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"How do we use this site anyway?"

... and other burning questions ...

Should your question not appear among the below, then feel free to put it on Help:Questions. We will try and answer within a reasonable amount of time.

General Questions

Where is the proof?!

"I just visited Fundamental Theorem of Calculus (insert your favourite page) expecting to see a proof of this important result. However, despite the theorem being split up into two parts, I didn't find a proof for either of them."

As you can see, each of the two parts has a section heading in blue - it is a link. These links take you to an appropriate sub-page of the main result (e.g. Fundamental Theorem of Calculus/First Part).
The proof(s) of this part of the whole theorem are gathered on this subpage. Similarly, when multiple proofs are present, the headings "Proof N" often are also links, to the sub-page containing only that particular proof.
In this way, every proof (and definition) can be unambiguously referenced internally. This is important, for example, when establishing certain definitions are equivalent - we wouldn't want the proof of that to depend on its result. Thus, there is seen to be a need to be able to refer to a particular proof of a theorem. --Lord_Farin (talk) 12:25, 26 January 2013 (UTC)

I don't like the notation

"On such-and-such a page I found that the notation did not match the style I prefer. So I changed it to the correct form, but then when I returned to the page, I found that my changes had been undone. Why is that?"

The world turns, life evolves, continents crumble to dust, and mathematicians occasionally devise notation which is considered an improvement over that which was originally invented.
It will forever be the case that there is more than one style of notation to illustrate a concept. The people who are familiar with notation A are going to complain if we use notation B, and those who grew up with notation B are going to be upset with our decision to use notation A. You can't please everyone.
Hence we choose a particular style, and we insist that all pages adhere to that particular style. This causes controversy, as followers of a particular symbol which has been turned down in favour of another, usually more modern, one which (in general) is less prone to ambiguity are going to be more or less offended.
If you believe that your preferred notation for a particular concept is superior to that which we have chosen, please feel free to communicate your reasons. However, please note that we ourselves at $\mathsf{Pr} \infty \mathsf{fWiki}$ often have good reasons for choosing a particular aspect of the house style of notation (in particular, we take care to select a notation which is first and foremost unambiguous). It is time-consuming and tedious to change, so unless there are good reasons to do so, we would prefer not. --prime mover (talk) 20:11, 30 December 2012 (UTC)

What's the point of the Mathematicians page?

"The name of this wiki is ProofWiki. Thus I wonder if it is really necessary for this wiki to take on a huge historical task? Does it have a realistic chance to do a good job? At this moment the lists are far from complete, but it is hard to expect good results. Others are doing it already. Perhaps any historian can support other, more history oriented projects. It'll be hard to outdo them anyway."

A good question to which the only answer is "because I like it." If you really want the mathematicians page to be removed because it doesn't suit your idea of what this site ought to be, or that you want me to stop wasting my time on it and concentrate on what you think I ought to be working on (please provide a work schedule that you wish me to adhere to), you'll have to pry it from my cold dead hands. --prime mover (talk) 06:51, 20 December 2012 (UTC)

I sent you an email but you didn't respond in a timely manner

Although in the "Welcome" message on a new user page it says ""if you have any questions please feel free to contact one of the administrators", for matters of site content it is best not to use the "Email this user" tool, as then the following will happen:

  1. there is no record of your message on $\mathsf{Pr} \infty \mathsf{fWiki}$ itself, which means nobody else can get the benefit of your question
  2. it may not get answered as external factors can affect the reliability of response
  3. nobody else in the $\mathsf{Pr} \infty \mathsf{fWiki}$ community is able to contribute towards a cogent answer to your question.

It is best to raise questions about the site itself within $\mathsf{Pr} \infty \mathsf{fWiki}$ itself, either on a talk page relevant to your question, or (at last resort, if for some reason you need to discuss a particular point of issue with a specific user) on the user's talk page itself. --prime mover (talk) 05:12, 3 July 2013 (UTC)

Questions about Contributions

You undid my corrections

"I read such-and-such a proof and didn't like it much. I had a better one, so I removed the existing rubbish proof and put my better one in place. I went back next day to admire my work but found it had gone, and the old proof was back in place."

