One comment regarding Wikipedia: you may be aware of the “Simple English” language option, which can help with making some pages more accessible. It’s in the language menu, or you can just change the language prefix in the URL, such that your example above becomes https://simple.m.wikipedia.org/wiki/Taylor_series. Granted, it’s not immediately obvious that it’s there, but perhaps it’s one reason that the main article can be more precise off the bat rather than explanatory. Furthermore, I wonder if Wikipedia math editors are less concerned with the notion of an encyclopedia as learning device and treat an article as a canonical overview of a topic, with all of the baggage that comes with that.

I’ve been using wikipedia for years and never knew about this. I wish there was a prominent link on the page “Switch to simplified explanation” or something. As someone who knows barely enough maths to get by this would have helped me immensely over the years.

On the other hand, as someone who knows a bit of math, I love those Wikipedia articles that get straight to the point, and hate those where I first have to dig through a pile of (to me) useless "intuition".

I'm not sure if it is really possible to learn/teach math (like actual math, not just some loose intuitions, because those don't really help you with anything) without going through notation and prior knowledge. Notation exists for a reason.

Should Wikipedia or education itself then primarily serve those who already have the intuition?

I've found Wikipedia quite hit or miss. Sometimes it's straight to the point, other times it's impenetrable and I've had to do more research.

I run into that same problem a lot while trying to find tutorials that target beginners. Absolute beginners, the kind showing up to my organization's Google Summer of Code chat rooms. It's rare to find tutorials that just keep it simple enough.

I wanted a regex one recently. First off, they all presumed mastery of the concept of a string, but more seriously, none of them had a really good definition of a regex! I still can't think of one myself, but I know it's probably not "pattern to match specific strings", because it uses an uncommon meaning of "pattern" and a jargon meaning of "match". And of course they all immediately used terms like "formal languages".

The perldoc page 'perlretut' did pretty well with "a template that is used to determine if a string has certain characteristics" - ok, a bit abstract for my taste, but let's keep going - then a bit further down they use "modifier" (flag) with no definition. But I really had to look hard for flaws in that one. I guess the only way to actually nail this is to supervise successive groups of students as they try to learn using your tutorial-in-progress...

I explained regexp to my mum as a "single character string, which has the power to describe an amount of various, different character strings".

And then an example like "Look, you have your Word document and you are looking for ..."

Is encountering function notation and the symbol for the set of real numbers all that different from encountering unfamiliar vocabulary? It is slightly harder to Google for notation, but otherwise I do not see a major difference.

In the Wikipedia page you linked, I immediately encounter several terms that I do not know the meaning of. I must either click through or search separately to fill in my own gaps.

Your criticism is not totally disagreeable, but we have to wonder where to draw the line. Is a "Hacker's Guide to Numerical Analysis" obligated to hold your hand all the way through basic notation? The notation that you mention in your comment are the "Hello world" of mathematics.

I have found undefined notation to be the bane of my existence when trying to teach myself a field of math. How do you Google mathematical notation? It can be a giant and opaque barrier to deepening one's knowledge when studying the subject on one's own.

Maybe this will help: https://detexify.kirelabs.org/classify.html Then you can e.g. use the name of the TeX command for the symbol to Google its meaning (Stackexchanges are often full of questions looking for the TeX command for a symbol, so you could use these to infer in the other direction)

Thanks--this is most helpful! :)

Strongly agree. It's very difficult to work out what a symbol means if you've never seen it before.

In saying that, in general I've found it's not too bad. Mostly greeks and the occasional symbol like sigma along with some set notation.

I sort of agree. But there's no right answer here. We can't expect every Wikipedia article to take you through the basics of the subject from scratch. A certain level of knowledge just has to be assumed, and it's hard to know where to draw that line.

Off-topic, but interesting to see my former heart condition randomly linked on HN!

Hackers = engineers