Remote writing of master's thesis vs. taking a course
I am sort of confused. At least here in the states, at my university, a masters student is not expected to do novel research. When you state:

Actually this is what most students do, because generally it's thought that an advanced course is time better spent unless you have a clear path towards solving a problem in an area you're comfortable in

It sounds more like you're in a PhD program. In this case maybe speaking to your advisor and being appropriately direct (&quot;I am not sure what my goals are and I do not understand the problem domain&quot;) may give you the insight you need. Your advisor is there to first and foremost guide you through the relatively rocky terrain that is academia.
Next up:

On the other hand, my institution allows one to replace a master's thesis with an additional advanced class.

To be blunt here this sounds like you are copping out on a very good research opportunity. These options are great for students who wish to achieve a masters and head into industry, perhaps as an analyst of some kind, but you don't want to do that. In the comments you stated clearly:

@Vladhagen Being a research mathematician

Having a desire to be a researcher means you should take this opportunity to struggle. I have yet to face a problem where I had all the answers and many times exploring a subfield I am interested in results in me having to do significant research just to understand where I am going. Knowing this I have some suggestions:

Speak to your advisor. You meet for 2 hours once a week. That is a lot of time. I was fortunate to get an hour with my advisor once a week. Manage your time correctly. Since you are stuck now would be a great time to compile a list of things you are stuck on, ideas you've had, things you've tried, and direct questions on how to proceed. Speak to your advisor like a time-crunched colleague or a boss. Don't waste their time but instead come to each meeting prepared with things you want to discuss and things you want to get done. This is great in industry too. Never be the person to show up to the boss with problems and no solutions. If you present a problem have a solution. This will earn you respect in more ways than you'll realize.

You will never have complete knowledge on a problem domain. The more theoretical your field the worst this gets. So start from first principles. As you're reading literature on your problem domain highlight things you don't understand and make an effort to understand those things. Then return to the paper, proceed until you hit another point you don't understand, and repeat. Knowledge, like research, is built in a step-wise fashion. Knowledge cannot be willed upon you. You have to climb that hill on your own.


Good luck. If you wish to be in research you should complete your thesis and not take the class. The experience will be worth it's weight in gold. You will ALWAYS be able to take another class. If your research is impressive you may be able to even ask a field-adjacent colleague to write a recommendation letter for you. The politics of academia are often obscure and you can source recommendation letters from people you've worked with or people who are aware of what you're capable of. Many times it's not necessary to take a class. Please, if you plan on being a researcher do not fall into the &quot;milestone&quot; trap. Enjoy the journey and learn from what it gives you. The rest will follow.