Talk:Mathematics/Archive 11

message: Note: This article has a small number of in-line citations for an article of its size and subject content. Currently it would not pass criteria 2b.
Members of the Wikipedia:WikiProject Good articles are in the process of doing a re-review of current Good Article listings to ensure compliance with the standards of the Good Article Criteria. (Discussion of the changes and re-review can be found here). A significant change to the GA criteria is the mandatory use of some sort of in-line citation (In accordance to WP:CITE) to be used in order for an article to pass the verification and reference criteria. It is recommended that the article's editors take a look at the inclusion of in-line citations as well as how the article stacks up against the rest of the Good Article criteria. GA reviewers will give you at least a week's time from the date of this notice to work on the in-line citations before doing a full re-review and deciding if the article still merits being considered a Good Article or would need to be de-listed. If you have any questions, please don't hesitate to contact us on the Good Article project talk page or you may contact me personally. On behalf of the Good Articles Project, I want to thank you for all the time and effort that you have put into working on this article and improving the overall quality of the Wikipedia project. Agne 05:52, 26 September 2006 (UTC)
replies: text: The requirements of GA are now converging rapidly on those for FA, thus making the whole idea worthless. Also no one cares about GAs. Soo 12:57, 26 September 2006 (UTC)
replies: text: This change in criteria have caused some upset, some discussion of relavance of inline cites in mathematics can be found at Wikipedia talk:WikiProject Good articles. On the Template:Grading scheme GA is seen as a step towards FA. I see article grading as an important process for the mathematics articles, as it helps us get an overview of where there are weeknesses in our coverage. Work on grading mathematics can be found at Wikipedia:WikiProject Mathematics/Wikipedia 1.0. --Salix alba (talk) 13:28, 26 September 2006 (UTC)
replies: text: I offer myself as a counterexample to Soo's "nobody cares" assertion.  I'll get to work on in-line citations right away. Rick Norwood 13:30, 26 September 2006 (UTC)
replies: text:  I also am happy to help. And as it happens, I like in-line citations :-) Stephen B Streater 19:07, 26 September 2006 (UTC)
replies: text:  If it matters, I disagree that this article doesn't have enough inline citations, it looks pretty good reference-wise to me. (And I mean good as in, you know, Good good.) Homestarmy 19:24, 26 September 2006 (UTC)

text: Nice to hear that we have some citation volunteers. As well as mathematics Georg Cantor, David Hilbert, Alan Turing, Calculus, Euclidean geometry, Homotopy groups of spheres, Nash equilibrium, Ordinal number, Polar coordinate system, Pythagorean theorem, Rubik's Cube, (in fact all the maths GA's) received the same message. --Salix alba (talk) 00:55, 27 September 2006 (UTC)
thread_title:  GA Re-Review and In-line citations 

message: :Here are definitions of mathematics from several sources:
:*"Yet as a science in the modern sense mathematics only emerges later, on Greek soil, in the fifth and fourth centuries B.C.", Richard Courant and Herbert Robbins, What is Mathematics?, 1941, p. xv.
:*Originally, the collective name for geometry, arithmetic, and certain physical sciences (as astronomy and optics) involving geometrical reasoning.
::In modern use applied,
:::(a) in a strict sense,
::::to the abstract science
::::which investigates deductively the conclusions implicit in the elementary conceptions of spatial and numerical relations, and which includes as its main divisions geometry, arithmetic, and algebra; and
:::(b) in a wider sense, so as to include
::::those branches of physical or other research which consist in
:::: the application of this abstract science to concrete data.
:::When the word is used in its wider sense,
:::the abstract science is distinguished as pure mathematics, and
:::its concrete applications (e.g. in astronomy, various branches of physics, the theory of probabilities)
:::as applied or mixed mathematics.
:::Oxford English Dictionary, 2nd Ed.
:*the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations Merriam-Webster Online Dictionary.
:*the branch of science concerned with number, quantity, and space, either as abstract ideas (pure mathematics) or as applied to physics, engineering, and other subjects (applied mathematics). Compact Oxford English Dictionary.
:*a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement WordNet 2.0, Princeton University, 2003.
:*Mathematics is a science. Encyclopaedia Britannica, 1911.
:*the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. Random House Unabridged Dictionary, 2006.
:*The study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols. American Heritage Dictionary, 4th Ed., 2000.
:I prefer study, because it embraces industrial, hobbyist, and academic mathematics.
:And it is easier to spell.
:--Jtir 16:21, 30 September 2006 (UTC)
thread_title: Definitions of mathematics from several sources

message: I left in the Jourdain footnote while editing the lead, but it is not at all clear what it is sourcing.
Can someone add a quote and page number? --Jtir 14:00, 2 October 2006 (UTC)
thread_title:  need a quote and page number from Jourdain 

