I think that numbers create all sorts of problems because people focus on them as they are familiar and miss the bigger picture.
I think that numbers create all sorts of problems because people focus on them as they are familiar and miss the bigger picture.
Abstract algebra (i.e. actual algebra, as opposed to doing useless stuff to poor polynomials) requires one to have developed the mathematical maturity to iron out informal thinking.
Good luck explaining "prime" and "irreducible" are not the same.
I think a path that would work better is through problem solving, like olympiad problems. But even that definitely isn't for everyone.
Without the proper context, group theory and abstract algebra are deeply uninteresting subjects. It would be like trying to read Bertrand Russell before you learned your ABCs, ridiculous. It's important to start with numbers because they are familiar.