No, not a vacuum. Let me try to explain it this way. Some years ago I took my first class in mathematical proofs at college. The instructor wrote a proposition on the board, and then he proceeded to write the deductive proof of the proposition. When he finished, a student raised his hand and asked, "How did you know where to begin with the proof?" The instructor paused and then said, "Divine intervention."
The class burst out in laughter. The instructor used humor to explain that there is no formula that can determine how to write a deductive proof. There are some guideline but no formulas to tell you how to proceed. You simply need to work a lot of problems and develop some mathematical intuition.
Shakespeare was a great artist. We don't know very much about his personal life. We do have his works of art that have given pleasure to generations of men. That art came from a great imagination. That imagination cannot be explained by theories of childhood development.
The genius of Archimedes cannot be explained from childhood development. At the age of five the great German mathematician Gauss was able to add large numbers in his head without any mathematical training. How do you explain that?
I don’t think Gauss learned to count by himself; his gift required context to operate. We don’t have to capture the essence of genius in a bottle to understand that environment shapes and channels it.