell himself lay with a bare speck of life possessing his body. The back of his skull had been crushed and sixty percent of his brain stuff destroyed.
He was alone, but they were watching him, he knew. The room was dimly but pleasantly lit. Furnishings, books and journals were familiar. That was the way it was always arranged— the way it had been for the hundred failures before him.
But his Synthesis was no failure!
For the first time, the tremendous impact of this realization settled upon him. He was alive, aware of himself and his past. He was alive when he might have been dead. And the work of his own hands and brain had made it possible.
He sat up on the edge of the bed, examining the physical sensations. He felt normal, yet there was a new-ness that he could not define.
Then the door opened slowly, and Dr. Vixen stood there, letting himself be recognized.
David Mantell smiled. "Come in, Vic. Everything's fine. I feel as if I'd had no more than a slight bump on the head. I imagine you must have had quite a repair job, considering the jolt I got from Exter. Sit down and give me the details of
David stopped smiling. "What's the matter, Vic? Why are you looking at me like that? Why—?"
Dr. Vixen was staring, his face reflecting sickness of heart. Then he finally spoke. At least his mouth and lips moved, but his words were sheer gibberish.
David felt panic, like cold water rising swiftly about his chest. "What's the matter with you? Talk sense! Give it to me in English!"
Vixen spoke again, and still no understanding came. David had risen in greeting, but now he edged away until he collided with a desk.
He passed a hand over his face and heard the man’s voice again. He barely sensed a connotation of dismay and anxiety.
Then he thought of the others, the hundred others who had preceded him through the doors of Synthesis to a prison of aphasia that could not be opened. These had
spoken gibberish and had understood nothing said to them.
Dr. Mantell escapes the laboratory and makes contact with other people with "Synthesized" brains, and learns how they are superior to normal humans:
'Evolution appears to folldw the Law, but in a smooth and flowing curve along which mutations themselves are part of a continuous process.
“We have jumped the curve entirely. We are a discontinuity. If we understood more than a fragment of the Law of Random, we could determine if we are an error that is to be erased or if we are the beginnings of a new and higher curve. Perhaps in a sufficiently large scale of time the whole curve is naturally discontinuous. We'll never live long enough—the race may not—to know the answer empirically. Some day
we might solve it epistemologically.
"Without any way of knowing we may as well assume that we won't have to wait for the mutations of evolution. We have within our hands the means to make a new kind of man, one which can displace the old and bring reason into the world.
"Neurosis and psychosis have been driven beyond reach of us forever. I am very certain we are the most completely sane people the world has ever known!"