I’m saying the study of novel mathematical structures is analogous to such probing. At first, one can only laboriously perform step-by-step deductions from the axioms, but as one does many such deductions, intuition and understanding can be developed. This is enabled by formalization.
That certainly makes sense. For example, there are quite a few abstraction steps between the Fundamental theorem of calculus and certain commutative diagrams.
I’m saying the study of novel mathematical structures is analogous to such probing. At first, one can only laboriously perform step-by-step deductions from the axioms, but as one does many such deductions, intuition and understanding can be developed. This is enabled by formalization.
That certainly makes sense. For example, there are quite a few abstraction steps between the Fundamental theorem of calculus and certain commutative diagrams.