This paper is actually not a bad one to get started with. Obviously you need the proper background and I am not sure how much linear algebra you've taken. Going through a senior undergrad numerical linear algebra text might be a good way to learn the prerequsites. In particular, you'll never be able to read a math paper without developing mathematical maturity via textbook exercises.

Assuming you have the background, the boring answer is "patience and practice." For years I had to practically rewrite math papers word for word in order to get anything to stick. These days I am better at reading "mentally," but still sloppy and prone to misreading (just yesterday I misread GPT's proof because I was lazy and on my phone). More so than the empirical sciences, mathematics demands you understand every sentence before moving on to the next. Skimming does you no good. It really does just take patience and perseverance.

The nice thing about this paper is that the math isn't especially advanced, and it's broken up with qualitative historical discussions. If you know a decent bit of linear algebra (enough to understand artificial neural networks), I think you can muddle through this.

I really recommend Professor Gilbert Strang's linear algebra course and also would check out any Michael Penn videos, both on YouTube, but for linear algebra, the Strang/MIT course is the best resource anywhere that I know. The Gilbert Strang video series on linear algebra includes the 18.06 course, as well as an 18.06B or something like that where he goes into detail about the SVD and ML algorithms like gradient descent.

Generally if you're struggling with a math paper on the first or second page, no point in fighting it; gotta come back after you have the prerequisites. Nobody is born knowing this stuff, and also, all branches of math contain endless piles of really easy-to-describe but hopelessly difficult problems so never feel bad if you don't know how to solve a problem or even understand what you are reading. Just take your time, learn what you need, come back, a bit more hopefully makes sense, learn still more, and over time more things will become familiar.

Great book: An Introduction to Statistical Learning

PDF here:

https://www.statlearning.com/

Axler’s _Linear Algebra Done Right_ should get you at least part of the way there, content-wise, depending on what other math background you have.

As for reading math papers in general, it’s mostly a process of stepping through it incrementally and trying to verify the steps you don’t understand based on the surrounding context. Most of the concepts in this paper are accessible on Wikipedia or elsewhere, you can make small (e.g. 2 x 2) examples as you go and see what happens.

It’s not an easy skill to acquire from scratch, especially from outside the ivory tower.

I recommend asking an LLM to generate an interactive webpage to visualize, teach, and quiz you on the concepts. Or just chat with it directly.