renyicircle

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.

Have you opened the book? There are both theorems and proofs there.

Holy crap this Claude writing is actually impossible to read, it's like they specifically asked it to slop it up x10. The patterns are in every single sentence, every explanation of what the hell you're supposed to do is littered with fluff and analogies which change every time. I feel like I'm going insane. Can people actually read this?

Compared to the usual tools for the tools for the tools to help you program programming tools, this is a pretty good thing to have more of

I mentioned Langlands because it's one of the cool things related to Diophantine equations that the article mentions but I wouldn't expect it to be covered there. The connection between the Euclidean algorithm and unique prime factorization is simpler but also not obvious (the Euclidean algorithm on the surface just computes the GCD of two numbers and doesn't mention primes) so it would make sense to explain it in the article. However, they don't explain what the algorithm is, maybe assuming that the reader knows about it, while the rest of the article seemingly assumes no familiarity with basic number theory concepts like modular arithmetic. That confused me.

The article doesn't really tell us much about the "why" unfortunately. Diophantine equations are introduced but all the interesting stuff is promised in future articles which haven't come yet. All the reader can take from this is that these equations lead to some "profound hidden structures" without a good idea what they are.

I get that it's hard to wrap one's head around the Langlands program but I'd love to see at least more exposition on the following statement:

inventing the Euclidean algorithm is essentially equivalent to inventing unique prime factorization

Then the journalist wonders why they don't mention Jony Ive who left Apple 7 years ago whose company was acquired by OpenAI.

I guess they don't mention him because they don't have proof he tried to steal anything, as opposed to the other people mentioned in the lawsuit? Incredible really.

I'd say we're already well past that point. Short-form "content" already exists and is messing with people's brains, this is the same thing just taken a few steps further. By the time the tech companies start using it, it will already be too late and we'll be left discussing whether the next man-made nightmare they come up with is the point where the tech industry must be stopped.

This list was made by some guy on twitter. https://x.com/keshavchan/status/1787861946173186062

It's unknown whether it has anything to do with Ilya Sutskever.

The formatting of the articles on this website is bad. I've opened the first one and all the LaTeX formulas are messed up. The subscripts and superscripts are all flattened rendering the math hard to comprehend. Did the author actually try to read any of the articles?

∏ plocal(x|z) = i p(xi|z,xWindowAround(i))

Images and tables are not rendered at all. What is the point of this? Just keep the links to arxiv and leave it at that, otherwise render the articles properly

One gets bored exactly because it's transformative. I don't think most people have the capacity to adapt to "transformative technologies" every 10 years, especially when they change society irreversibly. It's not natural, it's just something progress demands of everyone. In this case there's a strong push to transform society before individuals can adapt to it. Not everyone can do it or should be expected to, it takes energy.

My first thought was "well of course it is, since pi is a little larger than 3" but it was cool to see an actual derivation of how much pi squared differs from 10 as a nice, closed form series.

I'd say integrals or differentials are not as important on their own as the kinds of differential equations that come up in physics. Integrals and differentials don't produce hyperoperations from non-hyperoperations, but a solution to something as simple as y' - e^x y = 0 will have a double exponential.

However a lot of DEs in physics are linear second-order with coefficients that are most often constants or polynomials, and if they're not polynomial they are made to be so using series expansions, under reasonable assumptions. This already brings you a long way towards solving the problem. The resulting equations usually have trigonometric/exponential/special function solutions.

It's still possible that hyper-operations like a double exponential might come up in the study of some specific non-linear problems. As in the example above, if you have an exponential function as a coefficient in your differential equation you might get a double exponential in the solution somewhere. I'm not familiar with any specific physics examples though.

The author has written two blog posts about their game (the latter is more about APL than the game itself though). You may find these interesting

https://homewithinnowhere.com/posts/2026-03-06-voxel-game.ht...

https://homewithinnowhere.com/posts/2026-05-10-one-line.html

Tractatus - highly aware of its limitations and refuses to speak about too many topics. Really likes numbering statements. Unusable due to a context window bug which is patched after considerable delay.

