But long after coercion is removed, the faith lives on. People who have the truth and know it are less likely to reject it. It’s like F=mA. It may have been imposed on us by that mean high school physics teacher. But now that we know how much it explains about the world, why would we reject it?
Faith lives on mainly because once enforced upon a people, it becomes engrained over time, it becomes a part of the culture. The oldest known exsting faith is the Hindu - probably over 6000 years old and before that, anthropologists tell us there was an even older form of the Hindu. Few Christians make the arguement Hindu is a “true” faith, even though it long predates Christianity. But clearly, Hindu is very much a part of Indian and certain eastern cultures.
And consciously rejecting a certain faith tradition is far more troublesome than simply accepting it once its engrained in the culture or society. In extreme orthodox cultures, rejection of the dominant faith tradition can lead to banishment, ostrcism, even death.
And even in our suburbanized, politely Christian cultures in the West, to reject a mainstream religion still makes one a pariah. The occasional suburban intellect who admits to being Agnositc, or who starts practicing another faith tradition looses a lot in his suburban community: Fellowship, business contacts, possible suitable mates, there is generally some family strife, etc. all of which makes people “remain” with the “truth”, if only to avoid the loss of community.
As for mathematical proofs, I hardly think one can assert them as an analogy to faith. We do not accept math or science on faith. 2 positive things added to 2 positive things always, repeatedly and demonstrably leave 4 positive things.
The “truth” of any faith, is always subjective. That Jesus rose from the dead, walked on water or raised the dead exists only because one believes it to be true and a group of similar believers enforce that belief amoung each other and try to spread it to gain a large community of believers. However, what Jesus actually did has never been demonstrated and the only way we know it is because others told us it happened and we are told to beleive it lest we burn in hell if we do not beleive it - which is not proof of truth, but is emotional coersion that plays on human’s innate fear of death.