Mathematics for the Adventurous Self-Learner

The submission and this entire thread is about learning math. That, to me, implies learning to do, not learning about. Yes, you said:

> if you're not trying to write a dissertation or pass a qual (and you're just interested in learning and being exposed) then you don't need to do them

There's ground in the middle, and this thread is about that. This thread is not about learning for tests and qualifications, nor is it about "being exposed", it's learning how to do the math.

And for that you need to do the exercises. You don't need to do all of them, you don't need to be completionist about it, but if you don't do the exercises, if you don't actually do the math then you won't actually be able to do the math.

Specifically, you said (quoting again):

> if you're ... just interested in learning ...

There's a difference between learning about and learning to do. If you meant just "learning about" then you are at odds with the entire thread. True, in that case you don't need to do the exercises, but I don't think that's what people are talking about here. I think people are talking about being able to do the math.

And if you meant "learning to do" then in my opinion you are wrong, and one needs to do a large slab of the exercises.

Otherwise it's fairy floss, and not steak.

My apologies if all this seems overkill, but there's a real danger of talking past each other and being in violent agreement, and I wanted to state explicitly and clearly what I mean, and why I thought you said something different.

Practice makes a master. More importantly, the true understanding only comes through practice. Also, more often than not to "understand" something comes down to simply getting used to it (which is how we learn things in the elementary school). Practice is the key.

Are you in the current presentation of either 124 or 125 by any chance? I'm in both, planning to do the BSc too.

I've been pursuing mathematics as a hobby for the last 2 years or so. I got a mathematics major in undergrad so my motivating factor was mainly to explore some areas that I hadn't done coursework on, primarily algebra and number theory. (I focused more on logic in undergraduate/grad.)

I really enjoy how the subject is divorced from a lot of the modern attention demands and encourages more of a 'zen' thinking style.

As others have highlighted, it can be difficult. I work full-time as a software engineer and at the end of the day there's usually not much left in the tank in terms of "creative work". The morning is usually more productive for me - generally I'll spend 10-15 minutes on the commute in reading over the proof of some lemma or working through some computational exercise.

Things that have helped me:

- Focusing on a particular problem area rather than just "mathematics". The classical problems of Gauss and Euler tend to be more my speed than the modern mathematical problems of Hilbert or beyond. What started my journey was looking into the insolubility of the general quintic polynomial equation, something you learn in high school as a random factoid but has a lot of depth.

- Studying from small textbooks that I can fit in a backpack, so I can "make progress" during my commute. Dummit + Foote might be a great algebra reference but it's just too bulky to transport.

- Limiting the scope of how I think about the activity - my goal isn't to master these concepts on the level of a mathematics graduate student, it's more on the order of Sudoku. If I don't get something, that's okay. People spend their whole lifetimes learning this material and I'm just trying to fit this into whatever creative time I have left after the full-time job is done.

Khan Academy is great as they start from the very beginning. If you’re a good problem solver you can skip most of the videos. If you learn by videos, they’re very helpful.