A lot of fields in math expose a kind of API that abstracts away details quite well. You can use SVMs without fully understanding the specific QP optimization

A lot of fields in math expose a kind of API that abstracts away details quite well. You can use SVMs without fully understanding the specific QP optimization algorithm underneath, you can understand the kernel trick without all RKHS math etc. Or in classical vision, you can use keypoint extraction without caring about the details. Or in linear algebra you can understand what SVD is and does without knowing the detailed steps of computing it. I don't see neural nets as very special in this.