How can you do the math from scratch? i mean. this requires some understanding of advanced algrorithms... right? or am i missing something?

because some people may not know the maths directly and will program the code only when they have a full proof or some proof to validate the program they made and not just simple "code" writing. He would think about the mathematics from scratch rather than just translating an already existing maths paper. at least this is how I view it. I do the maths from scratch and then move on to the programming once I have something clear