Wikipedia is often the last on my goto resources to consult. The information is huge, but writing quality or style often irks me more than I can stand. I I always check Britannica first. If it's not there, then I move on.
Articles in biology, from which I understand nothing, are a wall for me. I could never understand anything biology related. Also for example, in Spanish, don’t ask me why, any plant or animal is always under the latin scientific name, and you have to search the whole article to find the “common” name of the thing.
> A Fourier series is a series expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood.
and
> In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input, and outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex valued function of frequency. The term Fourier transform refers to both the mathematical operation and to this complex-valued function. When a distinction needs to be made, the output of the operation is sometimes called the frequency domain representation of the original function. The Fourier transform is analogous to decomposing the sound of a musical chord into the intensities of its constituent pitches.
https://de.wikipedia.org/wiki/Fourier-Transformation
That is much more as it used to be in english. Anyway I stated clearly, it was a time ago, and now may be better, that it was just an example. In german is still shooting mathematical symbols that anybody who does not already know what FT is, will 99% not even start to understand what is it about.
Please get involved if you want to see improvement. There are some math articles which are excellent: readable, well illustrated, appropriately leveled, comprehensive; but there are many, many others which are dramatically underdeveloped, poorly sourced, unillustrated, confusing, too abstract, overloaded with formulas, etc.
there are many math teachers teaching math to people who don't know the subject, basically all mathemeticians. and wikipedia has guidelines for how to serve the audience, the math articles ignore it.
I (got into and) went to MIT (and graduated several times) in engineering and also in finance. I am way beyond the average wikipedia reader in math knowledge. the mathematics wiki articles are imho worthless. the challenge is not how to write articles that are explanatory and reasonable, the challenge is all the gatekeeping of the wiki editors who make it the way it is, that is an unreasonable fight. I tried to make a change a couple of weeks ago to correct an error that was in an article. I got reverted by a person who wanted to collaborate on making the article more abstruse as a solution. "but the error" I said. It's still there.
I have a fair amount of edits on Wikipedia and the wikis that preceded it. Whenever I read this sentiment here I never really understand what the problem is. I never have it myself. The only fight I have been involved in was if Wikipedia should have an article on Bitcoin. Which was not obvious in the beginning.
You could always link to the article and we can have a look. I have no clout on Wikipedia but I do understand why facts can be problematic in any text book. It once took me a week to correct an article about a Russian author.
I'd say there's significantly less gatekeeping on Wikipedia than most parts in academia. YMMV.
But: there are a bunch of random clueless people trying to promote their obscure papers to boost their citation counts, push weird nationalist POVs, add fringe pseudoscience, make "fixes" that turn out to be wrong, add vague explanations which they find personally helpful but nobody else can make sense of, remove clarifications and explanations in the name of rigorous purity, change the wording of sentences that have been subject of years-long dispute and careful compromise, and so on. Wikipedia maintainers are constantly fighting against these agents of entropy (or when an article is not actively maintained, it tends to get a lot worse over time), which unfortunately can sometimes also negatively color interactions with helpful contributors. They're also part-time volunteers, and fallible humans; try to cut them some slack.
To the extent that there is "gatekeeping", it is mostly along the lines of: you can't use Wikipedia primarily for self promotion, you can't add your own new claims that have no published source, and you have to abide by existing norms of project/community engagement. In general, people are judged by their contributions and behavior, not their credentials (though editors also include a bunch of world-class experts in the topics they contribute about, and it does have some pull when someone can say "I literally wrote the top cited paper about this" or whatever).
But beyond that, the difficulty is that there's no one correct way to explain difficult topics, no single audience for Wikipedia articles, a lot of strong opinions about how things should be one way or the other. Trying to satisfy everyone takes discussion and compromise and sometimes a minority is still unhappy with the resolution. The biggest problem though is that there are not enough active participants (including in mathematics) to write great articles about every topic, and writing a really excellent article about something takes a huge amount of work; there are many mediocre articles that have never really had the time put in to make them great.
When someone new to the project gets into a heated dispute about a minor point, they routinely get extremely frustrated and occasionally then run around the web complaining about how awful the people on Wikipedia are. Several times times in the past few years I have asked such complainers for specifics, and remarkably I have gotten a reply ~4 times. In all but one case, when I went to investigate further it turned out that they were clearly in the wrong. In the last example there was a misunderstanding and I fixed the issue. If you want to provide a specific article and error, I'm happy to go take a look.
Alternately, when people run into an unresolvable dispute on one local article talk page, they can seek opinions from wider groups of Wikipedia editors, e.g. on the math "wikiproject" talk page https://en.wikipedia.org/wiki/Wikipedia_talk:WikiProject_Mat.... If you make a post there about your issue, you will get more eyes on your problem, and it will likely be resolved correctly.
- https://en.wikipedia.org/wiki/Introduction_to_quantum_mechan...
- https://en.wikipedia.org/wiki/Introduction_to_general_relati...
They were created because the main articles are, as you say, difficult for a layperson to read.
The same principle applies to IPA transcriptions. I know some IPA but often find that it is less intelligible than the originals in some cases.