Should Wikipedia Allow Mathematical Proofs?

Beetle B. writes "An argument has arisen over whether Wikipedia should allow pages that provide proofs for mathematical theorems (such as this one). On the one hand, Wikipedia is a useful source of information and people can benefit from these proofs. On the other hand, how does one choose which proofs to include and which not to? Should Wikipedia just become a textbook that teaches mathematics? Should it just state the bare results of theorems and not provide proofs (except as external links)? Or should they take an intermediate approach and formulate a criterion for which proofs to include and which to exclude?"

Sure

[lenmaster (598077)]

Of course they should allow proofs. Proofs are useful and factual information and proofs alone don't really "teach" mathematics are far as I'm concerned. They should take care to properly separate proofs from higher level information, as not everyone is interested in them.

Wikibooks

[eean (177028)]

Yea I agree, though perhaps the longer/more complicated proofs belong in Wikibooks.

Mod Parent Up

[saibot834 (1061528)]

As Jimbo Wales once said, Wikipedia is - as an encyclopedia - only one book in our "wiki library", and one book is not a whole library. Of course mathematical proofs are important and should be freely available, but so is tons of other sort of information, too, and we can't just put everything in Wikipedia. Wikibooks [wikibooks.org] offers a place for some book-like-stuff (and I think mathematical proofs belong there). There are also other projects [wikimediafoundation.org] for different kind of information, like learning materials and dictionaries. We should start to transfer Wikipedia's success to other free wikis and projects.

Re:Mod Parent Up

[cnettel (836611)]

I don't agree about mathematical proofs in wikibooks. Proofs for individual theorems only rarely require a book-sized volume of text. It also makes little sense to collect proofs of separate theorems into "books", or about as much sense as collecting articles on different subjects into an encyclopedia. Maybe there should be a separate wiki namespace equivalent to Mathworld, but proof of central math theorems certainly should be readily available from wikipedia.

Re:Sure

[Sorcha Payne (1047874)]

>a) how do you know the proof is correct? Other people would read the incorrect proof, see the errors, and change it so that it is correct just like any other article. >b) how do you organize all of the mathematics coherently? This could be done just as it is done for other articles; if its badly ordered, someone will come along and fix it. If they separate the proofs, by say, including them towards the end of the article, then there should be no problem. It's often said that at least half the insight of a theorem is the proof used to get it.

Re:Sure

[GuldKalle (1065310)]

But it's the only field where you can get proof, at least in the meaning it's used here.
In other sciences, background knowledge is based on observations, and thus you can only get theories. Good and reasonable as they may be, the background is a posteriori, and therefore does not prove anything.

Please correct me if i'm wrong.

Re:Sure

[nebosuke (1012041)]

Computer science is a branch of mathematics. Perhaps applied mathematics if you feel the need to make such a distinction.

Re:Computer Science != Science

[nebosuke (1012041)]

CS is both a branch of mathematics and a science in that it is a branch of mathematics specifically developed to be directly applicable to 'real-world' problems and developing and refining models of real-world problems according to the scientific method.

You are correct in thinking that "computer engineering" and "software engineering" are not scientific disciplines, because they aren't. They are also not computer science. A software engineer is to a computer scientist what a mechanical engineer is to a physicist.

The lines seem to be blurred when it comes to computer science because, more so than with any other scientific discipline, great computer scientists have a tendency to also be great engineers. As Fred Brooks wrote in The Mythical Man Month:

For the human makers of things, the incompletenesses and inconsistencies of our ideas become clear only during implementation. Thus it is that writing, experimentation, "working out" are essential disciplines for the theoretician.

There is very little separating the science from the engineering when the medium is information and logic, so computer scientists have the luxury of taking their science through to an actual concrete implementation very quickly and by themselves.

A physicist, on the other hand, would usually require an enormous amount of education in material properties, state of the art in manufacturing technologies, and/or a massive amount of infrastructure to provide power etc. to engineer an actual implementation that tests his theories. For physics, and most other sciences, application of theory requires a non-trivial and entirely different set of skills and knowledge than it takes to develop theory, which is why there is a much more distinctive break between the science and engineering in physics, biology, chemistry, etc. than there is with computer science, where a program might not only serve as the definition and description of a theory, but also as a concrete implementation.

