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.
The continuum hypothesis is more like Euclid's parallel postulate than a Gödel sentence - assuming ZFC consistent there are models with CH true and CH false (the cardinality of the continuum doesn't have to be the first uncountable cardinal).
Everything gets qualified with "assuming ZFC consistent" or "assuming Peano consistent" because any inconsistent theory proves any statement. More of a proof technicality than anything too profound.
As someone who took a number of mathetical logic classes between undergrad/graduate I always found this Gödel-sentence argument on the face-laughable, since the logical inconsistency was so easy to repair. My favorite critique of this was Hans Moravec's dialogue between Penrose and a robot AI, having resurrected his brain long past humanity's extinction: http://www.calculemus.org/MathUniversalis/NS/10/10moravec.ht...
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'd guess comments like this come from people thinking the primary complexity of Redux is the data store, rather than the "all changes to your state are represented as plain objects". The Redux FAQ goes into this: https://redux.js.org/faq/general#when-should-i-use-redux
Can't blame them missing the forest for the trees when you spend all your time writing the reducers and connectors vs the actions themselves.
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.
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.)
I've been attending a local UU Church for the last few months (raised no religion, this is my first spiritual community). While there's mention of the spiritual life I think about half the congregation would identify as atheists. There's no creed or mention of 'religion' and the individual search for meaning is repeatedly stressed. It's been a good addition to my life and very nurturing for the soul.
Agree. The assumption underlying this is that you should use a bulk of your outside-of-work time to advance your career and grow your technical skills. True for some, not true for others.
My personal favorite is _The Tombs of Atuan_ - it introduces a new character, creates an entire world around her, then pulls all the assumptions beneath the world apart.