Greetings, I am a 12 year old who is vastly intrigued by the wonders of theoretical physics (experimental physics has not exactly been to my liking) as well the subtle art of mathematics. For the past six months, I have attempted to work my way up to mastering mathematical prerequisites required of basic quantum mechanics. While I have learned some of the conceptual aspects of QM, I understand very scarce amounts of the mathematical formulation of it. The Dirac notation is bearable, but the issues turn up when there begin turning up partial derivatives, partial differential equations, esoteric metrics, topological spaces and so forth. How would I potentially overcome such a barrier? My math repertoire is currently exceedingly limited, consisting of merely 75% of differential calc., 50% of integral calc and mastery of the prerequisites. I have dabbled a bit in the fields of complex analysis and linear algebra, albeit now I fear that by learning excessive theory, I am not gaining much out of it. For instance, there were questions in a national math olympiad past paper that completely stumped me, even though the answers operated on basic mathematical principles such as the pigeonhole principle. Thus, I desperately want to enhance my mathematical problem solving skills, not for the sake of time management, but for the sake of finding innovative and creative methods to solve a problem by applying the theory. I have read a bit on The Art and Craft of Problem Solving by Paul Zeitz, but I feel that it isn't allowing my problem solving (which is exceedingly important in research mathematics) to improve by a vast amount.
As for theoretical physics, I have read up a bit on the underlying basics of special relativity and quantum physics (e.g. Minkowski spacetime diagrams, Bell's inequality, Lorentz and Gallilean transformations, Kochen Specker theorem and the EPR paradox), albeit I honestly don't know what to do now, considering my limited math knowledge. General relativity simply overwhelms me with excessive differential geometry, Griffiths' introductory quantum physics book is just too advanced for me, special relativity provides with a relief but nonetheless, I get perplexed by the most seemingly simple things. I don't know how to go about such.