Whether or not you like a particular proof or not is of zero relevance. The fact is: it's a proof, and (at least believed by its author) it's valid. What we do on this site is allow multiple proofs for any given theorem. So, rather than replace the existing proof with your own proof, add your new proof as an additional proof to the one that is already up there.
There are quite a few pages up now which do have more than one proof. An excellent example of this is found at Real Numbers are Uncountable. What we do is put each separate proof into its own subpage which is then transcluded into the main page.
Basically, deleting stuff is rude. If you have objections about something on a particular page, then feel free to raise it as a topic on the associated talk page. It is possible the person posting it up may just have made a mistake. --prime mover (talk) 07:46, 20 December 2012 (UTC)

Why do we need \left and \right with every pair of parentheses?

"Do we really need to put \left({ ... }\right) for every parenthesis, even things like $\sin(2x)$ and $(2n)!$? Out of curiosity, what difference does the extra curly inside \left(...\right) make? It seems to display the same."

The curly braces are grouping indications for $\TeX$; they serve to ensure that every \left is paired with the intended \right. Especially when using an external editor (e.g. via the Firefox plug-in It's all text) that highlights matching braces, such can greatly simplify the frustrating search for an occasional omitted or excess brace.
We enforce it to avoid problems with copy-pasting and subsequent editing of stuff inside parentheses. In this way, the parentheses will always size appropriate to their content, even if that content vertically grows or shrinks due to changes.
Equation references like $(1)$ and $(3′)$ are excepted from this admittedly strict style rule. --Lord_Farin (talk) 17:57, 13 December 2012 (UTC)
UPDATE: This has now been more or less superseded by the new custom $\LaTeX$ commands which have recently been added. Please consult Symbols:LaTeX Commands/ProofWiki Specific for an idea of the sort of thing we are moving towards, for example: $\map f x$ is now generated using \map f x, and $\tuple {a, b, c}$ by \tuple {a, b, c}, and so on.

Why a sentence on each line?

"I wrote a perfectly good dissertation, but then someone has come along and broken it up into simple kindergarten-level "the cat sat on the mat" style sentences, one on each line. This makes it look like a baby's first reader."

It makes it easier to follow a proof.
This is one of the more rigidly-enforced stylistic practices. Information is assimilated more easily if the flow of the argument is broken up into well-defined steps. In text books this practice is rarely seen, because that would increase the physical size of the book and the amount of paper it is printed on, hence the cost. This is why logical arguments in printed texts can be hard to follow.
On a website, there is no need to save space in this way. Therefore, we don't. We spread out the argument so it is as clear as possible.
(Little feedback has been received from the outside as to whether this approach has made the learning of mathematics in general easier as a result, but it may be worth setting up as a research project for anyone with a postgraduate degree to complete and a total lack of inspiration as to what to base the dissertation on.) --prime mover (talk) 10:51, 21 December 2012 (UTC)

Why the extra blank line?

"I did an edit on a section of one of the pages, then after I'd done so, someone else came in and edited the page just to add an extra blank line at the end of the section. Isn't that a bit pointlessly silly?"

The house style is such that the sections on the pages are spread out more than usual. This is a deliberate design decision: research has shown that information is taken from a webpage with greater ease when it is spread out more widely than it is on printed material. I have no intention of searching for documentary info on the web to back this up - it's just something I learned when I had an involvement in professional web design.
To that end, two blank lines are inserted in every page (with a few specialised exceptions where breaking the rule improves the presentation) at the end of every section before the next (sub)header. This needs to be done deliberately by hand.
Unfortunately MediaWiki software, when you edit an individual section, not the full page, removes any extra blank lines at the end of that section, making it necessary to go back and edit that whole page again to add the line it removed.
As a consequence, editing an individual section of a page is discouraged. It should not matter too much, because the policy of this site is to keep pages small. There are few pages over ten thousand characters, and many of those have been flagged as candidates for refactoring anyway. --prime mover (talk) 10:51, 21 December 2012 (UTC)

Why bother to keep all those useless redirects?

"The name of such-and-such page has been changed from something that wasn't very meaningful to something that makes a lot more sense. But you're keeping the not-so-meaningful redirect. Why not just delete it and tidy up the site?"

