Friendly advice: you'd be more persuasive if you yelled less.

As someone who jumped into WP with the primary intent of improving technical software security coverage, I know where you're coming from. WP can seem hostile to experts, because it is --- unlike the real world --- structured to prevent experts from carrying higher status. Whole WP forks have been created to allow acknowledged experts to contribute without arguing with laypeople.

Having said that, all those projects failed, and WP is perhaps the most impressive resource on one of the top 5† most impressive information technology projects in human history. I don't love WP's attitude towards expertise, but I also don't love tilting at windmills. WP will continue to be successful without your mathematical expertise. That's just a fact. Knowing that, maybe you can understand how people on HN would feel it's unproductive to loudly complain about your experiences on WP.

† Prepared to concede the human genome project as more impressive than the Internet.

Whilst my posts on this subject are all over the place here. I'm not arguing that Wikipedia is not useful, nor impressive, nor successful. It is all of these.

Nor am I suggesting that having "Dr" in front of your name should give you more power on Wikipedia.

What I am alleging is that Wikipedia has a problem with plagiarism, with incorrect information and it has not brought a technological solution to the very difficult problem of verifying information in technical areas (I have also alleged elsewhere that Wikipedia has a problem with deletionism). The general Wikipedia approach works extremely well for general knowledge, but badly, IMHO, with specialised knowledge.

For that reason, some academics prefer to devote their time to writing primary peer reviewed articles (the corpus of which is vast compared to Wikipedia, and much more successful if quantity and quality is the metric). As I have already noted, there are many academics who do spend time adding to Wikipedia. They are not wrong to do so. But I personally see limitations to the approach, with no workable solution, technological or otherwise, in sight.

I understood the point you were making. I was attempting to add to it, saying that these are issues that are going to be especially annoying for academics, who are accustomed to different norms (in particular, respect for expertise earned through study and publication).

Academics like yourself are much better off writing primary and secondary sources outside the encyclopedia. It is the goal of the encyclopedia to aggregate and promote primary and secondary sources. It is not the goal of the encyclopedia to itself be the authoritative source for information on any given topic.

You will find that having written even a simple survey paper that your ideas and critiques are far more readily incorporated into WP than by bloodying your forehead against the brick wall of other editors following what they know to be well-intentioned and, empirically, effective rules.

At the risk of carrying on a conversation... I would like to reply to that. I certainly agree with that and appreciate your clarification.

However, what is happening is that Wikipedia is attempting to deal with very technical topics. As such there is a great divide between the techniques that are empirically observed to successfully collate general knowledge and the tried and tested techniques, developed over hundreds and even thousands of years for collating technical knowledge.

Precisely because academics have so little time to communicate their knowledge to nontechnical audiences there is a dire need for an approach that can successfully deal with this very difficult problem. My claim is that the wikipedia approach is so far not as successful in this area.

On forums where ignorance is king, I frequently advocate the use of Wikipedia to inform. Both aspects need to be understood. There are many people for whom Wikipedia should be a tremendously important tool. In forums like this, I emphasise the other side of things. The Wikipedia approach has its limitations as a means of disseminating precise and technical information.

Of course Wikipedia is limited for technical topics: it's limited by the quality and accessibility of primary and secondary sources. The way to improve WP's coverage of highly technical topics is to generate credible, reliable, accessible source material for it to incorporate.

This is the great thing about the Internet, and it's something WP management has been saying for years and years. Start your own wiki. Limit it to experts. Make it an amazing source. Wikipedia can then cite it, and use its content to resolve disputes and correct mistakes in its sourcing.

Arxiv has existed for a long time, and yet Wikipedia coverage of MSc-level math is pretty awful, and coverage of research math seems to be mostly nonexistent. eprint.iacr.org and cryptography: maybe a little better, but not that much.

Wikipedia needs "popularized" knowledge, to some extent, not just primary sources. Experts probably don't have a use for those resources, though.

You're doing a better job than I did of explaining the gap in available sources that experts could address to improve WP.

