Which one is correct? And if both of them are correct, what is the difference?
- Life is a mystery
- Life is one mystery
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In general, "life is a mystery" is correct.
"Life is one mystery" could be correct depending on the context. Namely:
(a) If you were saying it is not two mysteries or three mysteries, but only one. "Some people say life is made up of many mysteries. They are wrong. Life is (only) one mystery."
(b) If you were contrasting it with other mysteries. "Life is one mystery. Death is another."
There could be other cases. The point is, you would have to be making a point of the number in some way.