Re:Sure

[killerkalamari (528180)]

Why exactly is it not wise? You cite some examples of including more, then your last sentence restates your opinion. Please support your claim that all knowledge shouldn't be included in Wikipedia, for I believe the exact opposite.

There are some topics which used to be on Wikipedia, but were removed. Why were they removed? "not notable enough". See, that makes no sense to me. I would like to see EVERYTHING (everything that is legal of course) in Wikipedia. Why exclude some bits of human knowledge while including others? Does Wikipedia need more hard drive space or something? I can't imagine that being the reason. Perhaps arcane or highly focused knowledge scares some people. Or, perhaps since they are not intelligent enough to understand it, they decide that it has no value. If there are a bunch of less used articles (since they are unused) it won't be raising bandwidth costs either.

Recently I went to the "quantum gate" article. There are equations and technical language everywhere. I certainly did not understand it.. I'd first need to read more about the underlying concepts. I hope this disproves my "lack of intelligence" point, but I am not convinced. A while back I went to Wikipedia to learn more about Encyclopodia, and it was useful to me. But then I noticed an RfD. I got lucky when I searched, because now I wouldn't be able to learn what I learned then... the article is gone! Why? Because it was highly focused. Not notable enough for some people. Well, you know what? It was useful information to me.. and now that information has been lost. I consider that a step in the wrong direction.

Besides math, there is knowledge out there that, while I may be completely uninterested in it (celebrity trivia, for example), some people find fascinating. How about articles on "everyday" people. Does including it make Wikipedia any less useful for me? Absolutely not! I cannot predict the future.. who knows but I may need to know some weird fact, read some proof or book, find some arcane piece of knowledge, read about my friend from high school who I lost contact with. Why limit it?

Now please don't misunderstand what I'm trying to say. I am not saying that factually incorrect information be included in Wikipedia as if it were fact... or sarcasm, etc. We're talking about knowledge here, not fantasy.

There are already user pages for personal information as well, in case people are concerned with Wikipedia turning into MySpace or something.

So I ask again.. why not include everything?

Re:Sure

[by Anonymous Coward]

Wikipedia has been ruined by self-importance. The idea is cool beyond imagining - why *not* put all of human knowledge (even "fancruft") in one searchable, categorizable archive?

See, you've just demonstrated once more that the people who whine about Wikipedia are the people who don't understand Wikipedia.

I realise this appears to be a difficult concept to grasp, but you'll get there if you stretch yourself: Wikipedia is not about creating an archive of all of human knowledge. It is about creating a free online encyclopedia. An encyclopedia is a well-defined type of reference work, not an archive of random facts. There are many things an encyclopedia excludes by design. Mathematical proofs are one of these things.

Re:Sure

[Kjella (173770)]

It is about creating a free online encyclopedia. An encyclopedia is a well-defined type of reference work, not an archive of random facts. There are many things an encyclopedia excludes by design. Mathematical proofs are one of these things.

I guess I don't understand Wikipedia then, because I find it so incredibly useful for all the things I wouldn't find in an encyclopedia. YMMV.

Re:Sure

[pimpimpim (811140)]

Wikipedia has the potential to hold everything, but that may not be wise

Results 1 - 10 of about 9,830 from en.wikipedia.org for "anime" "list" [google.com]

This includes the:

List of video games based on anime or manga

List of video games based on anime or manga

List of H anime (but not including fan parodies, have to keep up standards)

And 9827 more lists of this kind. Shall we keep the mathematical proofs for now, ok? By the time hard disk space becomes scare we can think about where to start deleting.

Yes.

[One Childish N00b (780549)]

They're obvious academic knowledge with clear educational merit. Where exactly is the problem?

New playground for the delitionist

[Pinky's Brain (1158667)]

That's about it ... they must have gotten sick of webcomics.

Re:

[rucs_hack (784150)]

The problem is in ensuring that the proofs are accurate. That's no trivial task, especially if too many such proofs get added to Wikipedia.

Re:Yes.

