This page is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
This is an encyclopedia, not a collection of math texts; but we often want to include proofs, as a way of really exposing the meaning of some theorem, definition, etc. A downside of including proofs is that they may interrupt the flow of the article, whose goal is usually expository. Use your judgement; as a rule of thumb, include proofs when they are part of an explanation; don't include them when they are a justification whose conclusion is merely "... therefore, P is true".
Since many readers will want to skip proofs, it is a good idea to set them apart in some way, for instance by giving them a separate section.
Actually. I would say, just write proofs as normal prose in English. I'm not in favour of importing conventions from mathematics textbooks here as a rule. If that means WP has more descriptions of proofs than actual proofs, so much the better; textbooks exist, but mostly they are not so good at giving thumbnails of proofs to give access to non-specialists. So basically I disagree with the initial comment. I would certainly prefer to have the Wilson's theorem proof described loosely as 'by pairing residues with their modular inverses ...'. Also it is misleading to imply anything about the date of such a proof. Charles Matthews 08:35, 17 Nov 2004 (UTC)
I'd like to present a contrarian view. As wikipedia develops, it will de-facto become more detailed and, as a side-effect, more authoritative. This is unavoidable; more readers will beget more authors, and it will grow. We don't yet know how far, or what will cause it to stop growing. As it becomes more authoritative (and this is truly unavoidable), the question will come up: How can I trust that what is written here is accurate? The current mechanism, involving watchlists and maintainers, is adequate for insuring the accuracy of WP, in most cases, for the most part. However, its worth asking what steps can be taken to take WP to the next level, and whether these should be taken.
I see proofs and citations as a valid and effective mechanism that can be used to maintain and improve accuracy. Now, let me make clear one critically important point: I think almost all such proofs should be out-of-line, in their own separate articles. The references to such proofs should almost always bee teeny, tiny foot-note like bullets. Also, let me make clear: proof is maybe too strong a word. A demonstration might be a better term. A bit of twiddling to show how a formula in an article was derived. Let me not be vague: lets take a look at some examples -- these are from PlanetMath --
The first two might have some marginal utility in WP. If there had been something like this for the Fourier transform, maybe some of the recent controversy about possible, misinterpreted, well-meaning vandalism might have been avoided. See this talk page. But these kinds of demonstrations should not be prominent in the article in any way.
The second two could arguably be merged with the article on Bohr-Mollerup, but might also sit more elegantly on their own.
If you accept this contrarian viewpoint, then what I want to know is: what is the manual of style, how should we put a ticky-mark/footnote on a formula to indicate that there is a proof/demonstration on some other page? May as well establish a convention for this now. One a related topic, I'd like to know how to mark up a single formula with a specific book (or online) reference for that one formula.
To conclude, WP will grow. Its unavoidable. It won't be an encyclopedia much longer; it will get much bigger and denser than that. It will subsume the contents of entire textbooks, it will become far more comprehensive than MathWorld. It already has done so in several areas. Neither you nor I can stop this evolution from "encyclopedia" to something vaster. I suggest only that the groundwork be laid so that there will be some uniformity of presentation. linas 03:20, 3 Apr 2005 (UTC)
Regarding proofs and accuracy: please note that reference works can contain errors as well. For example on 11 April 2005, a young college student made changes to the article Bessel function to bring it into line with a well-known and respected work, Numerical Recipies in C: The Art of Scientific Computing from Cornell. Unfortunately, this book is in error (a tiny error) in this particular case (it must have slipped past the proof-readers). I reverted the change, and provided discussion on the talk page. I believe that having a "proof page", as described below, could provide a more permanent and reliable repository for this correction, than the talk page could. linas 00:50, 28 Apr 2005 (UTC)
I tend to agree with linas's contrarian view.
After some discussion about whether certain formulas in an article were correct or not, and the proper means of deriving them, I was movitivated to construct a prototype experimental page demonstrating a "proof" for a claim made in an article. The goal of this page is as discussed above: to provide support for claims, without cluttering the main article itself. To see this in action, please visit the article Laplace operator (as of april 27 2005). About 2/3rds of the way down will be a formula, and to the right of the formula, in some smaller letters, a link (proof) which will take you to an article Laplace operator/Proofs which will provide the detail for the claim.
The current standing proposal is to put all article proofs into a /Proofs subdirectory, so that any such secondary, supporting material always ends up in the same location for any article, and is thus easy to find. However, this is appearently a controversial area within WP, see Wikipedia:Subpages.
