Your question makes me very happy. There is nothing more beautiful than math which man has created. It is because it is pure and complete in perfection. The answer to your question is FOUNDATIONS and ALGEBRA.
"Foundations, Set Theory and Logic" is the diamond pure cystral on which math is based, it took many of the most brilliant minds to develope it.
"Algebra"-not the one you learn in school-it is strongly connected with "Foundations" it is the foundation of many numbers which we use. For example, what is a real number? A scientist will think this is a stupid question, but in reality we define them with Dedikind Cuts and Cauhy Sequences (a construction of the reals) to answer this extremely complicated question you must be fimiliar with Algebra. And you will see it makes sense complete and perfect sense, like nothing else which makes more sense than math. So the math you want to learn (without balls, tables, moving bodies in a vacuum) is called "Pure Math". I promise you, you will love it.