It's very illustrative to look into the history of discovery of laws of motion, as it's quite well documented.
People have an intuitive understanding of motion - we see it literally every day, we throw objects, etc.
And yet it took literally thousands of years since discovery of mathematics (geometry, etc.) to formulate a concept of force, momentum, etc.
Ancient Greek mathematicians could do integration, so they were not lacking mathematical sophistication. And yet their understanding of motion was so primitive:
Aristotle, an extremely smart man, was muttering something about "violent" and "natural" motion: https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion#Anti...
People started to understand the conservation of quantity of motion only in 17th century.
So we have two possibilities:
* everyone until 17th century was dumb af (despite being able to do quite impressive calculations)
* scientific discovery is really a heuristic-driven search process where people try various things until they find a good fit
I.e. millions of people were somehow failing to understand motion for literally thousands of years until they collected enough assertions about motion that they were able to formulate the rule of conservation, test it, and confirm it fits. And only then it became understanding.
You can literally see conservation of momentum on a billiard table: you "violently" hit one ball, it hits other balls and they start to move, but slower, etc. So you really transfer something from one ball to the rest. And yet people could not see it for thousands of years.
What this shows is that there's nothing fundamental about understanding: it's just a sense of familiarity, it is a sense that your model fits well. Under the hood it's all prediction and curve fitting.
We literally have prediction hardware in our brains: cerebellum has specialized cells which can predict, e.g. motion. So people with damaged cerebellum have impaired movement: they still can move, but their movement are not precise. When do you think we find specialized understanding cells in the human brain?