Some articles about mathematics like for example that of determinants are noisy for me because of the well-intentioned “educational” parts. In this example I even think they do more harm than good for people who are struggling with the concept.
The first part of the section “Definition” starts with explaining in horribly ununderstandable natural language english a way to compute the determinant of some matrix. That text is unnecessarily confusing and complex. That text also serves as a good example where formal language can be easier to grasp than natural language. Would you explain quicksort in natural language rather than with a formal description?
If mathematics is taught like in that article, no wonder kids find math boring and hard.
Use natural language for what it's good at. Where did this mathematical idea originate? Who introduced it? What was the problem this mathematical idea helped address? How much does it help address that problem (assuming the why and how are beyond the layman, just describe how helpful it was.)
The Quicksort intro by gohrt is a perfect example.
You're not using the natural language to do away with the thorough mathematical explanation, you're giving the lay reader an idea of why the concept is important, why they should care, in the most general sense.
> Quicksort (sometimes called partition-exchange sort) is an efficient sorting algorithm, serving as a systematic method for placing the elements of an array in order. Developed by Tony Hoare in 1959,[1] with his work published in 1961,[2] it is still a commonly used algorithm for sorting. When implemented well, it can be about two or three times faster than its main competitors, merge sort and heapsort.[3]
Having a plain English lead paragraph that put the article in context is very important, but the leads are often hopeless.
I really wish more articles had a summary for laymen with a more detailed explanation below.
Also, what one reader calls a layman's explanation another calls gobbledygook.
That's one of the reasons for inventing hypertext. For example, https://en.m.wikipedia.org/wiki/Riemannian_manifold has a nice introduction paragraph, but it presupposes quite a bit of knowledge. If you want to know more, feel free to click some links to learn more.
And yes, things probably aren't presented in a way that is optimal for _your_ learning, but there is no way to do that for every reader.
I feel there's definitely room to make the Wikipedia description more friendly when it runs for pages and is unreadable from my side.
I had a very similar discussion with someone involved with the Wikimedia Foundation earlier this year and he highlighted math/science as having exactly this issue. Way too many articles seem to be written by people who are far more comfortable and interested in using the equation editor than in providing an intelligible explanation.
The problem isn't universal to be sure. But it is widespread, especially in less popular topics.