This is a much harder problem for an encyclopedia than for a textbook chapter or a journal paper, because each article is supposed to (somewhat) stand alone and be both broadly accessible and somewhat comprehensive. For a textbook chapter you can systematically build up prerequisite knowledge from earlier chapters and you can assume that students will spend significant time and effort working problems and will have some expert guidance and support if they get stuck. For a journal article you can assume readers have deep subject-matter expertise, e.g. have a PhD in the field.

Traditional encyclopedias typically punt by just not including much technical detail at all. (Some Wikipedia articles also do this.)

* * *

As a basic example, let’s think about what might be included in an article about “circle”. You can look at this from a kindergartener’s point of view, or a high school geometry student’s, or an ancient astronomer’s, or a physicist’s, or a signal processing engineer’s, or a 19th century projective geometer’s, or a complex analyst’s, or a group theorist’s, or an algebraic geometer’s, or a topologist’s, or a number theorist’s, or an ergodic theorist’s, etc. Some of these audiences are easy enough to satisfy, but to provide deep comprehensive coverage of the way a fundamental concept like the circle is related to every mathematical field is going to take careers worth of background. Which parts to attempt, which parts to skip, and how to organize them is a very challenging set of editorial choices.

It has very strong moderation, and low quality answers are deleted. Their papers cite methods and hypothesis which removes a lot of "fiction" from the equation.

Also, they get quoted in mainstream media too. The content quality is out of this world.

Can you name a example?

I found them to be generally of higher quality than controversial topics. So maybe not always with the best didactic approach, but usually a good start. And then I follow the links, if I want to dive in deep.

Wikipedia is useful for me, for quickly checking something. Not scientifically dive into a deep topic.

Repetitive content, written at several levels simultaneously, weird fixations on tangential topics.

PDEs are a significant enough thing that the article is probably correct. But once you get into more niche math articles, a lot of the writing is incorrect.

I know enough to know the examples for Base sqrt(2) are not correct, but I don't know enough to write a proper example.

For example if this is true "Base √2 behaves in a very similar way to base 2 as all one has to do to convert a number from binary into base √2 is put a zero digit in between every binary digit"

Then Base(10) 3 aka Base(2) 11 converted to Base(sqrt2) would be 101. But it is actually 1000.000001

> Once again,

This is your first comment to me

I don't see how. As per the expansion definition in the article 101 = 2+0+1 = 3

1000.000001 = sqrt(8) + epsilon.

I don't understand why this bothers people. If something on Wikipedia is above or below my level, I just skip it. It takes all of three seconds to recognize. I've consistently found it to be a great starting point for self-study in all sorts of math.

It’s an incredibly common cause of anxiety in math education, and even if you’re not personally affected by it others may be.

Now it surely would be nice, if it could work more like it.

That wikipedia knows my skill set and automatically hides or show additional paragraphs in certain topics etc. or even the paragraph in a simpler language etc.

But this a bit more ambitious - and not really achievable with the current approach. So if I want a math course, I search for a math course.

I question whether this can be a root cause of anxiety. Simply not understanding stuff does not normally cause anxiety. Most people don't get anxious looking at, for example, Chinese characters.

On the other hand, imputing that something should be frightening can actually cause a fear response:

https://psycnet.apa.org/record/1993-20380-001

https://www.sciencedirect.com/science/article/pii/S030105110...

https://www.nature.com/articles/nn1968

Teaching students that incomprehensible math should frighten them doesn't seem like a good approach. There are no grades or critical teachers when you're passively reading a Wikipedia article.

[1] What is a "natural number" (do they start at 0 or 1?)

[2] What is a "function"? Does it carry along a "co-domain"?

A lot of those articles seem to follow a pattern of: "An A is a B that also does C".

If you click on the link to understand what a B is, you get "B is a D in the space of Es with properties F and G".

and so on...

I can understand that this appears logically consistent and very satisfying for people who have already understood the concepts, but it doesn't help at all if you're trying to gain an understanding.

