TITLE: how mathematicians do research?
QUESTION [9 upvotes]: I am a first-year physics graduate student with a deep interest in mathematics. I am specifically interested in algebraic geometry and algebraic topology, and I would like to employ advanced mathematics in my physics research. So far, I haven't chosen an advisor. However, I have been trying to do research on my own without any guidance for a few years and I failed miserably. I do not have any good idea how the best mathematicians do research. I will try my best to summarize one of the problems I am currently facing hoping that someone might help:
I never start by stating some open research problem. I start with the goal of understanding some well-known result or subject. In particular, suppose I want to understand the known ideas about the quantum dynamics of $\mathcal{N}=2$ Super Yang-Mills theory. I try to derive everything starting from scratch e.g. by deriving the SUSY algebra, Lagrangian, and so forth. I try to do this in my own way. I pretend that these results are unknown, and I try to re-derive them. However, it seems I'm not able to go so far in the subject. I'm not sure what the reason is. I believe that $\mathcal{N}=2$ supersymmetric theory is connected to some ideas in mathematics, such as algebraic geometry and supergeometry, so I try to motivate the study of these mathematical subjects using supersymmetric dynamics.
My question is: is this how mathematicians do research? is this approach good? I find that recent papers are impenetrable because they assume I have a lot of background knowledge/ did a lot of computations that I did not do. So I have to study the background. However, when I decide to study the background, it takes me a lot of time because it seems I'm trying to re-invent the wheel, re-deriving everything on my own.
I hope my question is not too vague. Any help would be greatly appreciated.

REPLY [2 votes]: To answer your original question, you could try reading these books:
J. Hadamard The Psychology of Invention in the Mathematical Field (1954)
J.E. Littlewood, "The Mathematician's Art of Work" in Littlewood's miscellany (revised edition, 1986)
I. Stewart Letters to a Young Mathematician (2006)
C. Villani Birth of a Theorem (2015)
However, I suspect that your real question is along the lines of "what's the most effective way of learning algebraic geometry and algebraic topology, so I can use them as tools in my research?"
The resources at https://mathvault.ca/ may be useful for this purpose.