Learning math is hard. Those that have braved some of its depths, what did you discover that allowed you to go deeper?
This is a place to share insights, methods, and tips for learning mathematics effectively, as well as resources that contain this information.
Thank you, my main goal at the moment is to get a handle on statistical learning approaches and probability. I hope to read Jaynes's book and the nature of statistical learning theory once I have some time to devote to them. however I would love to find an overview of mathematics. Particularly one which focuses on practical applications or problems. One of the other posts mentioned the Princeton companion to Mathematics and that sounds like a good start. I think what I would like is to read something that could explain why different fields of mathematics were important, and how I would concretely benefit from understanding them.
At the moment I have a general unease about my partial mathematical blindness, I understand the main mathematical ideas underlying the work in my own field (computer vision) and I'm pretty happy with the subjects in numerical recipes and some optimisation theory. I'm fairly sure that I don't need to know more, but it bothers me that I don't. At the same time I don't want to spend a lot of time wading through proofs that are unlikely to ever be relevant to me. I have also yet to find a concrete example in AI where an engineering approach with some relatively simple applied maths has been substantially weaker than an approach that requires advanced mathematical techniques, making me suspect that mathematics is as it is because it appeals to those who like puzzles, rather than necessarily providing profound insight into a problem. Although I'd love to be proved wrong on that point.
Upvoted for a thoughtful comment.
I don't know anything about statistical learning theory.
I don't know what kinds of probability you're interested in learning, but would recommend Concrete Mathematics: A Foundation for Computer Science by Graham, Knuth and Patashnik and William Feller's two volume set An Introduction to Probability Theory and Its Applications.
I would second the recommendation of the Princeton Companion to Mathematics but would also warn it does not go into enough depth for one to get an accurate understanding of what many of the subje