[notthe9 (800486)]

That "problem" is not unique to proofs. That is the issue on Wikipedia.

In fact, it is usually a lot easier for someone to check a proof than for someone to look verify who the last prime minister of Malawi was.

Re:Yes.

[Entropius (188861)]

Can't they just look up the "Malawi" article on ... ... wait...

Re:

[larry bagina (561269)]

A detailed history of the Star Trek universe doesn't appear in a general purpose encyclopediae either.

A mathematicians view

[2.7182 (819680)]

I find wikipedia useful, and the math is generally well done. The biggest problem is that I hate reading math symbols in anything but latex generated documents.

Re:A mathematicians view

[the_other_chewey (1119125)]

I hate reading math symbols in anything but latex generated documents

No problem for you then: Wikipedia's math content is exactly that.

Re:A mathematicians view

[aminorex (141494)]

The math is generally well-done in the sense that it is accurate, as far as it goes. It usually doesn't go very far, for the technically inclined, and it is usually far too abstract and technical for the general reader. It's sort of the worst of both worlds, really: It's impossibly shallow for the serious student, and impossibly jargon-rich for the layman. There are exceptions to both pessimialities, clearly, cases in which a given article is well-suited to one or the other audience, but in those cases, it has just lost one of its major audiences -- and really, the specialists are a major audience for wikipedia math articles, simply because there is nothing fulfilling that function for the serious student and professional right now, so that wikipedia math articles get more attention from this audience than they would, if such a facility existed. The result is that most of the articles become unusable for the general reader very quickly, but can never really satisfy the needs of the specialist audience.

Dictionary - Encyclopedia - Textbook

[FalconZero (607567)]

As I see it, all three are essentially the same but vary in their level of details. Given that wikipedia is electronic, and can essentially (re)represent it's data in various forms, why limit the amount if information present (assuming its factually correct)? Surely the level of detail of an article should be up to the user. Perhaps a better solution in this case would be to include the proofs but make them 'rolled up' by default - IE 'click here for details'. I know 'rolling up' is possible in wikipedia; I've done it on my page there.

As a side note, its worth noting that the article submitter engaged in the discussion [wikipedia.org] about the article for deletion. They voted to delete the article.

Re:Dictionary - Encyclopedia - Textbook

[wren337 (182018)]

The usual arguments for brevity don't apply here - are you worried about the "book" getting too "thick"?

They've started something - a compendium of knowledge - and they're preventing it from growing because they want it to fit a publishing model that no longer applies. Why limit yourself?

Re:

[Pinky's Brain (1158667)]

Editing can be reverted ... the ability to do it doesn't give you a feeling of power. Deletion, now that's a power trip.

They thrive on the attention, the ability to destroy ... hell they even thrive on the hatred. The fact that one of the deletionist in question even posted this story when it's obvious that no one here is going to agree with him is pretty telling.

Re:Dictionary - Encyclopedia - Textbook

[Beetle B. (516615)]

Yes, indeed I did. But I tried not to have my view imposed on you when I wrote the summary here. I was curious to know what everyone else thought. For the record, here is my comment:

Delete. I feel only notable proofs should be kept in Wikipedia - not proofs of notable theorems. The proof of infinitude of primes is notable - it's often the first proof by contradiction many encounter. Cantor's proof is also notable (and again, may often be the first of its kind seen by students). Both of these may also have had a great deal of historical significance. The proofs provided in this article are in no way special. Yes, totient functions are important, which is why there is an article on them. The proofs of its various properties are just details. I agree that it should be transwikified - Wikibooks if there is a book on number theory being worked on there. Beetle B. (talk) 23:56, 15 December 2007 (UTC)

In retrospect, I chose a bad headline. I wanted this to be a discussion not on whether they should have proofs, but on what criteria should be used to decide which proofs to include - for which there was little, but not much discussion. It seems many here want Wikipedia to allow all proofs.

Another analogy no one pointed out is that when scientific results are posted on Wikipedia, is it "acceptable" to post along with them the raw data from the respective research journals (ignoring copyright for a moment)? Is this a valid analogy, and if not, why not? In a sense, that data is "proof" of the "correctness" of those scientific results.

