I did lots of programming/cybersecurity/other similar flavor things in the past. I'm currently in college and am focusing more on developing my mathematical skillset. I've done linear algebra/multi/group theory, and am currently taking a more advanced class on algebra and rings/fields. In my classes, we do weekly problem-sets and then lectures where we see proofs and go over textbook content. What I feel like I'm lacking in my mathematical learning is exposure to how the experts are thinking about the things we're seeing. What are they tracking or considering? How do they approach the problems and what do they consider?

I usually try to understand what motivates new mathematical object or content, but professors don't focus enough on this. How can I get more of seeing the gears-level model of why things are in a certain way and especially what / how different problems are approached? Do you have recommendations in terms of links/books/articles where I can find more of this kind of perspective?