A few weeks ago I was giving a talk in meeting. I made the statement that our eternal occupation will be to learn about the Father and the Son. A brother in the meeting called me on that: he wanted a chapter and verse to support my claim.
Let's point out that this is exactly how the assembly is supposed to function. When someone makes a statement, it is imperative that the other people in the gathering should be willing to challenge it. Now, this brother didn't come out swinging, he didn't tell me I was an heretic, he cast no aspersion on my family. He simply challenged me on my statement and asked me to prove it from Scripture. This is what 1 Corinthians 14 specifically commands: the prophets are to speak, and the rest are to judge. That's not to say I consider myself a prophet, but the idea is that the assembly is a place where we judge what's said.
So this brother brought up a legitimate point, and I'm ashamed to say I didn't have an immediate answer. So I told him I'd get back to him. It's taken me longer than it ought to have, but I've been trying to piece together a reply. I thought this would be a good place to do that; so you get to read my rough draft, so to speak.
Probably the best place to start is with the Lord Jesus' statement at the start of John 17:3, "this is the eternal life, that they should know thee, the only true God, and Jesus Christ whom thou hast sent". So according to the Lord Jesus, eternal life is knowing the only true God, and Jesus Christ. This, I suppose, almost completely answers the question. Knowing Him is eternal life.
It's no stretch to say that if knowing Him is eternal life, then it will be at least a huge part of what we're living for in eternity.
Scripture doesn't tell us a whole lot about what eternity will be like. Scripture isn't, after all, written to satisfy our curiosity. But there are some positive statements made that touch on our question. One is in Ephesians 2:
but God, being rich in mercy, because of his great love wherewith he loved us, (we too being dead in offences,) has quickened us with the Christ, (ye are saved by grace,) and has raised [us] up together, and has made [us] sit down together in the heavenlies in Christ Jesus, that he might display in the coming ages the surpassing riches of his grace in kindness towards us in Christ Jesus. (Ephesians 2:4--7, JND)I find this statement interesting, it says one of God's purposes is to use the Church as a display of His grace in the coming ages. It doesn't say who's looking at the display, it merely says the Church will be on display.
This seems to support the notion that eternity will be all about getting to know God better. Not in the sense of a classroom, but in the sense of getting to know Him. As we look at the Church in Heaven, we'll see His grace on display. And the more we look at it, the more we'll see of His grace.
Ephesians makes another statement about eternity:
To me, less than the least of all saints, has this grace been given, to announce among the nations the glad tidings of the unsearchable riches of the Christ, and to enlighten all [with the knowledge of] what is the administration of the mystery hidden throughout the ages in God, who has created all things, in order that now to the principalities and authorities in the heavenlies might be made known through the assembly the all-various wisdom of God, according to [the] purpose of the ages, which he purposed in Christ Jesus our Lord, in whom we have boldness and access in confidence by the faith of him. (Ephesians 3:8--12, JND)This one is a little different, it says God will use the assembly to demonstrate His wisdom to the principalities and authorities in the heavenlies. Here we have an audience named for the display, but once again the whole point of the display isn't the Church itself, it's the character of God that will be seen as they look on the Church.
So the two eternal purposes of God in the Church in Ephesians are certainly centered on getting to know God better. In the Church we'll see His grace and His wisdom. And that means we'll have an eternal job to do (if I can say it that way): we'll be on display to show Him off.
1 Thessalonians 4 says the whole point of His coming to get us is for us to "ever be with the Lord" (1 Thessalonians 4:17). That was the apostle's encouragement to the Thessalonians, it should encourage us too. He's coming to get us so that we can always be with Him. Notice the Lord said almost exactly the same thing to Peter, "if I go and shall prepare you a place, I am coming again and shall receive you to myself, that where I am ye also may be" (John 14:3, JND). So this is, in a sense, the promise of eternity: there'll come a time when we'll be with the Lord Jesus forever. It's the thought of Scripture that we would be excited by this prospect, that it would be something to keep us moving forward.
Paul said something similar in Philippians 3: "that I may know Him" (Philippians 3:10). This is a striking passage, because Philippians was written late in his life. He'd already learned more than I'll ever know about the Lord, but his goal was to know Him. This suggests to me that we'll never come to know the Lord Jesus completely. I'm not saying He is completely unknowable, but He's definitely not completely knowable. We'll still be knowing Him better for all eternity: even with all eternity, the infinite God will be a mystery to our finite minds.
Having said that, I think I dropped the ball when I was giving that talk. I think I probably talked about knowing about Christ, as opposed to knowing Him. There is a huge difference between the two, although they're not entirely unrelated. I wouldn't say I know a person if I know absolutely nothing about him; on the other hand, knowing all about someone isn't the same as knowing him. It's possible to know a great deal about the Lord Jesus without actually knowing Him. That's not eternal life.
So no, our eternal occupation's not going to be classes in theology. But we will spend eternity getting to know God better. We'll spend it getting to know Christ better.