Before a page is deleted, you need to make sure all the pages which link to it have their links changed to point to the new page. Otherwise you break the links. An easy way to do this is to select the link "What links here" in the Toolbox section in the menu bar down the left. Only when every page linking to this old unwanted redirect page has been so amended, and only then, is it okay to delete the page.
BUT: Even then, there may be external websites which may (however misguidedly) have a link to that page themselves. If this is the case, then their link to $\mathsf{Pr} \infty \mathsf{fWiki}$ will be gone. And that is a Bad Thing.
If the page being renamed is new, however (for example, you just wrote it then noticed a spello in the title), then (after the renaming) it is usual for that particular redirect to be deleted, as there has been little opportunity for the page to have been noticed by the outside world and linked to. --prime mover (talk) 12:29, 21 December 2012 (UTC)
More recently we have taken to deleting the redirects, as soon as the pages linking to them have been appropriately redirected. So this FAQ is now of limited relevance.

What do you mean "sign your post"?

"I entered a comment on one of the talk pages, and I was told: "Please sign your post." What does that mean?"

The talk pages are where discussion is held of matters arising from the entry to which it is attached.
As these pages are for discussion, it is useful to have a record of who said what, and when they said it, and to be able to follow the conversation.
So, whenever you enter a post on a talk page (not one of the main pages: definition or proof), you are required to sign your post. This is done by pressing the button at the top of the edit pane which contains a logo that looks like a squiggle. It should be the third icon from the left, and if you hover over it, it will say "Signature and timestamp". What this will do is enter two hyphens followed by four tildes: --~~~~. When you save that page, it will replace the four tildes with your user "signature" and the date at which it was posted, like you see at the end of this paragraph. --prime mover (talk) 17:38, 27 December 2012 (UTC)

Why do you make such a fuss over the links in the "Sources" section?

"I moved one of the pages somewhere else and gave it a different name, then cleared out the original page and filled it with something else, then (etc. etc.) - and then you complained about me not having sorted out the citations? What's the point of that?"

In the "Sources" section, there is an attempt made for some of the sources to provide a path through the site which parallels the reading experience of that source. This flow is accomplished by means of "previous" and "next" links, which impose a strictly linear ordering of a subset of the site which corresponds to the path through those works.
If you change the name of these links, or copy a page complete with that link, this flow will be compromised, and it may no longer be possible to perform that reading experience.
If you change the pages such so that flow may have become compromised, then at the very least put an invocation of the {{SourceReview}} template into the "Sources" section of the page to indicate such. --prime mover (talk) 09:04, 12 January 2013 (UTC)
Also note that if you copypaste a page with such a citation into a new page, then unless you can confirm that the new page corresponds to material in the source work cited, then it is important to remove that citation. If the new page does correspond to material in the source work, then you are encouraged either to amend the links that define the source flow (remember to do that on the pages before and after the page in question), or to invoke the {{SourceReview}} template to alert the maintenance team that there is work to do. --prime mover (talk) 09:15, 26 November 2015 (UTC)

How can I learn how to refactor if you don't allow me to refactor?

As a new contributor looking for something to work on, it can be discouraging to see that the majority of undergraduate mathematics has already been conquered. As a result, it is tempting to plunge into the considerable task of tidying up what already exists.
One of these tasks is "refactoring". This is a blanket term which encompasses the ongoing task to split existing pages with many subsections into a series of smaller pages which are then transcluded into the main page from which the subpages are extracted.
While on the surface this looks like a straightforward task, there is more to it than just extracting a section, putting it into a new page and then transcluding that subpage in. For example:
  1. The new page needs to be standalone. Thus, if a page with "Proof 1" and "Proof 2" is being refactored, it is not sufficient just to extract those two proofs – you also need to extract the statement of the theorem itself and place it at the top of the page. The proof itself is then braced within "onlyinclude" tags so as to ensure that only the proof is transcluded into the master page.
  2. At the bottom of many pages are citations of source references. (See above.) These need to be attended to. While it is easy to extract the sections and blindly copy these link sections into the new page, this compromises the linear flow of those works.
Because of this, it is considered that refactoring is a task best left to experienced editors. By "experienced", we specifically mean "experienced in $\mathsf{Pr} \infty \mathsf{fWiki}$". While it is appreciated that many contributors come to $\mathsf{Pr} \infty \mathsf{fWiki}$ from other wiki sites (often Wikipedia), the philosophy of $\mathsf{Pr} \infty \mathsf{fWiki}$ differs from that site significantly. To put it bluntly: anyone can post up mathematics on a website – it's easy. The more challenging aspects are to achieve a consistent style and to ensure a high level of rigor in the context of cross-linking.
The recommended technique for learning how $\mathsf{Pr} \infty \mathsf{fWiki}$ is structured is to spend some time and effort in exploring it, to see how pages are structured and to get a feel for how code is styled, in particular with reference to the house style. One will also take note of what amendments have been made to pages one has built oneself (with particular reference to the maintenance tags which may have also been added to such pages).
It should be accepted that in the early days of your involvement, you may find a multitude of amendments made to pages you have added. This is understandable, and will result in you adjusting your style so as to match the house standard. As contributors are by definition mathematicians, or at least mathematically literate and motivated, it is taken for granted that they have the ability to learn well, and to teach themselves by example.[1]
If it is apparent that a particular user has not yet taken the time either to learn the house style or to philosophically accept it, then that user is respectfully requested not to embark on refactoring tasks. --prime mover (talk) 10:11, 7 July 2013 (UTC)

