Faith is often described as belief without evidence. The famous definition in Hebrews, in its best-known form, is close to that:
"Now faith is the substance of things hoped for, the evidence of things not seen." - Hebrews 11:1 (King James Version), often attributed to St. Paul
This is the way the term "faith" is used by religious people when they argue against the primacy of reason, as demonstrated in these quotes, which is the context I am concerned with. (It's also the meaning used by atheists arguing against religious faith, eg. Sam Harris in The End of Faith.) But the New International Version, which is less pretty, but translated more carefully by better scholars from more and older texts, says:
"Now faith is confidence in what we hope for and assurance about what we do not see."
The Wikipedia and Plato entries on faith give information on the use of words translated as "faith" in English in different religions and philosophies. Wikipedia cites the New American standard exhaustive concordance of the Bible as saying,
In English translations of the New Testament, the word faith generally corresponds to the Greek noun πίστις (pistis) or the Greek verb πιστεύω (pisteuo), meaning "to trust, to have confidence, faithfulness, to be reliable, to assure".
Scientific theory is also assurance about things unseen. (If you can observe something directly, you don't need science.) Science builds an abstract mental structure that interprets data and makes predictions from it. It is also an epistemology for belief in things we can't see, like atoms, oxygen, radio waves, vast distances, or circulation of the blood.
The history of faith and theory
I've read many accounts by Christian missionaries of how they persuaded people living in tribal cultures to convert to Christianity. Faith is not a factor in these debates. Tribal cultures don't need to protect their religions with rationalizations. In these narratives, the tribe members often seem unaware that not believing their religion is a physical possibility; they are sometimes less surprised that the white-skinned stranger descended from the skies, than that he pretends to be unfamiliar with their gods. Tribal people are more reasonable about the matter than people from advanced civilizations; they never defend their religion by making arguments against reason itself. They are pragmatic and opportunistic: Can the missionary cure the sick better than the tribal shaman? Yes? Then his god is stronger!
There are numerous verses in the old Testament about faith, and many more passages describing the same sentiment. But "faith" in these passages seems synonymous with "obedience", or possibly "trust", when it isn't something else entirely that was lost in translation or history (e.g., "And there shall be faith in thy times: riches of salvation, wisdom and knowledge" ... what?)
Nothing described in the Wikipedia or Plato pages on faith definitely antedates Buddhism1. The concepts of faith, and of scientific theory, both may have developed primarily between the 6th century BC, when mathematics, philosophy, Buddhism, large parts of Hindu philosophy, and Phariseeic (intellectual) Judaism were being invented; and the time when Jesus spoke and Paul wrote about faith as a kind of power and a means of justification (a technical Christian term).
By the time Jesus spoke of faith, it had one main feature distinguishing it from theory: The truth of the belief was proportional to the strength of the belief. Luke 17:6 (NIV): "If you have faith as small as a mustard seed, you can say to this mulberry tree, 'Be uprooted and planted in the sea,' and it will obey you."2 Paul's chapter on faith (Hebrews 11) describes faith as having causal power.
How many people living during that time could have distinguished between faith and theory?
Faith as reaction to theory
One theory of mine is that faith developed as a reaction to theory. How to keep a religion alive, when these pesky philosophers are corrupting the youth with reason? Declare that reason is not the final arbiter! Faith is thus a sort of early post-modernism.
You could alternatively see it as the post-philosophical epistemology for people who value winning over being right; it lets them retain adaptive beliefs that their society had evolved, even after philosophers found disproofs of those beliefs.
Faith as popularized theory
"Christianity is Platonism for 'the people'". - Nietzsche, preface to Beyond Good and Evil
Another theory is that faith is a faulty theory about theory. Ancient people could have observed proto-scientists, and their ability to make seemingly-impossible predictions - such as the time of eclipses. The first prediction of a solar eclipse was perhaps in 585 BC. What did non-astronomers believe the astronomers were doing? Did they think that the power of the astronomer's belief caused the eclipse? How many Pythagoreans understood why the sum of the squares of the sides of a right triangle equalled the square of its hypotenuse, or why the square root of 2 could not be rational? Did they take these claims on faith, like most high-school geometry students do today? If you imagine that understanding has magical power, it would be easy to read what Paul wrote about faith, and substitute the word "understanding". Is that what some Gnostic Christians were doing?
Faith as proto-theory
Another theory is that theory is faith++. The mental commitment of faith is very similar to the mental commitment of theory, if not the same. People practiced in having faith in things unseen, would be more likely to be able to have theories about things unseen. They would just have better heuristics for what to have faith in. This suggests that faith is a necessary historical precondition for theory.
Faith ≈ theory
Perhaps my favorite theory - and these theories are not all mutually exclusive - is that many pre-modern thinkers did not distinguish between faith and theory. It's not clear that Gnostic Christians, Hermetic philosophers, or alchemists were able to make that distinction. Many Gnostic Christians may have thought they were practicing a kind of natural philosophy. Many Renaissance alchemists may have regarded their studies as a spiritual practice. Therefore, in modern debates between faith and science, when people cite pre-modern texts and try to claim their authors for their side based on their usage of terms like "faith" or "reason", it may be those authors weren't even aware there were different sides to be on.
2. Faith performs work, and is therefore a type of energy. A mustard seed weighs about .002g, which is the mass equivalent of the energy of 43 tonnes of TNT. So Jesus was being conservative.