tildedave

got it, thanks!

steve yegge is not tptacek (thanks for cryptopals, tptacek!)

This book is the reason I was able to pass my computer architecture exams in grad school. Just lugged the 800 page monstrosity around an entire semester and read it every chance I could. A really wonderful book ... I should get a recent copy and re-read it again.

Not a historian, but _Why the West Rules - For Now_ by Ian Morris was a good read. Covers the sweep of world history with the audacious goal of quantifying human development at all moments in history. It mainly focuses on the west (starting in the Mesopotamian region) and the east (starting in the area surrounding the Yellow river) and addresses questions like "why didn't China discover America" (basically - too far away). You might also find it interesting!

I'm really excited for the movie and the casting looks incredible so far. I wonder how the 2 movie split is going to work narratively. The book itself has kind of a perfect 3 act setup but I'm not sure breaking the story at the end of the book's part 1 (or halfway through part 2) is going to feel very satisfying.

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.

Appreciate what you're saying, but the linked paper is talking about results in F_p[T], the polynomial ring.

Even if the number field is finite, there are an infinite number of polynomials for it. For example the finite field F2 has two elements {0, 1} but an infinite number of polynomials 0, 1, x, x + 1, x^2, x^2 + x + 1, x^2 + 1, «x^2 + x, and on and on. Some of these have nontrivial factors (x^2 + x = x(x+1)) and some don't (x^2 + x + 1 has no factors beyond itself and 1).

(The other answer to your question is more complete but also a bit more advanced, figured this was worth surfacing.)

Ah, just making the point that the questions don't occur in a vacuum. By the time something's bad enough to consult random strangers on Reddit the problem has sometimes escalated beyond the point. Often the "dump him" answers come with people also sharing their own life experience. (I've seen my share of the silly questions/answers too of course.)

A more charitable interpretation is that people have gotten into situations bad enough where they've ended up seeking advice from strangers on the internet. (Not every relationship squabble ends up in a reddit post.)