Faith

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".^[22]

Theory

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

The most popular belief appears to be that faith is ancient, and scientific theory came along later to supersede it.  But I'm not aware of evidence for this.