To muddle the waters further, I actually went to the totient proof page looking for something, and reading one of the proofs did help me with my work...

What's the problem?

[teslar (706653)]

On the one hand, Wikipedia is a useful source of information and people can benefit from these proofs. On the other hand, how does one choose which proofs to include and which not to?

That says it all, really. On one hand information that is clearly useful and valuable can be presented, on the other hand we can bicker about how we write it down exactly, even though that doesn't really matter as a proof is a proof as long as it's correct.

To elaborate a little bit, some proofs are more elegant than others. Some require more knowledge than others. You can prove Pythagoras' theorem on two pages using only elementary geometry or in two lines using vectors. Which version you present depends on your audience, but that doesn't change the fact that you should present one. Proofs are useful, they help you understand not only that a theorem is correct but, much more importantly, why it is correct; so why is there even a discussion about whether or not to include proofs? Especially on a system like Wikipedia, where multiple versions of a proof can coexist peacefully (in theory) on a page - it's not like you'd have to choose one over all others (like you might have to, for instance, when teaching a class or giving a talk).

So - what's the problem? Unless it's political, in which case, well, you know, *yawn*.

Re:What's the problem?

[Ibag (101144)]

The joy of being a mathematician is that I got to have this debate with a few of my friends a week ago.

Quite frankly, I am torn. On one hand, wikipedia is supposed to be an encyclopedia, and this is not the kind of thing that would generally make it in an encyclopedia. Even though wikipedia doesn't have the space concerns that regular encyclopedias have, there are issues of aesthetics and flow, as well as not cluttering up what the user wants to find with too much noise (which many proofs will be to many people).

On the other hand, there isn't an a priori reason why wikipedia should be bound by any of the limitations of a regular encyclopedia, and most of the problems mentioned above can be solved by creating appendices for any proofs that cannot be tastefully inserted into the text, either at the bottom, in a collapsible section, or on another page.

However, it can be argued that even this leads to clutter, or that certain proofs do not meet relevancy or quality standards. Wikipedia is not, and should not be a general storehouse for everything that happens to be true. It might be appropriate to have a proof of the Pythagorean theorem but not appropriate to have a proof that a fibration leads to a long exact sequence of homotopy groups. In fact, for some things, it is probably for the best if no more than a sketch of a proof and a reference to an edited book/paper are given.

Personally, I would like to see a companion site, wikimath or some such, that integrates well with wikipedia but contains the things that wikipedia should not. I envision a site which subsumes the content planetmath.org but is closer to the style of wikipedia, both editorially and aesthetically. With enough interlinking between the two sites, it could easily serve as an appendix to wikipedia, placating both the people who wish to add proofs and the people who wish to keep wikipedia pure and relevant.

In any case, I don't believe that the issue is as clear cut as many people want to claim, and I don't think that a completely satisfactory solution will be simple and easy.

Re:What's the problem?

[jesup (8690)]

Ah, but you're wrong. Wikipedia is a type of encyclopedia. It isn't a book, but it has a set of goals, one primary one of which is to be "encyclopedic". Just because they have a website you can add to, it doesn't mean it's a free-for-all - you shouldn't host your blog there. And, though it may seem so at times, Wikipedia is NOT a repository for all known facts in the universe. Random lists (members of the RPI Science Fiction Club in 1980, 1890 US Census house-by-house data, etc) do not belong there. Not only do they clutter it up (including search listings and providing dusty un-watched corners for vandalism to persist), but it also costs the Wikipedia foundation money. If mathematicians use this, edit them, discuss them - all of that costs the foundation for something that's not part of its goal.

As the grandfather post indicated, the best solution is a separate wiki, such as WikiMath.

Re:

[aminorex (141494)]

That's precisely the problem: In wikipedia, everything is political. The content is driven purely by politics. There is a strongly empowered set of vested interests, there are vast astroturfing armadas from various constituencies, petty cabals that lay claim to tracts of information space in order to control the track of public discourse and groupthink on a given topic, for whatever reason, economic, political, etc., in the real world or other.

Among these political factions is a major movement called de

Absolute truths on Wikipedia?

