If someone wanted to learn more about this type of mathematics, without matriculating at a university, what would be some good starting points?
Mathologer would be my second recommendation. Once again not sure he has touched the Riemann Hypothesis, but he does a number of great videos where you can start expanding being comfortable with often untouched fields of math (like modular arithematic) while introducing a how seemingly unrelated fields end up having connections.
Videos can go between 20 minutes to an hour and I often enjoy watching one every few days.
I've found that 3Blue1Brown (youtube) gives a great starting point for many topics. Provided you actively participate in them, the videos will build up some intuition so you know what questions to ask (and why they're worth asking).
The author usually links to followup resources so you know where to go next. I've found his resources a bit hit-or-miss, but they give me enough to know if I want to continue exploring. If I do, I usually check out a good textbook (I refer to https://news.ycombinator.com/item?id=17617825 often).