Terence argues that explanation of results ("understanding") will be the new bottleneck in math research but I am not sure this is the real bottleneck for progress.

Understanding was critical for the field to progress when only humans were involved but if humans are not needed to make progress, I wonder if we split into two worlds: an AI math-world where amazing new results continue at a rapid pace bottlenecked only by compute/cost and a human math-world where we understand a subset of the AI math-world as a hobby (similar to Stockfish vs human chess).

In some sense "understanding" (understanding if it is true, if it is important, how to use it) is about the only bottleneck in math. Any theorem that you can write down or imagine is already true, false, not provable already. In some ways we can already start iterating through all the theorems. We will never get to the end (or really get very far down the line) and most all of them be trivial (I think the Busy Beaver[1] project is a fascinating example, ymmv).

I am wary of AI in all aspects I am seeing it in but in many ways in mathematics seems to me the least troubling. It will change things in and the field will not be the same. Blacksmithing has not really gone away. You can still work as a farrier, if you like that sort of things. The tools that replaced a man working over a forge with a big hammer are part of a giant industry that is still producing works for the modern world.

[1]: https://bbchallenge.org/8226493

How is either of those situations more or less like a hobby than the other?

Somehow, I feel that progress, in your understanding of what progress is, loses all meaning.

It will be the same as before: some effort will go into checking proofs and the other into creating them. AI speeds up both.