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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.
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.
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
That's about it ... they must have gotten sick of webcomics.
I don't see why anyone besides the occasional Wikipedia purist of sorts would actually complain about this. It's convenient for proofs to be on there, and it's not like accurate information is degrading Wikipedia's "standards" at all.
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*.
Speaking as a postgraduate mathematician, it's clear that many people have made an effort with the mathematics articles, but they're almost always waffly. Mathematics is about the beauty of patterns, not a thousand cooks tweaking a proof to highlight their own difficulty or misunderstanding. It might be a good place for a paedagogical commentary on proofs - indeed, unbiased commentary on original research is precisely what an encyclopedia should be. It's not a place to post what is essentially the research itself, and then edit it out of all recognisability.
(Unfortunately, I don't feel Wikipedia comes close to that. But since you're asking...)
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.
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.
They should have links to each mathematical symbol to explain what the symbol means in the current case... Trained Mathematicians are use to seeing this symbols and use them in their current focus. But the symbol can mean different things for different forms of Math. For example Pi in geometry is roughly the number 3.1415926535.... in statistics it is its own function, completely unrelated to the geometry pi.
Mathematicians seem happy to officiate their ideas so only Mathematicians can read them and leave the common man out of the loop, making math look that much harder and scarier. If wikipeadia took an approach of helping people understand the proofs vs. then just giving them but allowing someone to understand it, even on the more basic levels such as clicking on the Uppercase Sigma (looks like a big E) it should bring you to the link on summation.
Math is not actually hard it just has been formalized over thousands of years by Mathematicians to make sure their jobs stay relevant, keep the common man out of the study, and little work has been placed to opening up math for the common folk. Wikipedia has a great opportunity to break down this class structure and allow someone say in high school to lookup a College Level Proof and in time following links get a basic understanding of the proof and able to work it out. But as for the example wikipedia gave as a High School student or a college with a non math focused major it would be literarily all greek to me. And look it up I wouldn't know where to go next... Like knowing the Big E is actually sigma, If I would have guessed I would say it was an Epsilon Shaped like an E Epsilon logical connection huh...
I am actually quite tired of the "Dumbing Down" excuse to fix problems in education that are classically created complex just because some nobles wanted to seem special. Dumbing Down is saying just take this as fact and get the next step. What we can do is open up math so people can understand the details in language they understand or can jump into without having to be formally taught all the prerequisites.
Simplification is not Dumbing Down, but to dumb things down you need to simplify things. The Ven Diagram would be a Big Circle Labeled Simplification the little circle will be labeled Dumbing Down.
If something is so important that you feel the need to post it on the internet... It probably isn't that important.
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
Wikipedia has policies and guidelines for this. Include it if it's notable, and not original research, etc.
Patrick Doyle
I mod down every jackass who puts his moderation policy in his sig. Oh, wait a sec....
Err...what is the argument for _not_ including proofs? I can't come up with any good reason for that...
Please correct me if I got my facts wrong.
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
While I am sure that it is easy to argue that proofs should be included (I don't really mind either way), as a Wikipedia administrator I know that one of the hardest things to do is to find a source for something, especially something as specific as a proof. I don't mind the extra information that a proof provides, but it is a manhole up from which crackpot theories may crawl, looking more authoritative because they have a mathematical proof which might not even be valid.
The problem is verification, that editors are not violating the policy against original research (another barrier to crackpot theories). The idea of verification in Wikipedia is that if you look something up in Wikipedia, you should be able to find it elsewhere - and Wikipedia should provide a citation of that source to make it easy to check.
As long as they can be cited to some particular source, and don't otherwise disrupt the flow of the articles to which they are added, I think proofs are fine - there's no reason I can think of to exclude them. If they are used randomly or someone makes up their own proof, however, that is unverifiable original research that is much more likely to lead to errors.
I don't want to exclude information - I want the information there to be reliable.
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!
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.
"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".
"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.
I agree with the parent--I don't see any reason not to include any proofs that people care to submit (as long as they actually are proofs--i.e. aren't fallacious or invalid). Different kinds of proofs are good for different kinds of things. Some proofs provide elegant verification of the result in question (I find many proofs by induction to be of this variety), while others tend to be much more explanatory in character--they can help us "see" why the result has to be the case. These categories are neither exclusive nor exhaustive, but it is often the case that the best explanatory proof is not the best justificatory proof and vice versa.
Another, particular-to-wikipedia, problem is what results one should take as previously proven in presenting proofs on Wikipedia. Strictly speaking, you can't offer proof of something if your proof depends on unproven results. Most textbooks can easily avoid this problem since they (the textbook editors), of course, have complete control over what results are proven in the text. This isn't a problem for justification of results, since no one is using Wikipedia as a platform for proving new theorems (as far as I know anyway), but it could make it more difficult for offered proofs to be helpful, since they may depend on results which themselves are not proved in wikipedia.