I really loved that article. Creating games always seemed so daunting to me since I don't know a lot about how it's done, there are so many different processes involved. The solutions described here are so satisfyingly compact and so easy to understand given the simple constraints, and yet they produce an actual game that looks nice.

Well can't you at least appreciate how it's all in this cool and down-to-earth lowercase? Clearly there was a stylistic effort.

Humans trust symmetry because it feels like intelligence made visible I hope this one didn't make it into the author's math blog. I don't understand what this means. I don't "trust" symmetry, I never think of symmetry as having to do with "intelligence". How did it even come up with that.

writing flawless English

Is there still grammar police on the Internet, calling out people for making grammatical mistakes in their writing? Who is asking for flawless English? Thinking that the LLM style is an example of flawless writing is a common mistake of ESL people. It's not flawless. A single rhythm, structure and flow permeates every piece of LLM writing. There is no variation whatsoever. People have been reading so much of that stuff recently that they don't bother to read the article if they spot one of these patterns. They're so easy to avoid, too.

Fired. And the part that gutted me: His proudest accomplishment at AWS? Restoring my account.

change to

I was gutted to read that his proudest accomplishment at AWS was restoring my account.

Is it flawless? Probably not, I'm not a writer, or a native English speaker. However I think it's more sincere, explains the feelings without any fluff, and is just simpler.

If the author's goal is to have people read their article, they should consider that people are tired of reading these patterns over and over again, it's not "flawless English" and it's not "writing clearly" because the patterns are unnecessary and obscure the message.

The way the author thanks the person from AWS who helped him with a human approach is an AI generated article blaming AWS for using AI. Brilliant.

Remember sharing simple thoughts between each other? Now you can do the same thing but with two AIs in between, one that produces words out of an idea and one that collapses them back. This is the way of the future.

Agreed, I can't read articles anymore with that Claudish stench of confidence, impactful sentences and dramatic negative parallelism. At some point you just start to skim it and reverse engineer the simple original prompt which is "write an article about how people don't speak up because it can hurt their career, use real world examples".

To be honest I don't know anything about marketing or publishing books, but I couldn't imagine promoting anything on tiktok either. Thanks for the response. Best of luck with your book.

get a self-published novel noticed on booktok

Can anything that's not young adult fantasy pornography actually get noticed on booktok?

I didn't want to paste all the job requirements from that link here, but fair point.

You can just check any of the vacancies on their website to see what they're looking for.

Example: AI Agent Engineer (https://search-careers.gm.com/en/jobs/jr-202606937/ai-agent-...)

We are seeking an AI Agent Engineer to design, build, and operationalize AI-powered agents that enhance employee productivity and decision-making in a complex enterprise environment. The ideal candidate combines strong AI/ML foundations, hands-on experience with agent frameworks, and a pragmatic approach to delivering business value in partnership with cross-functional teams.

Does not look like pure vibe-coding to me. More like developing wrappers over LLMs.

I am not an AI-hater. In fact, I think AI-haters are on the wrong side of history. It’s just that I know when to keep my crayon-drawings to myself ;) And I am getting increasingly sad and frustrated seeing communities that I value slowly wilting under the onslaught of shit

Disliking AI, even for reasons admitted by the author as valid, and on which they post rants, has become so low status that people now have to preface their articles with this. It's fine to be be happy with the good aspects of a thing and be mad at the bad ones. We don't need to split between sides of history (whatever that means) because of this. Eventually you might want to weigh the benefits against the damage though.

The link to paper documentation seems wrong, it's for some Minecraft server.

It's as if it's marketed to the students who have been using ChatGPT for the last few years to pass courses and now need to throw together a bachelor's thesis. Bibliography and proper citation requirements are a pain.

I'd love to see a root cause analysis post by Cloudflare for this one. The ones they do after outages are always interesting to read. How did this make it into the blog? What is the review process for these posts and what failed this time? What measures will be taken to restore Cloudflare blog's reputation?