Questions about House Conventions

Definition or Statement of Equivalence

"Some concepts have many Definition pages: Definition 1, Definition 2, and so on.

Other concepts have few such pages, but instead implement a number of theorem-and-proof pages demonstrating that the concept is logically equivalent to another form of the concept, but do not actually express that other form as a definition.

Why are some logical equivalences implemented on $\mathsf{Pr} \infty \mathsf{fWiki}$ as actual alternative definitions, whereas others merely as a theorem-and-proof page?"

There are often many ways you can express a concept in an equivalent way. However, not all of these are "useful" as definitions, as such.
That is, in order to demonstrate that an object is an instance of a particular concept, it may be difficult, tedious or unwieldy to manipulate such an object into a form such that it can be used as a definition.
There can never be a consensus based on an intuitive "feel" for whether such a definition is suboptimally useful, so in order to decide whether to instantiate as a definition or an equivalence proof, we use the criterion:
Can this concept be found in a hard copy of a source work in this specific form?
If so, then implement it as a definition.
If not, then implement it as an equivalence theorem.
It is of course to be noted that if you do implement such a concept as a definition, then it is essential that there be an independent proof that this definition is equivalent to every other definition in the group of existing definitions to the concept.
That can of course be done by showing that it is equivalent to just one of those definitions, as there will already be such an equivalence proof demonstrating the existing definitions are all equivalent.

--prime mover (talk) 07:59, 23 June 2022 (UTC)

Technical Questions

Problem with Eqn template

"I've added a proof sequence using the {{eqn}} template, and despite my best efforts the parser barfs on it. It makes a horrendous mess that I can't work out how to clear up."

What's probably happened is that you have included instances of {{ or }} or | in your $\LaTeX$.
The MediaWiki template parser takes precedence over the MathJax one, and views {{ and }} as the beginning and end of the invocation of {{eqn}}, thus breaking the $\LaTeX$ in two. Similarly, it interprets | as the MediaWiki instruction to interpret what follows as a parameter value.
In order to get round this, you need to:
  1. Put a conventional space between all instances of {{ and }} to make them { { and } }
  2. Replace all instances of:
    1. | with \vert
    2. || and \| with \Vert, which renders as $\Vert$.
--prime mover (talk) 08:58, 8 March 2013 (UTC)

Can't get a maintenance template to register my parameter

"I am trying to (for example) get the "explain" template to show:

{{explain|Why does $a = b$?}}

... but when it appears on the page, the "Why does $a = b$?" bit does not show."

This is because the MediaWiki template parser takes precedence over the MathJax one, and interprets your $=$ sign as being part of a parameter invocation. That is, it thinks that Why does $a is the name of the parameter being passed to the {{Explain}} template and that b$? is its value.
In order to get round this, the {{=}} template was developed, which allows you to put the $=$ sign into an invocation of the template, like so:
{{explain|Why does $a {{=}} b$?}}
This should fix it.
--prime mover (talk) 08:58, 8 March 2013 (UTC)


  1. Once, at a formal evening attended by half a dozen logicians and mathematicians, one of the latter ventured the opinion that to become a good mathematician you should not have good teachers, as they prevented you from learning by yourself. He then added, courteously, "I was lucky. I had only one great teacher — Dr. Kasner here." Kasner looked up; his eyes twinkled; he said, mildly, "I had none."
    From the introduction to The Mathematical Magpie, edited by Clifton Fadiman.