Allow them. Period. Otherwise you set up circumstances for vandals to thrive like they do around all other ambiguous rules. Put another way, if there are any rules specifying when you can delete proof, I guaran-frickin-tee that some kid will use them to remove articles about the four-color theorem and Godel's incompleteness theorem. They'll claim that they're doing it for nebulous purity reasons; that's just because you won't be able to see their smug little grins as they exercise their power.
The last think Wikipedia needs to do is give the Deletionists more ammunition. They're pissing off enough people as it is.
Dewey, what part of this looks like authorities should be involved?
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
Yea I agree, though perhaps the longer/more complicated proofs belong in Wikibooks.
I am a Physics undergrad student (so IAAP :P), and I've found Wikipedia to be an excellent source for mathematical information. The reason for this is the depth of information available. If, for example, I've forgotten a certain equation, my first port of call is Wikipedia:
The first section usually gives a concise overview.
The second gives the equations.
The third gives the derivation.
This is exactly what Wikipedia should be, in my opinion. I can get as much or as little information as I require, and I can't see any reason for intentionally removing or leaving out relevant data. I'm all for keeping articles free from pointless clutter, but derivations aren't pointless.
I thought Wikipedia was about "Free Access To All Human Knowledge", not "Free Access To A Good Percentage of Quite a Lot of Human Knowledge, But Some Things You'll Just Have To Accept, OK?".
One of the problems with Wiki's math content is that too much of it is not acessible to someone who is looking up a concept out of the blue or landed on the article randomly. Heavy use of math notation is one of the reasons for this - it tempts authors to create what is technically a complete treatment of the topic but does not have sufficient plain-language content to be meaningful to non-experts.
I am by no means arguing for dumbing down of content, but it's important that at least the first few paragraphs avoid relying on heavy use of math notation in favor of giving a casual user an idea of (1) the gist of the math concept (2) why it's important and (3) some basic uses or a simple example.
The question of whether proofs should be allowed in Wiki depends on discipline of the average math author. Can they avoid the temptation of making the proof be the article? If they can, then there's nothing wrong with supplementing an already-good article with the proof. But if it's impossible to glean anything from the article other than by stepping through the proof - then the article is crap and the proof is what enabled the author to think he was done.
Perhaps there should be a separate sister site that housed proofs which are linked to from the main articles. I think that's probably the best idea - keeping the article meaningful to non-experts - and allowing those who care to "drill down".
-e
http://ed.markovich.googlepages.com
Absolutely! What's the big deal with admins deleting stuff from Wikipedia? Need to manage something?
Wikipedia is oraganized knowledge in electronic form. It's electronic, so there's no "wasted paper", and it's organized, so it proves taht a large amount of knowledge can be organized - and so also a large amount of knowledge within one article.
I am afraid that, if Wikipedia admins persist on deleting stuff they don't like (because that's the only objective measure they have, they didn't go asking anyone if what they are going to delete is useful to them), they risk alienating contributors, which are the pillars on which Wikipedia exists.
"The agriculture ministry is not in charge of Gundam" - Japanese ministry official.
But the basic principle, that the Wikipedia should host as many proofs as anyone cares to type up, seems basically right. Of course, all of it should be in MathML!
An "encyclopedic" web site that explains what the Sword of a Thousand Truths is http://en.wikipedia.org/wiki/Make_Love,_Not_Warcraft could use a little hard mathematics for balance, in my opinion.
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 a parent post said, it may not be wise to do so as it blurs the purpose of Wikipedia. If I were involved in Wikimedia, I'd create a wiki solely to hold proofs and explanations, and reference them from the Wikipedia article.
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.
"Wikipedia is not a venue for publishing, publicizing or promoting original research." Either a proof is published elsewhere, in which case it should be referenced, or it has not, in which case it is original research, and should not be on Wikipedia.
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.
"The use-mention distinction" is not "enforced here."
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)**
Computer science features empirical experimentation as well as mathematical rigor, making it a "true" science. Science and its relation to engineering has nothing to do with it. It's that simple.
After all, I am strangely colored.
The issue is real. How much depth should Wikipedia, as an encyclopedia, provide before one should seek-out more specialised sources. An encyclopedia entry on Albert Einstein might take up two or three pages. (I haven't checked Wiki's entry on Einstein). You could fill a library with books and papers about Einstein. It is not reasonable or useful for all this information to be provided comprehensively on Wiki. Most readers would be overwhelmed. Mathematical proofs to my mind are several levels down (or up) the knowledge chain in the realm of more specialised information requiring more specialised treatment