"The Computation" becomes progressively more unreal before taking a final swan dive into the supernatural. You don't realize exactly what the poem is about until about halfway through, when the number of years reaches the thousands. Then you might think, "OK, this cannot possibly be real, I'd better figure out what else is going on." Or at least that was our experience. The poem depicts the speaker's interior reality, which is inextricably tied up with the fate of his relationship with his beloved. Just when you are tempted to think that the speaker must be older than Methuselah, he tells you that he's not old at all. He's just dead. Oh, that clears everything up.
The claim of immortality is meant to reassure his beloved that he will never leave her, or give up on wooing her.
The poem argues that disappointed love brings people into a state of self-contradiction.