Sick! I've been building a little electronics project to render the ising model on an lcd screen, might have to do one for the potts model now too =D had never heard of it before.
I think zugzwang makes chess endgames richer - the fewer ways you can make a draw, the better, in my opinion. Maybe that's less appealing in go because games can go on for so much longer? At least in 19x19.
I don't think they are completely wrong - "=>" is just implication. A hidden assumption in their diagrams is that circles of different colours are assumed to be different elements.
A morphism from orange to yellow means "O <= Y". From this, antisymmetry (and the hidden assumption) implies that "Y not <= O".
Totality is just the other way around (all two distinct elements are comparable in one direction).
I guess we hang out in different academic circles. I met a single algebraic geometer in my whole academic career. But people are into very different stuff where I come from, which may have biased me (topology, number theory and category theory for the most part, and a lot of relativity/fluid dynamics on the applied side of the department). Based on rough estimates from papers published on arxiv over the last few years, I (very) conservatively estimate there are ~5000 working algebraic geometers in the world right now.
> The amount of people I know who would love to learn this material [...]
I am one of them =) but my point wasn't really about people who want to learn the material (which I assume includes many orders of magnitude more humans) it was about people who already deeply understand it.
> But if less people are exposed to those frameworks, then surely that means they will be less popular?
I agree, but I don't think the data suggests that is what's happening. The data presented in the article shows only that the number of new sites made with React has increased greatly since LLMs arrived on the scene. But there's a base rate fallacy here - we aren't shown data for any other frameworks!
>Of course it is.
That's not what I mean by a zero-sum game. There isn't a fixed number of websites that different frameworks are taking a share of (this would be a zero-sum game). The number of websites itself has massively increased since LLMs arrived on the scene. You can very quickly spin up 100 new sites using your new framework without all the other frameworks "losing" 100 sites, you know what I mean? Similarly I think the number of people making websites has exploded for the same reason.
And this is another explanation for the data in the article - that there are simply way more sites being created now that it's so trivial for anyone to make one. Have a look at the StackExchange links I gave in my last comment. There isn't much evidence there that React is overwhelming the industry (especially amongst professional devs), although I grant you it would be difficult to measure if it were true.
> The actual tools themselves are using React. [...] These tools have taken over the industry.
Yes, but so have plenty of other tools that don't use React by default, like Claude Code or Codex. There are plenty of new websites being made across all of the major frameworks.
> I don't think you read the article as closely as you think you do.
Do you mind cutting it out with the ad-hominems? I've been nothing but respectful to you, and in each of your replies you've made little jabs at me about "not understanding the article". I just disagree with you, friend, be nice =)
I think you overestimate how many people exist in the world with a professional interest in algebraic geometry! The vast majority of mathematicians have no idea how to compute with schemes (and there aren't that many of them to begin with).
I don't buy the premise - that LLMs being trained on more React code than other frameworks is going to cause the collapse of alternatives. The data presented in the article isn't very convincing to me - it's absolute numbers, it's not a zero-sum game, and besides LLM coding is the worst it's ever going to be. Hypothetically, even if the data was convincing (showing a massively increasing relative share of React usage since LLMs entered the scene), I don't think it's sensible to extrapolate from current trends about LLM coding anyway. This stuff is barely a few years old and we want to make confident predictions about it?
That's a theory, but I think it's more likely that the few people in the world who deeply understand schemes are locked in the basement of a mathematics department somewhere, and not on hacker news =P
Interesting, yeah. I guess he was the mathematical equivalent of the "rogue" archetype. Brilliant, did things in his own way, total lack of respect for authority, shrouded in mystery. I can definitely see the appeal =)
I don't buy it, I've used LLMs (well, mostly sonnet 4.5 and sometimes gpt5) in a variety of front-end frameworks (react, vue, htmx) and they do just fine. As usual, requires a lot of handholding and care to get good results, but I've found this is true for react codebases just as much as anything else.
Why is this on the front page of hacker news? Hopefully that comes across as a genuine question and not snark. I mean as an ex-mathematician I'm thrilled, but schemes are an incredibly abstract object used in an incredibly abstract branch of mathematics (algebraic geometry).
This is very cool as a science experiment, but if you're interested in getting the best results (for you) you should just taste as you cook. We're born with high-fidelity chemical and tactile sensors - use them!
Can you provide examples of software that should have literally been a spreadsheet or an ETL? Not to call you out specifically but this feels like "I could have written that in a weekend". Personally whenever I have felt that way about a project it turned out I was just missing 95% of the business context/domain knowledge (part of the reason I think rewrites are a bad idea - chesterton's fence).
Is LLM output the kind of clever we're talking about here? I always thought the quote was about abstraction astronautics, not large amounts of dumb just-do-it code.