Why are programmers always so attracted by these interactive/over-simplified/lightweight versions of linear algebra? They all focus on the visual aspects while ignoring the real stuff (theorems, proofs, etc.).
As a programmer who uses math heavily, I can answer this. As a programmer, your intuitive understanding of the world is infinitely important. You use it to formulate ideas, rule out solutions that would not be feasible, have an estimate of the expected cost and quality of solutions, etc.
Being able to dig deeper is important, but what's more important is to have an intuitive understanding of many many things: psychology, economy, finance, physics, art, etc. It's important to know the limits of your familiarity with any of these. For instance, my understanding of the fundamental practices in Accounting is really good (I've led a budget aggregation software for a huge conglomerate), but details is bad (tax rules for each industry, etc).
When I needed to create a software for optimizing stone cutting, I needed to know enough from computer vision, computational geometry, and optimization to know that our solution is feasible, task team members to learn what they need to do, and get into implementation, debugging and optimizing with them when needed.
After that, I still can't write code in computational geometry that handles all corner cases.
It's really good if we know everything with infinite precision, but for a programmer it's not efficient. We need to know where to stop.
In my experience, mathematicians are attracted by over-simplified/lightweight versions of programming. I think "just tell me what I need to do my job" is a universal human principle.
Because, realistically that's all programmers ever need, would be my guess. I do think linear algebra is an extremely interesting topic in its own right / outside, but yeah.
All this LLM stuff uses pretty basic linear algebra, and that’s a hot topic these days (not to turn my nose up at it, doing easy linear algebra at massive scales turned out to be a really good idea). Maybe that explains some of the attraction?
For the same reason mathematicians who aren't computer scientists or logicians are attracted to proof assistants implementing ZFC object languages while ignoring the stuff underneath (type theory, systems theory, etc.)
Maybe I should’ve been more clear: what I meant is that these programmers-oriented resources are all about applications…maybe a bit too much. For instance, In this book I cannot find the algebraic structure of vector spaces, theorems about how certain linear operators such as the kernel or the image led to subspaces (which is a very important result) or a proper introduction to the spectral theorem, for both Euclidean and Hermitian spaces (which also allows you to introduce some nice functional analysis).
I get where you're coming from but linear algebra is one of the most applied branches of mathematics out there. It's easy to visualize and easy to teach the computational side of it so it makes sense that some books focus more on that and these are popular among people whose main interest is in how to apply it - like programmers. You don't need to know what a ring is to learn how to multiply numbers.
I wouldn't say this one is programmers-oriented either - it was posted to HN, sure, but maths and physics students could benefit from some visualizations too as a supplement to a more rigorous text.
As for the things you mentioned as omitted, I think if you want to do a complete treatment you have to introduce more mathematical prerequisites which limits the audience of your book. For a mathematician, I'd say classical linear algebra in itself is not particularly interesting - it's very well-behaved and pretty much "solved". What you care about is how it relates to other structures (groups, modules, fields), how it develops into other topics (functional analysis) and how it's used to study other objects (representation theory, tangent spaces of manifolds). In isolation, most of what's left is the computational aspect which is what non-mathematicians mostly care about.
What makes someone a "programmer" vs a mathematician? If you suspended your arrogance for a few moments you might realize you've wasted our time with a question that answers itself.
I mean it's also a generalization of very little value. Is someone doing linear algebra in lean not doing "the real stuff"? What is a programmer to you? Your question is why do some people not follow an area that is tangential to them to the maximal extent? Or to some arbitrary level of "real" as you subjectively define it? Is your claim that the level of linear algebra offered here is inherently useless unless paired with the "real stuff"?
Or did you just want us all to know you are a practitioner of such arts? Gold star for you.
Besides, I've never met a physicist or a (real) engineer who would go to such lengths to oversimplify the math part, even if it was only “tangential” to them.
I don’t think they are simplified but they are an introduction course for sure. I think what’s usually missing is integrating (heh) linear algebra with calculus for solving more interesting problems but I think the audience for that needs to have a big appetite first. And those are hard to come by unless it’s pushed on you to finish your degree. And even then, people barely scrape by in those classes.
My personal favorite is a former NASA employee who recorded a series of lessons for students to use to supplement their normal undergrad studies, prepare for exams, that kind of thing. He has a YouTube channel which has all sorts of topics (for free), but his site has paid videos on math, chemistry, electricity, some electronics, statistics, and a few other topics. You can find it on the high seas if you want a preview. Look up MathTutorDVD. It is not the end all, be all, but it is very helpful and I’ve learned in my own spare time lots. He covers high school math to Calculus 3 and probably beyond. I haven’t looked in a long time.