[Pyrion (525584)]

Lemme see if I got this right: posting absolute truths on Wikipedia is up for debate?

Re:Absolute truths on Wikipedia?

[Daimanta (1140543)]

I brushed my teeth this morning. This is an absolute truth. Should it be included in Wikipedia?

Re:

[Rich0 (548339)]

Ok, devil's advocate - why not?

Is there any reason that absolutely ANY trivial fact can't be included in wikipedia?

Just have a ratings system to put less-noteworthy material someplace where people won't have to browse through it. Companies like google can specialize in finding data in these kinds of articles.

Disk space is getting to the point where an encyclopedia could be built capable of containing the continuous typing of every human on earth for the rest of time. So why not let them type?

Heck Yes!

[tjstork (137384)]

The whole promise of wikipedia is that computers allow us to accumulate an incredible amount of knowledge. There's no need to draw an artificial line and say "no, you can't have this, because, book form encyclopedias don't have it". If volunteers were willing, it ought to have proofs. And, also it would be good if it had experiments in the other sciences as well. It would certainly make discussions over GW and evolution more accessible to more people as well. How does one infer historic atmospheric chemistry? How does one understand the genetics of evolution? Right now, a lot of this stuff is locked up in scientific journals and these are invariably organized more by article. Wikipedia could, hypothetically, allow us to apply a taxonomy to all of human knowledge. Donations welcome.

The crazy wikipedia admins....

[Raisey-raison (850922)]

Part of the problem is the insistence in Wikipedia that it cannot contain x,y or z. Here there is some rule that 'Wikipedia is not a manual, guidebook, or textbook.' It's very difficult to argue with people about this. When you point out that since wikipedia is not a paper encyclopedia it can contain a lot more information than a regular one and therefore can have characteristics of a textbook you get circular reasoning of 'Wikipedia is not a manual, guidebook, or textbook.' If you dare to ask to change the policy people say there is already consensus.

But this 'consensus' is 'weird'. Sometimes even when there is a clear majority in favor of saving some article or changing some policy admins will say that 'Wikipedia is not a democracy.' If you then ask well what does determine it you also end up with a tautology. I once asked someone why they wanted to delete article x and they said they were a 'deletionist'. Again I asked why and ended up with circular reasoning.

As far as this issue is concerned I think without proofs you are missing a whole lot in math. This also makes Wikipedia a difficult forum to discuss math and science in terms of what goes into an article. As someone in this area I often try to explain to people that their idea about y or z here is doesn't work because of some scientific concept.

The problems occur when they consider their generalist approach most important even if they are ignorant of the topic area. For example I might be talking about Unsolved problems in biology or Unsolved problems in medicine [wikipedia.org]. Well to really address the issue you need expertise in that area. Generalists without it go in and presume to understand what is an unsolved problem in a field in which they lack knowledge. I heard all sorts of bizarre ideas from people in the unsolved problems in chemistry [wikipedia.org] deletion debate [wikipedia.org] about the 'nature' of chemistry, how chemistry itself was not very precise and easy to define. It's so crazy because Science magazine had a whole issue [sciencemag.org] on the topic of big unsolved problems in chemistry. Oh well I guess those people who are actually scientists just don't get chemistry in the same way as a wikipedia admin.

It gets really crazy in that although the above articles got deleted enough people kicked up a fuss to save unsolved problems in neuroscience, unsolved problems in chemistry and unsolved problems in economics to save them. To really converse on these issues you have to really understand neuroscinece but wikipedia admins seem to think not. They play sneaky games. If they can't delete them the first time around keep on referring it for deletion. They did this with Unsolved problems in biology here [wikipedia.org] and here [wikipedia.org]. Then if you try to recreate the article you get slapped down by an admin because the article has already been deleted so you lose not matter what.

I finally gave up on getting any logical argument from the admins when I pointed out that if unsolved problems in neuroscience [wikipedia.org] could exist then why not have unsolved problems in biology [wikipedia.org]. I even talked to some practicing biologists about what these problems might be and low and behold they gave me some. Then the admins said well its not biology, its really biochemistry. Then I asked well why not have Unsolved problems in biochemistry. And it went

Middle Ground

[squoozer (730327)]

As with most things in life the best solution is probably somewhere in the middle. Hundred page proofs are not really suitable for Wikipedia and a complete ban on proofs would leave the site lacking. If it is sensible to include the proof or part of the proof then it should be included.

