If mathematicians and math teachers and textbooks in all cultures in all eras say that a certain theorem has been proved, then the reasonable layperson trusts them.
At the same time, a student who wants to understand mathematics works each day on trying to understand independently of such authorities why things in mathematics are as they are.
How widespread is knowledge of the point in the second paragraph above among those who have finished secondary-school mathematics? I.e. how many students know that pursuing independent understanding is the principal activity among those activities that constitute learning mathematics? Has anyone attempted to measure this objectively?