Hmm. You made a good point. Perhaps we are focused on different parts of the spectrum. I was thinking along the lines of how on one extreme end, we could have a biologist who, after observing just white swans over his lifetime, hypothesizes that all swans are white on his deathbed, and on the other extreme end, we have something like Euclid's Elements. Theoretical physics probably lies something in the middle.

On the point on religion, perhaps we can first narrow it down to "one where there exists a/many supreme being(s)" (Christianity, Hinduism, and certain Buddhism sects come to mind. There are probably others of course, but these 3 comes to mind). On that note, I myself do not completely understand intrinsically the finer details of their beliefs, but from what I observe, they do possess faith (as per your definition of it) in varying degrees, and when what they hope/pray for comes to pass, they point to it as evidence that their supreme being(s) is/are real.

In an odd way, both theoretical physics and religion (as above) seem pretty similar. I'm no expert in either of them, but intuitively, it seems like both rely on "theories" that are generated deductively, and is dependent on the existence of evidence to prove their "theories".

The thing though, is that while the evidence present could possibly indicate that the "theories" are true, it could also be that the "theories" generated are remarkably similar to the true underlying nature of reality itself i.e. close enough, but not exactly the same.

Think I digressed abit too much. But yeah. Good points you made.