generationP

This one is not just in Dummit and Foote; it's just too easy to miss. I'd guess it appears in half the places that state this result. Fixed it in my own lecture notes a few months ago.

Those habitual mitigations go a long way. Just like there is defensive programming, there is defensive usage.

Under Windows: Don't put your files into "My Documents" or similar folder hierarchies; you never know if old software will correctly deal with the abstraction.

Working with files in general: Avoid nonstandard unicode names or long paths so your external hard drive doesn't choke on them. Avoid case sensitivity even when it is allowed on Unix systems, since you can't assume Windows won't ever touch them. Avoid whitespaces in names because sooner or later, some script won't escape them.

On the internet: Never draft long comments in the browser; always use a local text file. Anything can happen in the browser.

In games: Never save your game during what looks like a complex scripted scene even if the game does allow saving.

Using search engines: Avoid keywords that are likely to confuse/distract the search.

With dropbox-likes: Give it some time to sync even after the icon is green; god knows what is being predictively shortcutted under the hood.

Everywhere: Restart the program or system if certain signs of corruption appear. You don't know what's going wrong, but you know something is, and barring some unusually careful compartmentalization, a piece of software is still a state machine which, once it has strayed from the right path, cannot be trusted at all. OSes nowadays are adapted to this, but much of software is not, and you do not want to have it corrupt your file.

Why should anyone want to have copyright on AI-generated content?

In pure maths:

- pre GPT-5.4: very limited use; some smart people got some mileage out of the models, but it always required serious work and a very suitable problem. Of course the models could solve homework problems, but that felt more like a downside to us who teach.

- since GPT-5.4 (Mar 2026): the "wow" release; suddenly answering MathOverflow-level problems that have previously been stumping experts. Still prone to hallucinations, but smart enough to use the built-in Python skill to verify its claims on small examples when possible. Probably a lot better at formula-heavy math than at the abstract "philosophical" kind.

- GPT-5.5: gave me a fascinating, significantly nontrivial and highly instructive "proof from the book" on an MO-hard problem that I'm in the process of writing up. Might have been luck and good prompting, though. Didn't really feel like a qualitative leap from 5.4, but I take quantitative any time. Still requires suitable problems, but it's much harder to rule out suitability from the get-go.

Claude and Gemini have been also-rans the whole time and still are. I use Claude for secretary-like tasks; occasionally it finds an easy proof too, but usually because I've missed something obvious.

Oh, and GPT, and to a lesser extent Claude, are great at hunting errors in maths. Probably 90% of my prompts so far have been for proofreading my writings.

Graham/Knuth/Patashnik is a lot less "basic discrete maths you're most likely to need" and a lot more "number sequences we've known and loved". Almost more useful for physicists due to the amount of summation fu you'll learn there.

I found the choice of material quite nonstandard. And the writing is witty, full of MIT humor. It's a bit sad that the writing has stopped in 2018.

Most of the dark patterns are not fun. The "psychological dark patterns" are, to some healthy degree.

Neat... but most good RPGs fit much of the "psychological dark patterns" listed at https://www.darkpattern.games/pattern/4/psychological-dark-p... . So the total scores won't be as useful as they might look like.

This looks like an index of Mir books, without any additional sorting or curation. You probably can get a good education on many topics out of these, but also waste significant time on reading out-of-date and out-of-order texts. Someone experienced could make this a lot more useful by proposing a reading order and giving some sort of evaluations of importance and quality.

And keep in mind that these are from the pre-1990 USSR, so don't expect any modern maths or CS.

I have a hunch that most of the slop is not just on CS but specifically about AI. For some reason, a lot of people's first idea when they encounter an LLM is "let's have this LLM write an opinion piece about LLMs", as if they want to test its self-awareness or hack it by self-recursion. And then they get a medley of the learning data, which if they are lucky contains some technical explanations sprinkled in.

That said, AI-generated papers have already been spotted in other disciplines besides cs, and some of them are really obvious (arXiv:2508.11634v1 starts with a review of a non-existing paper). I really hope arXiv won't react by narrowing its scope to "novel research only"; in fact there is already AI slop in that category and it is harder to spot for a moderator.

("Peer-reviewed papers only" is mostly equivalent to "go away". Authors post on the arXiv in order to get early feedback, not just to have their paper openly accessible. And most journals at least formally discourage authors from posting their papers on the arXiv.)

Look for anything written by Jesse Singal or Charles Murray for the well-researched anti-woke content I'm referring to (and there is a lot of more; these are just two authors who made it their focus; some of the best stuff comes actually comes from journalists with wider purviews).