The maintainers of Wikipedia really needs to ask themselves what they wants it to be. Do they want it to be an encyclopedia or does it want to be the source of all knowledge. Personally I think it should aim to be the best encyclopedia going as I suspect being the one source of all knowledge is probably impossible and there is a danger the real worth of the site will be swamped by too much detail.

Wikipedia should be the starting point of learning not the start, middle and end.

Ridiculous

[ytm (892332)]

It seems that admins are recently too happy with removing information from wiki, than adding it.

Mathematical proofs are as much important and informative as their theorems. The proof allows for better understanding of the theorem, you can see why there are certain assumptions in the theorem and what is broken when these assumptions are not met. For some applications the proof is a blueprint for algorithm to solve problem stated in the theorem.

But I guess that biographies of fictional characters and detailed descriptions of Japanese cartoon episodes have much more important place on wikipedia.

Re:

[TheLink (130905)]

"But I guess that biographies of fictional characters and detailed descriptions of Japanese cartoon episodes have much more important place on wikipedia."

I wouldn't say more important. A more accurate term would be more secure/permanent place.

There are typically far more rabid fans of japanese cartoons willing to wage a wikiwar, than there are rabid fans of math proofs.

Now add the fact that stuff can and does get deleted, and you'll see that a lot of stuff worth keeping could get deleted just because there

Wikipedia and deleting

[rangek (16645)]

What's the deal with wikipedia and deleting stuff anyway? It is not like this little bit of text is wasting space or something. I would think it would be much better to have too many articles than too little. One of the things that has made wikipedia sucessful is the sheer amount of information there.

Why are you asking us?

[p3d0 (42270)]

Wikipedia has policies and guidelines for this. Include it if it's notable [wikipedia.org], and not original research, etc.

Why not follow the path of Wikiquote?

[Reemi (142518)]

I do not understand the problem. A wikiproof site, just like wikiquote, could be a nice solution.

Existing articles are not 'polluted' with proofs and can link to the relevant wikiproof article. The wikiproof site can implement specific features that are usefull for mathematical proofs.

Reemi

Re:

[kryzx (178628)]

That's exactly what I thought when I saw this. I see the argument for not clogging mainstream wikipedia with full proofs, but a central, public wiki of proofs would be a fantastic public resource, a great place for communicating about such things, and might spawn a real discussion community. A wikiproof site would be a great way to separate this out while keeping it available, and wikipedia pages could reference the appropriate proof pages when needed.

Right. More of this.

[Garse Janacek (554329)]

Wikipedia has allowed mathematical proofs, for several years. I've found several of them useful, as it sometimes has nice proofs that would otherwise have been troublesome to track down without a more detailed literature search. I know other people who have found them useful as well. The fact that this useful information is now being opposed by some (including, apparently, the submitter) on the basis of "OMG, if we allow proofs, then there might be too many proofs, and then how will we stop it?!" is highly irritating to me. Proofs have been allowed for years without overwhelming the rest of the useful information. Wikipedia has not become a repository for opaque, useless 200-page proofs. Why are we suddenly worried about this? If you're really concerned, just put the proof on a separate page from the main theorem.

I still have never seen a coherent explanation of why Wikipedia is so concerned lately about deleting any material that is unworthy. It has greatly reduced the site's utility to me, and is the reason I use it less and less, and will refuse to contribute to its fund raisers until their deletion policy is substantially revised. The only explanation I've ever seen is a sort of question-begging, "But if we allow non-notable information without deleting it, then there will be non-notable information there!" Yes, so? Here's a nickel, kid, buy yourself a bigger hard drive. If you want to make "non-notable" information appear lower in search results, fine. That's useful. But a lot of information that I find useful is apparently now considered "non-notable" by the Wikipedia admins, and I'd rather there still be some way for me to find that information.

