renyicircle · HackerTrans

renyicircle

142 karmajoined 6 ay önce

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The background is that a counterexample to a famous mathematical conjecture was recently posted on X by an Anthropic employee. The counterexample, in form of a polynomial, is easy to validate by doing simple calculations, but it's not clear why it works and why it is the way it is, from a deeper mathematical perspective. Specifically, the properties of the polynomial suggest that it's not just an accidental finding but has some involved geometric construction behind it. This is what Terry Tao's conversation with ChatGPT starts with: "does this polynomial have any symmetry or structure that makes the counterexample seem less miraculous?". Using the counterexample, work backwards to get the intuition behind it so that it can be constructed by an explicit procedure rather than taken out of thin air. The result is his blog post, discussed here: https://news.ycombinator.com/item?id=48998362

7 gün öncediscuss

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.

8 gün öncediscuss

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

8 gün öncediscuss

It's not AAVE being mischaracterized as quirky slang, it's modern slang that evolved with AAVE as a major influence. Half of Twitter has been writing like that for years. You could take offense with how that happened but this is the state of things now

8 gün öncediscuss

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?

11 gün öncediscuss

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

11 gün öncediscuss

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.

12 gün öncediscuss

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

12 gün öncediscuss

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.

14 gün öncediscuss

Where I'm from children don't start school before they're 6 or 7, while teaching basic reading skills before that is something that's expected from parents. What bad grades are we talking about for a 5 year old? Is this an American thing?

14 gün öncediscuss

"Most of the world sucks, what's the big deal if we unleash the AI slop machine on their kids? It's not like they have something to lose" I was opposed to this tech at first but this kinda makes sense, I'm convinced

14 gün öncediscuss

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.

17 gün öncediscuss

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.

17 gün öncediscuss

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

18 gün öncediscuss

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.

19 gün öncediscuss

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.

geçen aydiscuss

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.

geçen aydiscuss

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

geçen aydiscuss

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.

2 ay öncediscuss

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.