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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?"
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 about the article for deletion. They voted to delete the article.
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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.
I used to have a better sig but it broke.
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.
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.
Inventions have long since reached their limit, and I see no hope for further development.-- Frontinus, 1st cent. AD
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
"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.
Hence the Memory Alpha wikia. Perhaps someone should create a Wikia for mathematical theorems and proofs?
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?
"The agriculture ministry is not in charge of Gundam" - Japanese ministry official.
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/) 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, although not targeted at solving this particular issue. It seems to have not gotten very far though.
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.
Even I don't understand wikipedia's articles on math sometimes.(and I have a degree in math) I had one of my professors tell the following joke...
"Wikipedia is proof that math majors can't find jobs."
Wikipedia articles on math/physics topics really need to develop a whole new format. One thing I would like to see is more casual articles on math topics. Sure, I can almost every popular mathematical proof on wikipedia....but wikipedia is a general knowledge database.
The proofs should DEFINITELY be on the same page, but a lot more care should be taken to make the articles more approachable. I used to use wikipedia in conjunction with my textbook...and several times I wound up preferring the textbook. This wasn't on instructional topics, but on rather general topics. The wikipedia article was simply to confusing, and too technical.
Basically, remember that wikipedia articles DO have an instructional quality. Most mathematicians aren't reading the wikipedia article on the "twin prime conjecture". Encyclopedia articles aren't written for people who know everything about the topic, they are written for people who need information.
**(BTW...this comment is written in the same manner as most of the articles. It has all the essential information, but in a very impractical format)**