find a problem without an answer(o) and try to answer it research as much as you can about the problem until you understand it well enough to explain it to som

find a problem without an answer(o) and try to answer it research as much as you can about the problem until you understand it well enough to explain it to someone else when you come across new concepts, research them.. recurse ;p if you like to program then try to write your own implementations of concepts as you learn them if you are unfamiliar with programming i would recommend trying it, you get to build this math you are learning and when complete you can develop intuitions by manipulating: constants, methods, models,..; as well as being a great learning aide.. debuggers as standins for instructors read original works: books,papers,..; where ideas are branched from the engineered complexity of the state of the art can obfuscate underlying concepts, and seeing how they were first formed can illuminate their present state these initial works can be very approachable because they often contain new concepts that need to be defined within them, whereas a paper referencing that initial work will often consider the concepts well known to anyone intending to read them and omit comprehensive description i think what is most important is that you research whatever is interesting to you (o) https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_m...