A good textbook has a sense of order in which dependent concepts are introduced. With Wikipedia, the task of discovering that order is outsourced to the reader. Maybe you could develop some kind of path finding algorithm to figure out the optimal reading order for understanding a given concept, but to my knowledge, that doesn't exist yet.

The other problem is that no shortcuts are offered. Even if you figure out the order yourself, Wikipedia gives you no hints how much of B, C, D, E and F you have to understand to get the idea of A. The expectation seems to be to read the entire articles on the dependent concepts, which can be long, rambling and full of obscure special cases.

Wikipedia math articles are not useful to get a shallow understanding of a topic. On the contrary, it pulls you into a rabbit hole of dependent concepts just for you just to be able to understand the words in the article's summary.

From an actual reference, I'd expect that it gives a brief, self-contained description of the basic idea of a concept, without going too deep into specifics, possibly with a "see also". That's not what Wikipedia does.

https://ncatlab.org/

https://kerodon.net/

https://stacks.math.columbia.edu/

The people who are looking up references to advanced math concepts are likely students who are already on a mainstream pedagogical pathway and are looking to fill in holes to a concept map they're already building.

The use case of someone who (1) does not wish to consult the vast and well-discussed pedagogy of math and (2) is not an advanced math student and thus wishes to have stand-alone math definitions is a Very special case.

Okay, but I don't think those communities are relevant to this conversation.

> The use case of someone who (1) does not wish to consult the vast and well-discussed pedagogy of math and (2) is not an advanced math student and thus wishes to have stand-alone math definitions is a Very special case.

Number 1 is a weird assumption! Unless by "consult" you mean spend weeks studying a textbook, the problem is that consulting is too difficult! And if I understand "harsher" correctly you just said the other sites are harder to use, didn't you?

So then it's just "not an advanced math student", which may or may not be a majority of people on these pages but it's a very significant amount and it's the more important target for a general encyclopedia.

What? I'm confused on what you're saying here. Are you stating there are no primary sources on history from more than a few hundred years ago? All history is made up? I'm sure there are poor quality historical articles, but I wouldn't go so far to call all history "fiction".

I once worked with someone in an important position in a major media organization who believed nothing was recorded before the printing press, and was quite vocal about it. He quite strongly believed that everything else was made up.

I always wanted to ask him what he thought about Egyptian hieroglyphs, but he was too far above my pay grade to approach or challenge.

And even then, records are questioned. Sometimes period historians really had to stick their necks out to speak the truth (and in the most literal sense) so direct impressions we have of certain elements of history may be reasonably called into question. And there are numerous historians that are known to have fabricated elements.

The entries are not exhaustive nor are all of them very scientific-sounding, but at least the basic facts which we sort of know of are there.

Not sure what went wrong with the Internet but it's not living up to the early hype, and doesn't really even seem to be heading the right direction.

To the point of this article, much of this is driven by the teachers, who say they will not accept sources that might have "social biases" (as if it were possible for any book to not have those!) The library then purges those books because "no one has checked them out in a couple of years".

The sad thing is that almost 100% of books being added to the libraries fall into just a few categories: Books promoting or "celebrating" perverted sex of any and all kinds (including pretty much all "youth fiction"), Manga, or "Graphic Novels" (let's face it, some have good artwork, but are really just nicely bound and printed comic books, usually with little to no redeeming educational value.)

Sadly, I don't know a single person under 30 who has a clue how to actually use a library to find real sources - they all just default to Googling. The web is amazing, but what's NOT on it is staggering, and of amazing quality and scholarship (which is itself a lost art...)

More worryingly, I've seen a LOT of valuable content vanish from the search engines, which just shoves that content right down the memory hole, using the same flawed logic as those high school librarians - no one's asked for it recently.

We lose access to and context for valuable information when our search engines (it's all about the money from hits and eyeballs) only keep what is "popular". Alas, we've replaced Carnegie Libraries with Kardashian libraries, to our great loss...