I'm in high school and interested in becoming a deep learning researcher. I'm studying proof-based linear algebra and real analysis, though I'm finding them difficult, and I'm considering a mathematics degree.
I prefer books to online courses and want to understand the theory rather than focus on libraries. Is Deep Learning by Goodfellow still useful as a foundation, and what should I study alongside it?
Don't leave probability and statistics out of the plan. Statistical learning gives you a way to think about what a model learns from data, and basic statistics makes that material much easier to follow.
An Introduction to Statistical Learning could be a useful next book after you have some probability and statistics under your belt. It would complement the calculus and linear algebra rather than replace them.
Deep Learning by Goodfellow is still a reasonable foundation. It won't cover the latest architectures, but the core concepts are useful well beyond any particular framework.
I'd work through multivariable calculus, linear algebra, probability and optimization alongside it. You don't need to finish every rigorous math book before looking at neural networks. Going back and forth can give the abstract material some context.
Neural Networks and Deep Learning is another book to consider if you want a mathematical explanation of training algorithms. You could use it to connect the equations to the code you've already written, especially where the mechanics still feel unclear.
A mathematics route makes sense for research. Avoiding libraries for now is also a reasonable way to concentrate on the mechanics, though there's no need to make a firm rule about what tools you'll use all the way through a PhD.
And struggling with rigorous books in high school isn't a reason to give up on the goal. Take the prerequisites at a pace that lets you actually understand them.
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