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Post Made Community Wiki by S. Carnahan
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Federico Poloni
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My feeling towards Wikipedia is that it is great as a quick reference to check facts and results, but it doesn't work as well for explaining well introductory material. The reasons are various.

It is difficult to provide a good explanation for everyone. Often, different intended targets conflict: you can't explain "kernel" to a layman, to an engineer, and to a mathematician at the same time, while making the exposition clear for all of them.

Moreover, often one would like to start from scratch and lay down the whole article from a different point of view; this is diplomatically difficult because it would trash the contributions of the previous editors (good or bad as they are). Yet, for some quickly-evolving topics it might be necessary to rewrite the page from scratch every few years, to reflect the recent advances and the new understanding.

The notation of an article might need changing; however, it's a difficult job to get to agree on "the best notation" for a given topic, even among three co-authors. Edit wars are a concern, and democracy often isn't the best way to solve them.

Pages in other languages are another concern. There is nothing wrong with having a good English page translated in several languages; on the other hand, local writers will tend to start their own new pages independently, even if their quality is worse. Even if someone translates an English page at a certain moment, future changes will get de-synchronized among the different languages.

I feel that many mathematicians would rather write a (part of) a textbook or a review article, and publish it on the internet. Often, too many cook spoil the broth. A good writer working alone can trump many writers working collectively. So, maybe we'd rather need to focus efforts on making good textbooks and lecture notes easy to find on the internet.