[ghaff]

A well-written encyclopedia article should still be able to instruct a generally educated lay reader about what a thing is and why it's notable even if the more detailed explanation heads into depths that someone without appropriate background may not be able to follow.

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.

[madez]

There is a formal language for mathematics because we need it for efficient work. This formal language is intelligible, clear and instructive, given adequate education. This formal language is mandatory to be present in an encyclopedia.

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.

[brownbat]

Yeah, if a "natural language" explanation is just writing out mechanical mathematical steps or formulae in clumsy english, it's completely missing the point.

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.

[gohrt]

https://en.wikipedia.org/wiki/Quicksort

> 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]

[detaro]

Next paragraphs as well: they name and link properties it has, but also give a short definition of them, where you'd otherwise have to follow a bunch of links and read the definitions there.

[DanBC]

The encyclopedia articles are not supposed to teach math. And most of the article can be incomprehensible to most people.

Having a plain English lead paragraph that put the article in context is very important, but the leads are often hopeless.

[Osiris]

I've had this problem with Wikipedia also when looking up various scientific or mathematical references I find here. Most do not have a laymen's explanation at the top of the article, requiring me to lookup other unknown terms referenced in the summary.

I really wish more articles had a summary for laymen with a more detailed explanation below.

[Someone]

Some scientific terms are too deep to directly describe them in layman's terms in a reasonable number of words.

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.

[technion]

I have read the Wikipedia description, and at least half a dozen other mathematical descriptions, and the only description of the Chinese Remainder Theorem that made sense was described here[0] (in the very challenge that prompted me to research it).

I feel there's definitely room to make the Wikipedia description more friendly when it runs for pages and is unreadable from my side.

[0] http://cryptopals.com/sets/5/challenges/40/