Khan Academy is also an option but I have not used it much so I can’t sufficiently comment on it. The things I’ve seen there have been decent and their main faculty are highly technical people who went into teaching. People have said great things about K.A., and likely they have a better way to track your progress and they might have better quizzes and tests.
One thing I remember specifically being called out is that majority of students who struggle with Calculus struggle almost exclusively due to linear algebra and formula manipulation. That the actual Calculus part is not the problem, it’s the lack of pre-requisite practice and learning more than anything.
The standard Calculus book by James Stewart will do. It covers most of the same. It is readable and quite affordable because it is so widespread.
A nice “1000 problems solved in Calculus” work book will also help. Practice is always good here, and it feels good when ideas learned from multiple sources work together.
Lastly, there are a couple of solid books that go into translating mathematical concepts so as to be usable in computer software, meaning how to take math formulas and turn them into usable algorithms. I want to bring to your attention their existence because eventually this is something that needs to be done, but trying to do everything at once will overwhelm you and distract you. It is however a “thing” when you get things down.
I recommend getting some notebooks - lined and square, a set of colored pens, and writing each and every exercise, lecture down. Color code notes, formulas, your own solutions and corrections. Grade yourself if need be. Keep your notebooks, labeled after each subject. I don’t know to what extent digital note taking is done today but I’ve always personally found it ineffective. So if you already self identify as a slow learner, writing things down in a meticulous way should help you greatly. Notebooks and pens are otherwise cheap, better to have an excess than not enough.
I hope this helps. I’m sure other people here have far better resources and I’ve forgotten all the stuff I used, but I’m not dead set on any one method.
Yeah people don't realize these "toy models" now completely destroy gpt-4o on most tasks, and no one called gpt-4o a toy model back in the day... It was OpenAI's flagship model from 2024 to 2025.
Tbh in 2024 most were calling these models useless for programming and a scam. It wasn't until this year things really changed. My experience with Qwen 3.6 is it can do things, and it's super impressive it can do things, but it's not any more productive than doing it myself.
Edit: it's gonna be slow if you're not using any VRAM. But it's possible. Software isn't going to speed that up anytime soon, it's just a hardware bandwidth limit.
I'm running llama-swap in a docker container with nvidia container utis to pass through the GPU. This then runs the correct llama-server command to provide the model I want. I have a folder full of guff s I mount in the container.
But this could be done with just llama-server normally. I don't use any special command, just ensure that it's using the GPU. I've found the default fitting to be good.
From memory:
llama-server -m models/Qwen3.6-35B-A3B-UD-Q4_K_XL.gguf -fa on -c 128000
> I don’t think a good learning resource gets worse[...]
Probably not, but they become irrelevant. The other day I found an old programming book at my parents’ and while it was still a terrific resource, I couldn’t image anyone learning a language from a book nowadays.
AI is doing the same thing but 100 times effectively than anything else.
Blog tutorials, guides, programming books and youtube tutorials. They are completely irrelevant in a time where you have a personal tutor willing to explain every single detail of a subject.
Relevance is overrated. I've been writing for myself. Writing articles about the implementation of my programming language helps crystallize my knowledge. It's been remarkably effective at ensuring I won't simply forget the subject matter in the future. The fact other humans might enjoy reading my articles is just a nice bonus.
That's like saying your grandfather is irrelevant now that he's spawned children and grandchildren. Good luck to those personal tutors without this source material.
What’s the appeal of an editor like Emacs in 2026? Why’d anyone still use when most jobs nowadays require you to work inside a container (and therefore use VSCode container extension)?
Can't you ssh into them? If so, in emacs you can just open /ssh:host:path/to/file and remotely edit that file.
Even if you didn't have emacs, I don't think you are forced to use VSCode. You could just use sshfs and use any local editor, but I guess other editors also have remote editing plugins
What I don’t understand is why people dismiss this kind of progress with false claims. Especially when discussing programming, people start to act irrational using arguments from back in 2022.
I think that you can easily address your concerns about this new technology (since we all are concerned about the future) but at the same time acknowledge how revolutionary it is.
It’s basically up to the domain experts. What I found interesting in mathematical optimization/combinatorics (my fields of interest) when an AI proved some major results some time ago was probably dismissed as a boring fact by someone else. What OP is mentioning is just their personal preference and doesn’t reflect the actual opinion of the mathematical world.
I know this book is not intended to be used as a first reading on Linear Algebra but, to me, this text isn’t good even for a second(or a third) read. The author hurries up too much on certain parts. I think that Serge Lang’s Linear Algebra does a better job in explaining pretty much every topic of the subject.
