Ask HN: How do I learn math/physics in my thirties?

I actually had to look into this recently.

The recent ones are less "textbook." The older ones are FILLED with information with graphics here and there but it's mostly text. The recent ones are very graphical so I would assume it has less total information. With that said, it's possible that there are techniques for learning that were not considered in the older texts.

It is possible to look at samples online for you to compare if you want to see the difference. I do recommend getting the book if you decide to use it but that's just a personal preference.

There are two approaches that work well. The first is to embark on the standard, formative curriculum. The second is to start with a handful of problems that interest you and go pick up stuff piecemeal on the way to solving those.

Approach 1. Decide if you want to learn physics or applied mathematics. They're not the same. The math you describe is more on the operations research side of applied mathematics, and not terribly relevant to physics. You say your goals are physics. In that case you're in luck. The curriculum is utterly standard and consists of four passes through the material.

The first pass is one or two years long and is roughly what's in Halliday and Resnick or Tipler's physics books: Newtonian mechanics, some wave motion, some thermodynamics and statistical mechanics, electromagnetism, and a little "modern physics" (special relativity and a bit of quantum theory). Meanwhile you study calculus of a single variable, multivariable and vector calculus, and a little bit of ordinary differential equations, and do a year of laboratories.

The second pass is a semester of classical mechanics covering Lagrangian and Hamiltonian mechanics, a semester of statistical mechanics and thermodynamics, a year of electromagnetism, and a year of quantum mechanics, paired with a year of mathematical methods (linear algebra, special functions, curvilinear coordinates, a little tensor calculus, some linear partial differential equations, and a lot of Fourier analysis) and a year of more advanced laboratories. Here ends the undergraduate curriculum. At this point astrophysicists tend to separate off and start learning the knowledge for that domain instead of the second semesters of electromagnetism and quantum mechanics. Their labs are also different.

The third pass is the first couple years of graduate school, and goes through the same subjects again in more depth. No labs this time. A mathematical methods course only if a student needs more help. Quantum field theory for those going that direction. General relativity for those going another. Advanced statistical mechanics or other special topics for those going into condensed matter.

The fourth path is the student by themselves, integrating it all in preparation for doctoral qualifying exams.

If this approach sounds like what you're after, start by getting a 1960's edition of Halliday and Resnick's physics (which is better than the present editions and quite cheap used), a Schaum's outline of calculus.

Approach 2. Pick a handful of problems. What actually interests you? Not what sounds fascinating or what seems prestigious. What's interesting? Cloud shapes? Bird lifecycles? What are you actually curious enough about to spend some time poking at?

Whats the progress / ETA for this? Sounds like the perfect thing for me right now

I am doing this now. I just took a Discrete Math class and I am taking a calc refresher in the Fall. I have been reading several text books as well for practice and reinforcement.

Honestly, despite all the crap universities get, taking an undergraduate degree with a double major in physics and maths is an awesome way to do this. You'll meet people who are similarly passionate, be naturally competitive with them which is a motivating force not to be underestimated, and you'll meet a diverse set of teachers who each will have some awesome insights into these fields and you'll get to see first-hand how they think about solving problems.

Physics, and to a lesser extent maths[1], are topics where the top 1% of ability are actually concentrated at universities. My advice would be find a cheap university nearby and start enrolling in courses. If you're bright, motivated and take ownership of your own learning, the faculty will love interacting with you. If you're doing it to learn, don't sweat about the prestige of the place. There are people everywhere who will be much better than you at this stuff, and in some ways it's extremely motivating if you feel like with some hard work you can surpass some of your teachers, and it's extremely motivating when the best teachers recognize you as having more potential than the average student. You're never gonna feel either of these things at MIT.

[1] The problem with maths in academia is that it's massively biased toward proofs of mathematics and not use of mathematics. I've met very few PhD mathematicians who are even as close to as good at applying appropriate mathematics to problems then someone with a PhD in physics who consider themselves >50% theorist. PhD mathematicians are wonderfully knowledgeable if you say "tell me about this field of mathematics" and it's a field they know. But there is a certain extent to which they like to work by building things on a frictionless ice world, and get uncomfortable if asked to build something on the rough ground of the real world.