I request the community to play a bit with the concept and the layout: How does it feel? Can we make this work? Can we get (proof) to sit to the far-right of the formula somehow? Replace it with a cute icon or a macro of some kind? What about the proof page itself? What should the "house style" be? Will we be able to keep proof pages from morphing into full-blown articles? Or will they morph into some other ugly beast? Give it a shot. linas 00:15, 28 Apr 2005 (UTC)
A list of all such "proof" pages can now be found at Category:Article proofs. There is a template, {{proof|Article name}}, that adds boilerplate to such pages. linas 01:29, 4 August 2005 (UTC)
I can't say I agree with the concept of cardioid article proofs. The kind of proofs that don't belong in a main article are potentially those we don't need ...
Charles Matthews 16:32, 18 May 2005 (UTC)
Wow! I think MarSch's edits to the cardiod proof makes it clear that User:AugPi actually struggled to find the proof, and his struggle/battle thus made him think that it was worthy of inclusion in WP. I can only conclude that a short, simple, clear proof such as MarSch's is exactly the sort of thing that can open doors for a certain class of readers. linas 05:33, 20 May 2005 (UTC)
I am a frequent user of the mathematical articles on Wikipedia, and I believe that at least a link to a proof adds to the usefulness and authority of wikipedia. After all, articles in other areas commonly provide links or references to their sources, so why not for mathematics?
Where to place the proof is a problem, the options seem to be:
Linking to proofs on external sites obviously has its problems (such as lack of control), but i reckon options 2 and 3 could be useful, in particular I believe wikisource would be an appropriate place for proofs. - 3mta3 03:26, 20 July 2005 (UTC)
The French Wikipedia has an elegant answer for this problem, in the form of a box which you can click to unroll/close up an optional section. The template's called fr:Modèle:Boîte déroulante and you can see it in action at such pages as fr:À la croisée des mondes (click "dérouler") on the right-hand side). I believe it's sufficiently magical that we can't just copy the template code—it needs some kind of stylesheet upgrade for it to work—but it does seem like an ideal solution. — Blotwell 08:54, 29 August 2005 (UTC)
This page is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
This is an encyclopedia, not a collection of math texts; but we often want to include proofs, as a way of really exposing the meaning of some theorem, definition, etc. A downside of including proofs is that they may interrupt the flow of the article, whose goal is usually expository. Use your judgement; as a rule of thumb, include proofs when they are part of an explanation; don't include them when they are a justification whose conclusion is merely "... therefore, P is true".
Since many readers will want to skip proofs, it is a good idea to set them apart in some way, for instance by giving them a separate section.
Actually. I would say, just write proofs as normal prose in English. I'm not in favour of importing conventions from mathematics textbooks here as a rule. If that means WP has more descriptions of proofs than actual proofs, so much the better; textbooks exist, but mostly they are not so good at giving thumbnails of proofs to give access to non-specialists. So basically I disagree with the initial comment. I would certainly prefer to have the Wilson's theorem proof described loosely as 'by pairing residues with their modular inverses ...'. Also it is misleading to imply anything about the date of such a proof. Charles Matthews 08:35, 17 Nov 2004 (UTC)
I'd like to present a contrarian view. As wikipedia develops, it will de-facto become more detailed and, as a side-effect, more authoritative. This is unavoidable; more readers will beget more authors, and it will grow. We don't yet know how far, or what will cause it to stop growing. As it becomes more authoritative (and this is truly unavoidable), the question will come up: How can I trust that what is written here is accurate? The current mechanism, involving watchlists and maintainers, is adequate for insuring the accuracy of WP, in most cases, for the most part. However, its worth asking what steps can be taken to take WP to the next level, and whether these should be taken.
I see proofs and citations as a valid and effective mechanism that can be used to maintain and improve accuracy. Now, let me make clear one critically important point: I think almost all such proofs should be out-of-line, in their own separate articles. The references to such proofs should almost always bee teeny, tiny foot-note like bullets. Also, let me make clear: proof is maybe too strong a word. A demonstration might be a better term. A bit of twiddling to show how a formula in an article was derived. Let me not be vague: lets take a look at some examples -- these are from PlanetMath --
The first two might have some marginal utility in WP. If there had been something like this for the Fourier transform, maybe some of the recent controversy about possible, misinterpreted, well-meaning vandalism might have been avoided. See this talk page. But these kinds of demonstrations should not be prominent in the article in any way.
