Exodus 3:14 — And God said unto Moses, I Am That I Am : and he said, Thus shalt thou say unto the children of Israel, I Am hath sent me unto you.

Now this is going to get tricky! Bear with me, please through this longish piece. I’m hopeful that we’ll finish with something worth scratching our heads about.
At the recommendation of some men whose insights I respect, I’m reading “Time and Eternity: Exploring God’s Relationship to Time” by William Lane Craig. Mr. Craig is a theologian and a philosopher, and even reading the list of topics he’s written about might make your brain hurt. He’s written about questions like “Did something cause the universe”, God’s foreknowledge, Christ’s resurrection and — in the case of the book I’m reading the question of whether God is timeless or temporal (that is, living in time).
Distinguished commentators take opposite positions on this very complex question. Here, for instance, is John Phillip Lange taking the “temporal” position:

Can it be that “I am that I am” means only “I am He who I am?” that it designates only the absoluteness of God, or God as the Eternal One? We suppose that the two “I am’s” do not denote an identical form of existence, but the same existence in two different future times.

On the other hand James E. Smith presents us with a timeless God:

God answered this objection by telling Moses his name: I am. The statement “I am who I am” can be rendered a number of different ways in English. The statement basically emphasizes the timelessness of God. He is the self-existing one, the Eternal, the one without beginning or end.

So there. Two very distinguished commentators taking the opposite side of a knotty question. It’s the subject Mr. Craig is attacking head on. Can I be honest? I’m finding it stretching. We’ve been through the general and special theories of relativity, the implications of the existence of music on ideas such as “past, present, and future”, and many more … and I’m only about one third of the way through. It’s like riding a rodeo bull. I can just about stay on it, but I’m definitely not in control!
I’m pretty sure that when I get to the end of “Time and Eternity” I won’t know “the answer”. In fact, the more I think about it, the less I’m sure that I should expect to. Isn’t me trying to understand God a bit like a flea trying to understand the dog that it’s riding on, or a mouse trying to understand an elephant. There’s a reason God says:

For my thoughts are not your thoughts, neither are your ways my ways, saith the Lord. For as the heavens are higher than the earth, so are my ways higher than your ways, and my thoughts than your thoughts. (Isaiah 55:8-9)

Perhaps what “I am what I am” means is just that. “I am what I am, and what I am is for Me to know and not you”!
So when the likes of Phillip Lange, James Smith and William Craig spend time thinking and writing about this stuff, and you and I read what they write are we indulging in the “philosophy and vain deceit, after the tradition of men, after the rudiments of the world, and not after Christ.” That Paul writes about in Colossians 2:8? You know, I really don’t think so. The heart of my Christianity is to pursue God, to get to know Him as well as I can. If you’ll forgive the analogy … it’s like getting closer to my beloved wife … I study her from as many angles as I can. Of course, I’ll never fully understand her but I’m going to keep on trying. So it is with God. I’m going to use every resource I’ve got to get to know him. I’ll never fully understand Him — but I’m going to keep on trying!