It was Vaughan Pratt who first introduced the Wikipedia thread, in response to someone who said that he hadn't heard of Heyting algebras. I added my penniworth, having in mind its treatment of Dedekind cuts and Locally compact spaces. Recently, however, discussion has centred on the notion of Topos. I have changed the Subject line because Wikipedia is not the only site of its kind. Anyone thinking of writing for it should perhaps also consider: - citizendium.org - which looks like Wikpedia because it is run by the latter's co-founder and now unperson; citizendium has a strict policy of using real names and qualifications; - planetmath.org - in which authors "own" the pages that they have written until they've demonstrably abandoned them; - mathworld.wolfram.com - beware that this is owned by Wolfram. It seems to me that toposes are not a good example on which to base this discussion, being too advanced a topic. On the other hand, if you have opinions about what Wikipedia and the other sites should say about them, then go ahead and write your article, instead of discussing it here! But before you write, please bear in mind that these are resources for the general educated user, not for specialists in the field. Have a look around for articles that you find informative about completely different subjects, for example a medical topic or a place of interest. It should begin by making sure that the reader has come to the right place, for example the word "topos" is also used about poetry. Then it should tell the lay person why anybody would spend their time thinking about this thing. As we all know, a topos is an elephant. Its trunk looks like constructive set theory, its legs look like topological spaces and its tail is a group. But I really don't think that a specialist in a particular topic in mathematics should be writing about their speciality. You need to see it from a distance. Wikipedia has policies forbidding original research. Encyclopedia articles should provide "general knowledge" about background topics. My research programme is a reformulation of general topology, so I need to talk about this against a background of general knowledge about traditional point-set topology, locale theory, continuous lattices, domain theory, constructive analysis and so on. However, since I am doing something completely new, I really don't want to have to give an account of these subjects before I say my own stuff, so I would like to be able to cite a textbook or other source that does so. And I would like that source to be accessible to student without specialist knowledge, and NOT depend on or be part of some other partisan presentation. Chances are that any account of a topic that is part of a research paper will depend on somebody else's foundational system. For example, I would like to refer to an account of locally compact spaces. Having been exposed to locale theory and continuous lattices for 25 years now, I regard it as a matter of "general knowledge" that the topologies of locally compact spaces are continuous lattices, and these in turn carry topologies, named after Jimmie Lawson and Dana Scott. However, I find NOTHING about this in the Wikipedia article. That and more or less every other article there about topological subjects adheres to the orthodox view in pure mathematics that all self- respecting topological spaces are Hausdorff. If I write a new article about locally compact spaces for Wikipedia then I will find myself in conflict both with Wikipedia's anonymous cliques and also with the mathematical establishment. If you're interested in rings and not non-Hausdorff spaces, then please substitute the commutative axiom for Hausdorffness in what I've just said. If some basic result about rings, fields or modules can be formulated without assuming commutativity or charactersistic zero, at no or a small extra cost, then surely it should be so formulated. If the more general treatment is more complicated, but throws light on the subject, the simpler one should be given first, and an overview of the more general one afterwards. Another example of this is excluded middle. Personally, I foreswore EM about 15 years ago because I was disgusted by some of the arguments that people were using in domain theory - "bit-picking", I called it - that didn't form part of any applications or philosophy. EM leads to ugly mathematical arguments, and in very many cases can simply be avoided by stating them more carefully. In others (for example intuitionistic ordinals and constructive analysis) there is a more interesting theory when you use the more delicate tools of constructive reasoning. Getting back to encyclopedias, remember that they are for teaching, not research. Tell students and the general public why the topic is interesting, and tempt them with some simple point that they may not have considered. I'm not claiming to be very good at these things myself, but there are others who regularly do so on their blogs, as well as in Wikipedia and the like. If you don't already know them, you might like to take a look at the blogs by - Andrej Bauer - math.andrej.com - John Baez et al - golem.ph.utexas.edu/category - Dan Pioni alias sigfpe - sigfpe.blogspot.com Paul Taylor