I don't know what "Cult of Personality" you are referring to; unless you are hallucinating this particular reference, I've gone to school in the wrong country for that particular report to be part of my assigned reading (and the right country, sadly, seems to have skipped it entirely; there might be an update out in a few years...). Either way, what is the relevance here? What I've been saying is that I'm far from sure of this project's success and would be doing it quite differently. Musk's personal characteristics may well be the reason why he did it the way he did, but ultimately the project won't live and die by them (already because he himself will likely lose interest soon enough).

Note that I've said "anti-woke content", not "anti-woke media". I am including the occasional "course correction" opeds and actually well-researched longreads you're seeing in places like NYT, Atlantic and such. Partisan outlets for partisan readers aren't doing the heavy lifting here, but the success of Substack and the unexpected survival of Twitter under Elon have convinced editors to listen. Elon's personality isn't of importance here; he mostly needs to just push a few buttons to make a sub-critical news item go super-critical.

Yeah, encyclopedias are meant to be indexes to knowledge, not repositories thereof. The WP feature-creeped its way to the latter, but it is not reliably good at it, and I'm not sure if there is an easy way to tell how good a given page is without knowing the subject in the first place.

Don't forget that public opinion and the media landscape are quite different in 2025 from what they were in the 2010s when most prior studies on WP bias have been written. Sufficiently pertinent (sadly this isn't synonymous with high quality) conservative and anti-woke content can reach wide audiences, particularly when Elon puts his thumb on the scale. Besides, to my knowledge, none of the prior attempts at studying WP bias has even tried to make a big enough fuss to change said bias; the final outcomes of the studies were conference papers.

Wondering if the project will get better from the pushback or will just be folded like one of Elon's many ADHD experiments. In a sense, encyclopedias should be easy for LLMs: they are meant to survey and summarize well-documented material rather than contain novel insights; they are often imprecise and muddled already (look at https://en.wikipedia.org/wiki/Binary_tree and see how many conventions coexist without an explanation of their differences; it used to be worse a few years ago); the writing style is pretty much that of GPT-5. But the problem type of "summarize a biased source and try to remove the bias" isn't among the ones I've seen LLMs being tested for, and this is what Elon's project lives and dies by.

If I were doing a project like this, I would hire a few dozen topical experts to go over the WP articles relevant to their fields and comment on their biases rather than waste their time rewriting the articles from scratch. The results can then be published as a study, and can probably be used to shame the WP into cleaning their shit up, without needlessly duplicating the 90% of the work that it has been doing well.

That's the longest pronoun signature I've seen.

NB: None of what you are saying is confirmed by the WP page you are citing.

And soon it will be "but I don't want to learn Lean".

The cube doesn't work, or at least it didn't for me. The goggly eyes really do make a difference.

When I get fired, the news better come in an email titled "Steps in the Right Direction".

I guess monks were procrastinating likewise when they illuminated their manuscripts.

Tikz is misplaced in this list; it is how you make any kind of vector drawings in LaTeX. It's not the only way, but perhaps the best documented and most expressive one. If you have any such drawings in your work, you won't get around putting some effort into it. Not comparable with boxed theorems or fancy headings.

That looks like the kind of paper that causes companies to lose lots of money by hyping up what is likely a less-than-impressive method. But it does not make any theoretical claims, so it cannot contaminate research.

You're right, the authors are not to blame for the lack of context -- I misdirected my anger at the phys.org nonsense towards the actual authors.

The actual article (OA!): https://www.tandfonline.com/doi/full/10.1080/00029890.2025.2...

This is about solving polynomial equations using Lagrange inversion. This method, as one might have guessed, is due to... Lagrange. See https://www.numdam.org/item/RHM_1998__4_1_73_0.pdf for a historical survey. What Wildberger is suggesting is a new(?) formula for the coefficients of the resulting power series. Whether it is new I am not sure about -- Wildberger has been working in isolation from others in the field, which is already full of rediscoveries. Note that the method does not compete with solutions in radicals (as in the quadratic formula, Tartaglia, Cardano, del Ferro, Galois) because it produces infinite sums even when applied to quadratic equations.

Phys.org has gotten no part of the story correct.

One day, someone will discover a use for across-the-page watermarks that is not better handled by marginalia and makes up for the loss in readability, copyability and compatibility with graphics.

Until then, we'll be seeing this...

What about a header/footer saying "DRAFT" (ideally with the date and other things that would perhaps not fit on a watermark)?

Yeah, not so much harping on you as on the whole ecosystem. You seem to have done your part well.

So an app that would probably serve a real need fails because the team is unable to bootstrap the two-sided market. The best dev moves to a bullshit "green habits" app that doesn't suffer from such problems because... it doesn't really do much in the first place. Not the greatest outcome for the world.

The most confusing errors are the ones spellcheck doesn't catch because they transform a word into a valid word. But it's them that we want the least.