[jdw64]

So what I’m most curious about is this: if there are axioms and proofs so enormous that a human could never prove them in a lifetime, but a machine can, does that make it engineering? That’s the point I’m really wondering about.

I mean, what if a human could follow every single step of the process in principle, but the sheer volume is so vast that a human can never see the whole thing—would that be engineering?

But I don’t think of that as engineering. In the future, maybe it will be called an Oracle

[oliculipolicula]

You might have gotten it backwards. Proofs are essentially rooted trees

The details could be painful but having a birds eye view is always possible?

And having a machine compress it for human consumption, sounds very plausible (and which I think of as engineering)

[pfortuny]

I would call it "Engineered (as machine-made trustworthy) Mathematics": you have results but nobody undrstands them but they were not produced by humans.

Despite that, people use them. In that sense, similar to the Finite Elements method. But the tools (statements) are machined like any other tool (screwdriver).

Similar to microprocessors in your example. But about statements.