I think chatgpt's effectiveness for self-studying would depend on the subfield of pure math. For example, real analysis I believe is still best self-studied by just reading baby rudin and doing the examples and exercises. However, I really could not make much progress on topology until chatgpt walked me through what the open set axioms actually meant in the context of metric spaces (which most of the topological spaces one encounters are), otherwise they just seemed very arbitrary.
In my opinion, it is less dependent on the subfield than the textbook you use for that subfield. Unfortunately, math textbook recommendations are relatively subjective, with many popular choices unsuitable for self-study, or even study.
With regards to topology, your experience rings true. In short, anyone with knowledge of calculus / basic real analysis wanting to learn topology should read "Real Analysis" by Carothers.
Usually topology is taught after real analysis, extending many results that hold on the reals as the main motivation. But this process is quite abrupt without the intermediate context of metric space, leaving many people confused. It doesn't help that Baby Rudin is quite terrible at teaching these concepts for you. On the other hand, Carothers' book is a paragon of mathematical exposition. It excels at telling you why metric space, topological space, and all the definitions are made that way.
With regards to the parent, I have to say "Proof is left as exercise" is probably the number one thing that forces students to actually read the texts. The best way to learn is to ask ChatGPT after you're stuck, not before.
I have worked through some of Carothers myself and like it a lot.
Are there other math books you think highly of that are similar, i.e. good for explaining why the definitions are the way they are as well as teaching the material?
