Let me start by saying I am not sure if this is the correct place to ask, but I would for sure prefer the question be answered by a mathematician.
I graduated as a physics major in 2021, I always loved math, and loved studying it alongside physics.
I began being aware of the more abstract side of mathematics in my third year, I self-studied Linear Algebra, it was my first exposure to the definition-theorem-proof formulation, I then studied Topology and Analysis on Manifolds by Munkres.
A critical point I have to make is that I hardly did any challenging exercises, I could understand most of the topics very well, however, when it was up to me to solve something non-trivial from scratch, I couldn't do it.
After I graduated, I immediately applied for a master's in Mathematical Physics, I got accepted, then dove right in. The topics were functional analysis and differential topology, it was quite a challenge to understand the lectures, even much more challenging to do any assignments.
This kept going back and forth with me for 4 months, everyday struggling to decide whether I should leave the program totally and start to study the prerequisites properly or whether I should just push through this thing.
It turned out it was close to impossible for me to contain all this dense information in such a short time, let alone be able to solve problems on my own consistently.
After I decided to ignore the program completely and do more self-study, I got stuck in a loop. I would start studying for two or three days, find out that I have no motivation at all, and therefore stop studying. A week passes, same thing happens, a month passes, same thing happens, over and over for two years now.
I'm getting the feeling that this might be because I'm no longer doing these courses formally (not having a syllabus, assignments, or lectures) and so I am just studying the topics in order whenever I want, and I do not really have a specified direction to aim for.
If anyone can recommend a place online where I can follow courses and develop a discipline to keep going, or if anyone got some solid advice for a person who loves mathematics but lost in his journey, that would be very much appreciated.
The best piece of advice I can give comes from a knowledge of how hard the homework is in graduate school versus undergrad. In my experience in mathematical physics (Ph.D.), the graduate tests are about the same difficulty as undergrad tests (unless they're take-home, in which case WATCH OUT!!!). But the homework is $5000\times$ harder. My undergrad strategy for doing homework was quite simple:
This was an utter failure in grad school, because I would hit brick walls and make no progress, which is quite demoralizing. One of my professors (real analysis) said that I needed to update my strategy to the following:
Why was this better? Because the homework is so hard that simply throwing more time at the problems won't help you. What helps you is the number of fresh starts. In addition, every once in a while, particularly if you are taking related courses, you might get cross-pollination, where an idea in one course helps you in another one. The second strategy above maximizes the potential for that to happen.
Having the established courses you're taking, versus self-study, has this distinct advantage: you have professors to bug during office hours. Now this is graduate school, so they're expecting you to do the lion's share of the heavy lifting in your own learning. But they are a resource.