I am essentially asking whether one could come to intuitively understand how a statement (the use of statement is intentionally vague) fits in with a universe of statements regardless of familiarity. For example, such a person might be able to synthesize a new statement from a set of statements in multiple different ways. They might be able to quickly intuit a set of statements that together are sufficient to synthesize another statement. If such a person were given two theories, perhaps they would be able to see how they might fit together. If such a person exists, I imagine that their understanding of the structure of mathematics would be much more profound than what I described above.
If it is possible for such a person to exist and has existed, is there effective practice that would condition the brain to think in the manner necessary?