As someone who is also largely self taught in cs terms, it's actually very amazing to me how even very abstract ideas which seem to be very far away from a "solution" to a "problem" often fall into place very nicely.
For example consider a unification algorithm (e.g. https://reasoning.page/29021/unification-sort-of-in-rust which is an explanation of it that I wrote). The individual parts of it do not seem that spectacular, and also seem quite abstract. It is so simple (in my mind) that it could not possibly be correct. However, there is an emergent property when the interactions between the different parts of the program are taken together.