The second two could arguably be merged with the article on Bohr-Mollerup, but might also sit more elegantly on their own.
If you accept this contrarian viewpoint, then what I want to know is: what is the manual of style, how should we put a ticky-mark/footnote on a formula to indicate that there is a proof/demonstration on some other page? May as well establish a convention for this now. One a related topic, I'd like to know how to mark up a single formula with a specific book (or online) reference for that one formula.
To conclude, WP will grow. Its unavoidable. It won't be an encyclopedia much longer; it will get much bigger and denser than that. It will subsume the contents of entire textbooks, it will become far more comprehensive than MathWorld. It already has done so in several areas. Neither you nor I can stop this evolution from "encyclopedia" to something vaster. I suggest only that the groundwork be laid so that there will be some uniformity of presentation. linas 03:20, 3 Apr 2005 (UTC)
Regarding proofs and accuracy: please note that reference works can contain errors as well. For example on 11 April 2005, a young college student made changes to the article Bessel function to bring it into line with a well-known and respected work, Numerical Recipies in C: The Art of Scientific Computing from Cornell. Unfortunately, this book is in error (a tiny error) in this particular case (it must have slipped past the proof-readers). I reverted the change, and provided discussion on the talk page. I believe that having a "proof page", as described below, could provide a more permanent and reliable repository for this correction, than the talk page could. linas 00:50, 28 Apr 2005 (UTC)
I tend to agree with linas's contrarian view.
After some discussion about whether certain formulas in an article were correct or not, and the proper means of deriving them, I was movitivated to construct a prototype experimental page demonstrating a "proof" for a claim made in an article. The goal of this page is as discussed above: to provide support for claims, without cluttering the main article itself. To see this in action, please visit the article Laplace operator (as of april 27 2005). About 2/3rds of the way down will be a formula, and to the right of the formula, in some smaller letters, a link (proof) which will take you to an article Laplace operator/Proofs which will provide the detail for the claim.
The current standing proposal is to put all article proofs into a /Proofs subdirectory, so that any such secondary, supporting material always ends up in the same location for any article, and is thus easy to find. However, this is appearently a controversial area within WP, see Wikipedia:Subpages.
I request the community to play a bit with the concept and the layout: How does it feel? Can we make this work? Can we get (proof) to sit to the far-right of the formula somehow? Replace it with a cute icon or a macro of some kind? What about the proof page itself? What should the "house style" be? Will we be able to keep proof pages from morphing into full-blown articles? Or will they morph into some other ugly beast? Give it a shot. linas 00:15, 28 Apr 2005 (UTC)
A list of all such "proof" pages can now be found at Category:Article proofs. There is a template, {{proof|Article name}}, that adds boilerplate to such pages. linas 01:29, 4 August 2005 (UTC)
I can't say I agree with the concept of cardioid article proofs. The kind of proofs that don't belong in a main article are potentially those we don't need ...
Charles Matthews 16:32, 18 May 2005 (UTC)
Wow! I think MarSch's edits to the cardiod proof makes it clear that User:AugPi actually struggled to find the proof, and his struggle/battle thus made him think that it was worthy of inclusion in WP. I can only conclude that a short, simple, clear proof such as MarSch's is exactly the sort of thing that can open doors for a certain class of readers. linas 05:33, 20 May 2005 (UTC)
I am a frequent user of the mathematical articles on Wikipedia, and I believe that at least a link to a proof adds to the usefulness and authority of wikipedia. After all, articles in other areas commonly provide links or references to their sources, so why not for mathematics?
Where to place the proof is a problem, the options seem to be:
Linking to proofs on external sites obviously has its problems (such as lack of control), but i reckon options 2 and 3 could be useful, in particular I believe wikisource would be an appropriate place for proofs. - 3mta3 03:26, 20 July 2005 (UTC)
The French Wikipedia has an elegant answer for this problem, in the form of a box which you can click to unroll/close up an optional section. The template's called fr:Modèle:Boîte déroulante and you can see it in action at such pages as fr:À la croisée des mondes (click "dérouler") on the right-hand side). I believe it's sufficiently magical that we can't just copy the template code—it needs some kind of stylesheet upgrade for it to work—but it does seem like an ideal solution. — Blotwell 08:54, 29 August 2005 (UTC)