The point I hope I'm making, though, is that the improvement needs to happen outside Wikipedia. The experts can't directly be duking it out on WP pages as their journal articles get published.

Definitely. But you're suggesting a real change: the current model is researchers -> papers -> popularizers -> books -> science journalists -> articles -> Wikipedia editors -> Wikipedia, or something like that. Reducing this to researchers -> papers + wiki -> Wikipedia editors -> Wikipedia would definitely improve accuracy, but I think both sides would need to learn a lot about the other to make it work. There are benefits to that, but I don't see it happening.

Agreed. Both sides would need to learn a lot for that to happen. I think there's a vast chasm in fact.

Moreover, most academics don't have time for the wiki part. They barely have time for the papers part. Some academics get to write graduate texts because they can get credit for that, but that's about it. They do get time to write lectures to give to students though (sometimes barely).

But there's a problem. In mathematics, a result may depend on definitions, e.g. whether a ring has a unit element or not, which definition of natural number you are using, or which definition of compact, whether you allow the axiom of choice, what definition of norm you are using, or how a function is normalised. The actual results may be completely different in different books depending on the assumptions made and the precise definitions given. Language also changes over time. Sometimes the same word is used to mean totally different things, and the meaning depends not just on context, but era!

What happens in Wikipedia is you sometimes get a mosaic view of things which are not compatible. Only an experienced expert in the field can spot that and correct it, and it may be days of work to cleanly demonstrate why it is an error. Wikipedians can add such errors far faster than they can be noticed, corrected and justified.

The issue is that people think of science in a reductionist kind of way as a list of true statements. Books are lists of true statements and you can pick and choose the ones you understand and collect them together however you like. But this is totally false. Maybe the only reason you can even understand the book is because the author took pains to define things in such a way that a pedagogically sound route through the material exists.

In the mean time, academics are marking the same wrong answers to homework assignments and in written projects and dissertations over and over again. So this is a huge problem.

(This is to say nothing of the fact that many students believe that using quotations from Wikipedia without attribution in dissertations is permissible, presumably because Wikipedia allows this for public domain sources or something like that.)

What process or processes can bridge the vast chasm between what academics are trying to do on the one hand (advance the forefront of knowledge and disseminate it through teaching to the next generation) and what is being done on the other hand by wikipedians (collate human general knowledge in a way that is easily accessible to all)? There's a vast gap and it is precisely at the intersection of these two great enterprises that things are going woefully wrong.

Here is a better example than the "Group action" one, and it's a real clanger. Look at the page on "Group representation". There it defines a notion of "irreducible representation" in the section "Reducibility".

Now, notice the phrase "A subspace W of V that is invariant under the group action is called a subrepresentation." Which group action is it talking about? This is completely orphaned.

You might think to click through to the page on "Group action" and see if you can get a clue what might have been meant before an edit orphaned this phrase.

In fact, a module can be thought of as a generalisation of a vector space. So in the case of an irreducible group action as defined on the "Group action" page, if R is a field, the module there is a vector space. That G acts R-linearly means precisely that there is a group homomorphism from G into GL(X), i.e. that you have a group representation into the vector space X. So, now the definition of an irreducible group action is that there is no non-trivial, proper vector subspace of X which is invariant under the group action. The definition of an irreducible group representation on the other hand states that there is no non-trivial, proper vector subspace of V that is invariant under the associated group action.

But how in a million years is anyone supposed to work that out from looking at either page? And if either page changes, the connection is totally lost.

A substantial part of the "Group representation" article would have to be rewritten to fix this. And similarly for the "Group action" article. Then the two would have to be connected so that a revert in one doesn't mess up all the hard work in the other.

Naturally people have pointed out in 2004 that there are problems here. But in seven years it has never been fixed.

Of course I can't point out the error. I'm asking you to, and provide a source to back it up. I'm no expert on math, but I've been editing for years and I know how to get corrected information included. I'm not suggesting that I, as a layman, could replace your knowledge as an expert. I'm suggesting that I, as an experienced editor, could help you fix a problem in a way that's likely to stick.