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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?"
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.
They're obvious academic knowledge with clear educational merit. Where exactly is the problem?
Dealing with lawyers would be a lot less tedious if they all looked like Casey Novak.
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.
Windows in 6 Bytes (IA-32) : 90 90 90 90 CD 19
I hate reading math symbols in anything but latex generated documents
No problem for you then: Wikipedia's math content is exactly that.
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*.
Lemme see if I got this right: posting absolute truths on Wikipedia is up for debate?
"There is much pleasure to be gained from useless knowledge." - Bertrand Russell.
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.
This is my sig.
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.
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.
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
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?
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....
I am the man with no sig!
"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: 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".
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. 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 deletion debate 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 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 and here. 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 could exist then why not have unsolved problems in biology. 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
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.
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 offers a place for some book-like-stuff (and I think mathematical proofs belong there). There are also other projects for different kind of information, like learning materials and dictionaries. We should start to transfer Wikipedia's success to other free wikis and projects.
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.