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Something that's near incomprehensible due to complexity; unintelligible.
Trying to understand a lanuage you know next to nothing about is tough! I mean really, imagine someone trying to explain something to you in an unfamiliar language; you're not going to grasp much of anything that's being said, it'd be unintelligble. Hence, the idea for this phrase is that, basically, the extreme difficulty involved with comprehending another language is being applied to anything that's considered challenging to grasp. For instance, upon seeing a complex algebra equation, someone lacking in experience with such math problems might describe the equation as being "Greek" to them. In other words, they don't understand it; it's like another lanuage to them.

The phrase goes back to at least the early 17th century, as it's used by two different playwrights from this time period; their names being Thomas Dekkar and William Shakespeare. In Dekkar's play Patient Grissel, for example, from 1603, it reads:

"FAR: Asking for some Greek poet, to him he fails. I’ll be sworn he knows not so much as one
character of the tongue.
RIC: Why, then it’s Greek to him."

Not long after, Shakespeare uses the expression in Julius Casear, 1616:

"CASSIUS: Did Cicero say any thing?
CASCA: Ay, he spoke Greek.
CASSIUS: To what effect?
CASCA: Nay, an I tell you that, I'll ne'er look you i' the face again: but those that
understood him smiled at one another and shook their heads; but, for mine own
part, it was Greek to me."
Note: Tracking the origins of popular sayings is tough! Usually, you can find these expressions written down in old books, poems, or newspapers. However, keep in mind that just because they are found there doesn't necessarily mean that they orginated from that source. Typically, the origins will be even older than these recordings, but they will still be quoted to give you an idea on how long a phrase has been in use.

Additionally, the origins of an idiom are not always clear, and in these cases, the popular theories surrounding them will be provided. Sometimes, even I'll throw in a plausible guess as to how it may have formed. At the end of the day, hopefully you, the reader, will have a clearer understanding of the phrase's definition, some interesting info on how the saying possibly originated, and an indication on how far back in history a saying goes.
knowyourphrase.com - Common Phrases and Idioms with their Meanings and Origins
* My parents were yelling at me, but it was all greek to me as I couldn't really make out anything they were saying.

* I've recently started to watch football whenever I find it airing on television, but as of right now, the rules of the game are greek to me.
Common Phrase Meanings and Origins > A-Letter Idioms
Phrases and Idioms