I consistently return to a passage from Hebrews 12:18-9:
" You have not come to something that can be touched, a blazing fire, and
darkness, and gloom, and a tempest,  and the sound of a trumpet, and a voice
whose words made the hearers beg that not another word be spoken to them."
as I think about what it means to live in faith. Faith can be described but not prescribed. Faith can be seen, but not measured. Faith can be lived, but not without thought. Faith becomes a part of who one is so that it cannot be put off and separated from self. Faith is the gift that allows one to go on even when the road is full of thorns and there seems no end to the problems.
The problem with living by proof is that proofs can be shown to be false and if you hold onto the proof in spite of evidence to the contrary then you make a mockery of the truth. Proofs aren't about faith; they are about a lack of faith.
Living by faith is a little scarier and a whole lot more satisfying. A lot of worries drop off when you can accept that your faith is incomplete and will grow through your life. You can stop worrying about getting the details correct and begin to look to where you should be heading.
Saying that you have proof finishes the discussion. But faith is not about stopping a conversation, but about a journey through life. Faith is the journey of a poor wayfarin' stranger wandering through a world of woe. Faith is starting out on a journey to a land where one has never been. Faith is what happens when you believe that salvation is coming and you continue to believe even though your family and nation faces destruction and is taken away to a Babylonian captivity.
Proving that scripture is true puts belief and faith into a category that can be measured. And while there are passages that talk about if only you had the faith of a mustard seed, those passages aren't about measuring faith in a way that is susceptible to proof but living faith in daily life. Faith is not about doubts or the absence of doubts; faith is about going forth into an uncertain world and trying to make that world a better place.
Asking for proof is the opposite of faith. And while proof is useful in many places and for many ideas, thinking that having proof will solve problems of religion and belief makes a mockery of faith itself. Faith is hope in things unseen, where proof measures and weighs evidence. Faith is looking for the now but not yet, where proof exists only in the present.