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.
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.
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.
Also, Wikipedia tried a wiki textbook project and no doubt people were very unsatisfied because they couldn’t compete with textbooks, which often have a singular pedagogical vision behind it. It’s hard to compete with famous well discussed texts.
I’m happy with Wikipedia as a reference which supplements those students who are already studying the material; in other words, those students looking up topics in Linear Algebra are taking or have taken the course already.
[1]: https://ncatlab.org/nlab/show/linear+algebra
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.
[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"?
Repetitive content, written at several levels simultaneously, weird fixations on tangential topics.
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.
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
As RDBury on the Talk page mentions, "bases that are not Pisot–Vijayaraghavan numbers are not guaranteed to terminate or even be periodic". Whomever wrote that example just happened to pick an integer where the Base(sqrt2) version terminates and has such a pattern, and treated it as if it applies to all integers.
> 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.