Also, what's with the policy of hassling articles with trivia sections? That seems so arbitrary to me. It's frequently a useful place to collect interesting information about the subject that doesn't fit neatly in earlier sections (and "if it's notable, you should merge it into the main article!" is just silly -- we should awkwardly insert this single notable and interesting factoid into an unrelated earlier section? That just makes it harder to find for those who care, whereas the people reading the earlier section will wonder why the subject jumps around. Trivia sections allow for cleaner editing and easier information searches.) Again, what is the harm in it being there? If you don't care about trivia, you don't have to read the section. And, again, if it bothers you that much, just put it on a separate page.

I'm a little bitter about this whole thing. Wikipedia used to be such a great resource, but lately all I hear is admins talking about ways to block useless information (for certain definitions of "useless"), not about how to actually strengthen the material that's there. Pretty soon, teachers won't have to tell kids not to cite Wikipedia....

Re:Right. More of this.

[Garse Janacek (554329)]

There's a difference between saying "Information should be cited and with neutral POV" (with which I agree), and "Information should be cited and with neutral POV, so trivia sections are bad" (which seems like a non sequitur). If trivia sections were allowed, but with the same requirements as the rest of the article, I'd have no complaint. Instead I keep seeing useful trivia sections (or no longer seeing them...) with ugly banners saying they shouldn't be there. It just reinforces the growing perception of Wikipedia admins as gatekeepers trying to keep information out rather than in.

trivia are by definition not notable, otherwise they wouldn't be trivia.

Yeah, I've also heard this argument. It conflates the formal definition of "trivia" (i.e. something unimportant) with the actual conventional use of the term (i.e. a small piece of information). I have trouble accepting good faith in those who make this conflation, since it's so self-evident -- if there are two possible meanings of a word, and one of them makes a sentence false by definition, try using the other one. However, assuming you are making this argument in good faith, let me clarify: when people talk about the notability of information in "trivia" sections, they are usually using the latter definition. Since this definition encompasses, just for example, every question/answer ever made on Jeopardy! or Trivial Pursuit, I'd certainly hope there would be a place for that sort of "trivia" on Wikipedia.

I've seen several articles getting their trivia sections removed or "integrated", and I must say it was an improvement.

I'll see your anecdote and raise you another -- I've seen useful trivia sections removed, or poor integration attempts, or ugly banners telling me that the useful information I'm reading shouldn't be there. It is appropriate to apply the same editorial guidelines to trivia sections as to the rest of the article. But there's no reason to make a blanket "discouragement" in cases where it really is the appropriate choice.

Obviously

[JamesRose (1062530)]

With text and facts wikipedia sites places where it got the information as a resource to prove what is written is true, or they state when they can't site the source. Now with mathematical equations the source is the proof, so it doesn't make any sense not to state how it was proven. However, that being said, some proofs are very long and often people don't want to see them, so possibly put the proofs as a separate page (like clicking on an image to see it at higher quality) See what I've written, its called continuity in policy and I think it's the only way for wikipedia to gain/retain their credibility as a source for mathematics.

Proofs belong into Wikipedia

[Aaron Isotton (958761)]

At the risk of being modded redundant, here's my position on the subject:

"Most people don't understand them" could be applied to most topics on Wikipedia, with or without proof. Just take any page about an advanced topic in philosophy, mathematics, astronomy, chemistry, biology or probably even history.

I agree that they should not be part of the *same page*, e.g. the previously mentioned proofs of the Pythagorean theorem should IMHO *not* be part of the page "Pythagorean theorem (http://en.wikipedia.org/wiki/Pythagorean_theorem)" (which currently includes 8 different proofs).

I don't think that something like wikibooks or wikiproof is a good idea. When I want to know more about the Pythagorean theorem, should I go to wikipedia? Or citizendium? Or MathWorld? There are already too many choices, and there is absolutely no advantage to having one more. I find it very useful to have *one* resource for "all knowledge". It's not like Wikipedia gets any heavier if it has more pages.

