Mathematics is one of those areas where words are very important.
Specific words have specific meanings, and the usual overlap in meanings doesn’t exist.
Sometimes, words have means that you wouldn’t expect in english.
A theorem, for instance, is an idea about something works, a theory, but specifically one for which a proof exists.
If a proof doesn’t exist, it is a conjecture.
There is one use which appears to be more colloquial, the sort used in classes, but not in text books.
Fact. A fact is something which you are asked to believe, but with no proof.
What is actually asked for, when given a fact, is faith.