To be honest, linear algebra is not that difficult to learn on your own, and plenty of people do. Gilbert Strang's course on OCW has made introductory linear algebra quite accessible.
Things like topology (e.g. TDA, persistent homology, etc.) aren't really mainstream yet, but even then most of it isn't really "hardcore" math in the sense that you can get away with a basic understanding, e.g. what a Vietoris-Rips complex is and why we use it instead of a Cech complex in TDA. Plus most DL research nowadays is pretty (advanced) math-light. That being said, taking the time to understand the math is absolutely worthwhile in my experience.
It should also be noted that a lot of real world ML/AI projects in industry aren't really about brand new algorithms using advanced math, but rather more about applying mostly existing techniques to messy, noisy real world data and taking the time to understand the domain you are applying it to.
I work as a data engineer, and i was interested in learning some of the stuff our data scientists do so i can better communicate with them. Teaching myself some statistics was fine, probability was fine too and quite fun and surprising. Both subjects have plenty of books that allow you to understand the intuition behind the things they do without having to dive deep into the proofs. Linear algebra was and still is a struggle though. I've sampled many books, from Strang's book to Linear Algebra Done Wrong/Right to some books that are used in the local university in CS courses. But they are all the same. It's clear they are all written by mathematicians for math students, probably to be used as a way to teach students how to write proofs at the same time? It's just one page after another of increasingly esoteric calculations and proof after proof after proof. Which is fine if you study math, but bad for me, because i dont want to work out the proof that taking the determinant of an inverted matrix works, i want to know what it means and why one would want to make the effort to do it.
Basically, i want a book like Statistical Rethinking or Blitzstein's Introduction to Probaiblity, but for linear algebra. And i havent been able to find it.
I think you might like my book, the No Bullshit Guide to Linear Algebra. It doesn't focus on the proofs, and instead gives lots of intuition and applications. You can check the reviews on amazon, and here is a link to a PDF with a few sample chapters: https://minireference.com/static/excerpts/noBSguide2LA_previ...
I won't lie to you and tell you linear algebra is "easy" by any means—there are a lot of things to pick up, so it takes some time, but it is totally worth it since LA is like the swiss-army knife of science: lots of features and super useful.
I self-taught myself linear algebra from Strang's book, combined with his lectures (on youtube). I wouldn't say that his approach is proof-heavy at all. Furthermore, the proofs in LA are rather easy and mechanical, compared to other areas of maths (and also, you can just skip them when reading).
Thanks for the pointer! (link[1] for those interested)
> you can get away with a basic understanding
Great news to me!
> taking the time to understand the math is absolutely worthwhile in my experience.
Strongly agree — for any topic, any field. My concerns are practical indeed, and less about the 10-year horizon (well enough to become skilled at anything) than the early stages of that, the best way to propel oneself far/fast enough on year 1, then 2, etc.
> applying mostly existing techniques to messy, noisy real world data and taking the time to understand the domain you are applying it to.
I hear that. I actually do like the sound of that, hence concerns that I was biased.
Linear algebra can be straightforward to learn on your own, if sufficiently motivated. But homology seems altogether different. The math undergrads who see it often have a tough enough time, I can't imagine an autodidact managing.
Things like topology (e.g. TDA, persistent homology, etc.) aren't really mainstream yet, but even then most of it isn't really "hardcore" math in the sense that you can get away with a basic understanding, e.g. what a Vietoris-Rips complex is and why we use it instead of a Cech complex in TDA. Plus most DL research nowadays is pretty (advanced) math-light. That being said, taking the time to understand the math is absolutely worthwhile in my experience.
It should also be noted that a lot of real world ML/AI projects in industry aren't really about brand new algorithms using advanced math, but rather more about applying mostly existing techniques to messy, noisy real world data and taking the time to understand the domain you are applying it to.