I interpreted this to be a top down vs bottom up argument. In mathematics, we certainly have ZFC as an axiom system now, but mathematics was performed for thou

I interpreted this to be a top down vs bottom up argument. In mathematics, we certainly have ZFC as an axiom system now, but mathematics was performed for thousands of years without a "stable" axiomatic base. For example, calculus was developed before the axiomatic delta-epsilon definition for limits was created. The math was developed first, and it was only after the fact that mathematicians went back and set the theory on a stable theoretical footing. Therefore, I believe Stepanov suggests a bottom up approach: You write an algorithm that performs your work first, and then once you have that, you can refactor the code into classes that encapsulate the various parts of your existing algorithm.