I love Wikipedia. It's amazing. It makes the world a better place. I'm a pretty decent programmer. I do video games so I do lots of 3d math. I'd say I'm decent at that as well.
I hate Wikipedia for math. Absolutely hate it. Unless you are a mathematician by trade Wikipedia is damn near useless for learning new math concepts. I don't even bother checking it anymore.
I had an idea for a couple of years now of creating a wikipedia-style mathematics textbook that will be crowd-sourced, standardized and cover all of math in a way that's accessible to learn from on your own. It would have a kind of a zoom function where you can expand details on explanations and calculations to a depth that you prefer. Ideally this kind of thing would start off with basic math and get progressively further into mathematics like the roots of a tree.
That is not a bad idea at all.,, It will be a lot of work but it could be done. Crowd sourcing might lead to the wikipedia-style schizophrenic-author voice of writing, though. See [1] for a prev discussion.
Interestingly, if the book is organized so it is aligned to the common core math standard[2], it would make a killing in the US market since current textbooks are so bad.
That's a good question. In the spirit of making learning easier it would perhaps "start" with what we teach children. However, that might be ultimately misguided because that would just mimic the curriculum and force the whole thing into a box. But then again the math knowledge itself forces a structure on any such textbook because to know A you need to know B, C, D, etc.
This is further complicated by the fact that most subjects in math can be approached from multiple equivalent angles. For example, complex analysis can be taught from the complex derivative perspective or from the power series perspective equally well. Ideally the format of the whole thing will allow the student to naturally learn things from the angle they understand better.
I disagree. There are math concepts that I've found impossible to pick up from wikipedia but can easily be learned in 5 minutes by having a conversation with someone who already understands them.
Honestly this article in question is a perfect example. I'd wager than almost everyone who reads Hacker News can read the blog post and understand every single step from start to finish. The same can not be said for the Wikipedia article.
For questions about mathematical correctness I highly prefer wikipedia. To me it's far more specific and clear, while the original article makes rather short work of proofs.
When it comes down to questions that involve first principles, I would much rather have rigor over a less time consuming but potentially wrong understanding of the material, and wikipedia does quite well in providing that rigor.
I have also found Wikipedia to be a convenient math reference, but it is not always the "best" that is easily available on the internet. If I'm looking at a topic, it's usually fruitful to Google "introduction to X theory" and go through a few possibilities to find a literature review. Often there is a review which is a good "companion" to the Wikipedia article in terms of explanation, since the style will be different and you get some breadth of perspective.
>that that's attributable to math being hard
(an easily underestimated property of mathematics)
I hate Wikipedia for math. Absolutely hate it. Unless you are a mathematician by trade Wikipedia is damn near useless for learning new math concepts. I don't even bother checking it anymore.