User:Sphilbrick/Mathematics articles

A brief comment about our mathematics articles.

I'll start with a confession — despite having a degree in mathematics, I haven't spent much time looking closely at our mathematics articles. I'll also note that one of my pet peeves is a brand-new editor with a dozen or so edits trying to lecture experience editors on how Wikipedia should work. I'm not exactly in that position — I'm definitely less active in the area than most editors who specialize in mathematical articles, but I've spent more time reading some of the material than the average editor.

While I haven't spent much time actively editing mathematics articles, I do spend a fair amount of time at OTRS. A common complaint there is that our mathematics articles in general and not very accessible to the layperson. I typically commiserate but haven't taken much action other than to suggest that they weigh in at WP:wikiproject mathematics and share their concerns. I recently interacted with another editor who does spend more time with mathematics articles, and suggested collaborating to work on this problem.

I'd like to make two observations based upon my experience that will motivate my approach to improving articles.

I lived through the largely failed experiment of New Math. I'm old enough that I had a decent mathematics background before new math came on the scene so I didn't suffer through it, but I think I understand why some people did suffer through it. I'm sure a lot has been written on the subject, but I'll share my possibly oversimplified concerns.

I think teachers looked at a concept such as operations, i.e. addition, subtraction, multiplication etc. and decided the best way to teach it would be to teach the general concept of operations. Once one fully understood the general concept, any specific operation is a special case of the general concept. In theory, it might be a more efficient, or perhaps more thorough coverage of the topic. In practice, it fell on its face. It's my firm belief that it is difficult to talk about general subjects without having one, or ideally several specific examples already well understood. My shorthand view is to teach one or more specifics, then teach the general, then show how all the specifics follow from the general. Trying to start from the general is the mistake.

It's also my observation that mathematically inclined people have a notion of mathematical elegance. While there is more to it than length, all other things being equal, a proof that takes 10 steps is preferable to approve the takes 20 steps. if your goal is elegance, I'm all in favor of the 10 step proof. If your goal is education, that's not necessarily the best proof. I see far too many academic articles that look like they are written with as few words as possible. That might even be a sensible goal in your audience is colleagues with a solid grasp of mathematics, but I contend it is not the ideal if you are talking to laypeople with a less complete grasp of the subject.

A simple example should suffice.

Consider
 * $$\begin{align}

Y &= 3x^2 - 2x - 2 \\ x &= 2\\ Y &= 6 \end{align}$$

Many mathematicians would find that perfectly adequate if a bit boring, and writing it out any longer than that would feel redundant.

However, I contend that the rank beginner would find the following redundant sequence more informative:


 * $$\begin{align}

Y &= 3x^2 - 2x - 2 \\ x &= 2\\ Y &= 3\cdot(2\cdot2) - (2\cdot2) -2 \\ Y &= 3\cdot4 - 4 - 2 \\ Y &= 12 - 4 - 2 \\ Y &= 6 \end{align}$$

I've taken six steps to cover something that can be done in three, but I contend walking through the intermediate steps helps the non-mathematically inclined reader follow what's going on.