We have thousands of years of precedent that suggests that breakthroughs in mathematics tend to accumulate into broader technology breakthroughs in other domains.

Why does this tend to be the case, even when some of the smartest people in the world have historically predicted incorrectly that certain branches of math would forever be useless (e.g., number theory)? I can only offer my own theory on that, but my guess is that mathematics is simply a predictive framework based on pattern compression. A more powerful pattern compression framework accelerates every single field that relies on pattern recognition or prediction of the unknown based on patterns.

You could have one really hard to understand proof of a theorem and then a lot of interesting human-understandable stuff that relies on that theorem. We already have lots of proofs with oracles, where you can work out consequences of what kind of structures and solutions could exist if you had some magic thing to solve a hard part, so it just seems like a variation on that. Many people learn calculus or even the real numbers without understanding the complete formalization from set theory.

One day it might be for the AI's pleasure, the same way it has heretofore been for ours. Or if you prefer, as a byproduct of its programming to acquire knowledge.