The reasonable thing to do would be to add a "Proof" section to things needing a proof, with one link per proof (e.g. "Euclid's proof of the Pythagorean theorem", "Garfield's proof of the Pythagorean theorem") etc. If using the current Wikipedia system is not good enough for that (but I think it is), it should be easy to introduce a new standard "Proof layout" e.g. something like this:

Proof of the Pythagorean Theorem
 
There are various ways to prove the Pythagorean theorem. Some of them are listed here:
 
Name....................Discovered by......Discovered when..Comments
Euclid's Proof..........Euclid.............300 BC...........Uses only simple algebra
Rational Trigoniometry..Norman Wildberger..2000.............Requires trigoniometry
 
A comprehensive list of proofs of the Pythagorean theorem can be found in Foo's book "1001 proofs for the Pythagorean theorem"; since it was published in 1989, the most recent proofs are missing, notably the Rational Trigoniometry proof.

If something is not in Wikipedia, it is *still* possible to link to Mathworld or wherever else you like. "No mathematic proofs because some don't understand them" is like saying "No dates in history pages because some can't memorize them".

The problem is not kind of content, it is anger.

[Futurepower(R) (558542)]

"Should Wikipedia just become a textbook that teaches mathematics?"

Wikipedia should become whatever people want it to be. Who knows in advance what that is?

With the approval of the author of a well-known open-source program, I posted information about how to use the program. Next day that contribution was gone, removed by someone who said that Wikipedia should not become a place for software manuals. But my explanation was the clearest, most complete available at the time; the author of the software did not want to spend time re-writing his own manual.

The problem is not to decide which kinds of content to include in Wikipedia. Wikipedia does not have that problem of paper encyclopedias, paper and printing cost. More pages in Wikipedia are almost free. The only problem Wikipedia has with more content is organizing the content so that it is easy for the reader to make use of what he or she wants, and easy to ignore the rest.

The problem with Wikipedia is not with content, it is a social problem. There are many, many people with some kind of anger problem. Such people don't have many friends. But although they reject and discourage other people, they are still human and need to socialize. So, they spend time with open social groups like Wikipedia. They are there with the hidden and not-so-hidden purpose of having targets for their anger.

Angry people have plenty of free time because other people usually don't want to talk with them. Angry people have the time to dominate social groups, and destroy them. Wikipedia's problem is how to recognize angry, destructive contributors and how deal with their anger.

Re:proof should be most simple

[Watson Ladd (955755)]

Simple is very hard to define. For instance, the prime number theorem has an analytic and elementary proof. The elementary proof has many unmotivated steps that leave you scratching your head asking "why?". The analytic proof uses more complex concepts, but applies them in a more straightforwards manner.

Re:proof should be most simple

[RallyNick (577728)]

Why the hell not include ALL proofs that someone takes the time to type into Wikipedia? They're running low on hard drive space or what? And what's gonna be next, drop proofs from textbooks because they can't figure which one to include?

Re:proof should be most simple

[blind biker (1066130)]

How would you know there aren't enough experts checking a certain information? Of course, IF YOU DELETE IT then you made sure there isn't anyone reading it and checking it.

So if you have something like a mathematical proof, and noone modifies it, is that a sign that nobody understands it, or that it's correct? I would guess the latter, but even if not, I would not go on deleting it just because I sustepct something. Who am I to delete stuff that smarter people than me have written?

Or do you mean to say that the basis/policy on which Wikipedia works is admins who are ignorant about topic X will delete articles about topic X?

Re:Why the /?

[bradkittenbrink (608877)]

In my limited observation of the phenomenon, the consensus has generally been reached among mathematical WP editors that the proofs do not belong in the main article about the "Foo function", and they are often not notable as articles themselves (i.e. "Proof of the foo function" pages). As a result, attaching relevant proofs to an article as a subpage has become something of a pattern. I've seen it well done in some of the General Relativity articles (it functions nicely as a sort of appendix for the article where all of the relevant proofs are collected). Anyways, this problem has been solved before with dictionary definitions. (i.e. moved to http://wiktionary.org/ [wiktionary.org]) It seems to me like a similar solution would work here. In fact now that I look, it seems that someone has proposed such a project [wikimedia.org], although not targeted at solving this particular issue. It seems to have not gotten very far though.