message: Since I'm new to wikipedia I was wondering if there is any reason why the talk pages are so badly organized? I believe it is okay to create subpages of the talk page, so is it okay if I create a FAQ based on previous discussion and create subpages /lead and /Popper on math (to begin with) and gather all previous discussion from the archive on those pages? --Vesal 21:20, 3 October 2006 (UTC)
replies: text: I looked around a bit, and found totally different layouts on talk pages. It seems doing a FAQ is not a bad idea (WP:RTP), the example given is Talk:Mother Teresa/FAQ. Otherwise, I also like the Talk:Abortion style. --Vesal 21:41, 3 October 2006 (UTC)

text: I was thinking along similar lines.  I have collected numerous quotes and definitions that are getting buried in the main page.  It would be more convenient to reference them with a topical name.  Indeed it seems to me that any project that needs to collect evidence from research and organize it for convenient access would benefit from your approach. I have just finished typing in two more quotes from Courant & Robbins' classic "What is Mathematics?" that I was just about to put on the main page. Where would you suggest putting them? --Jtir 22:04, 3 October 2006 (UTC)
replies: text:  Some projects have a /Sources subpage, maybe that is a good place to just collect and classify sourced statements. As I understand, we are quite free to structure the talk pages the way we want. I will focus on summarizing what has currently been said in this discussion pages, because I need to read them anyway (damn, you guys write a lot :), this will take some time. --Vesal 22:30, 3 October 2006 (UTC)
replies: text: /sources must be sourced.  I completely agree.  ISTM that some subpages might be subdivided by editor. This would allow each editor to develop, for example, a "personal" list of The Important Theorems and Conjectures with sourcing and possibly with annotation. --Jtir 23:16, 3 October 2006 (UTC)
replies: text:  Yes I have even seen people develop articles in their User namespace, but I've always wondered how such stuff is merged. By the way, I started on the /Sources page, set up very strict rules, but the idea is to collect and classify not so much discuss them there... I still added some discussion space at the bottom. --Vesal 23:38, 3 October 2006 (UTC)

text: Looks fantastic! Were you going to create a link to the FAQ on the Talk page? Also, I find all those boxes at the top distracting and would prefer to see the TOC first. --Jtir 17:00, 4 October 2006 (UTC)
replies: text:  Yes, but I don't know where to put the link, I was thinking about having it at the bottom of the archive box... But, about those boxes, I think we could add another box (the skip to TOC box) to make it even more annoying for you :)  --Vesal 17:06, 4 October 2006 (UTC)

text: There is a distinction between the citation style the reader sees and what editors use to implement it. Readers see a slightly modified form of Harvard referencing. The editors implement them with the so-called "Cite.php footnote system", which employs the inline  tags.  Further, the  tag goes in the Notes section, not the References section.  Basically, the names don't match the uses. --Jtir 17:19, 4 October 2006 (UTC)
replies: text:  Ok, well I was primarily targetting the FAQ to would-be editors of this article. Other than that, I will fix the mismatches, unless you already have... --Vesal 17:39, 4 October 2006 (UTC)

text: The forward link to the TOC works for me.  How about putting the FAQ link at the top of the topical subpage list -- it's a topic too. :-) --Jtir 17:27, 4 October 2006 (UTC)
replies: text:  Now, why didn't I think of that????? Instead, I created a general topics section and it's getting to big, I'm thinking of moving the precedents in discussions section into the FAQ, because it makes more sense to first summarize it and then give the links. As a new user I'm too inclined to click on those precedent discussion links anyway, a FAQ however, might be something to look at. --Vesal 17:39, 4 October 2006 (UTC)
replies: text: OK, The FAQ! link works fine. Regular editors probably won't need it too often. --Jtir 17:45, 4 October 2006 (UTC)

text: Wait, it will take some time to do that, and I don't know exactly what the best solution is. But I think a FAQ with a short answer and then links to the topics in the archive is helpful. --Vesal 22:54, 5 October 2006 (UTC)
replies: text:  Well, anyway, I removed the link to the Lead paragraph subpage. I moved the dictionary defs to the Conceptions page for reference. I sort of lost motivation (or gained some perspective)... I no longer think the lead paragraph needs focus or discussion. Well, when there are no more mathematics related stubs, say in 10 years, I will turn back to it :) --Vesal 18:04, 9 October 2006 (UTC)
thread_title:  organization of talk page... 

message: Maybe this should be renamed or incorporated into a Philosophy of Mathematics section... Mathematics as Science is quite POV (actually my own POV), but there are a also a few more things that could be incorporated:
* Relationship between mathematics and physical reality... This is a very important issue and should not be tossed into the misconception section.
* Psychology of mathematics, i.e Numerical cognition. 
Very much in line with the todo list. --Vesal 23:27, 4 October 2006 (UTC)
replies: text: The subpage Talk:Mathematics/Conceptions of mathematics is intended to collect all of the dueling quotes. ATM it is stubs. --Jtir 12:19, 5 October 2006 (UTC)
replies: text: This section should be moved into a separate article. The mathematics article is an introduction to mathematics for the rest of the encyclopedia, not a treatise. A phrase like "experimentally falsifiable" cannot possibly be explained in an introduction. Popper and Lakatos are far too advanced for an introductory article.  There are already articles on Philosophy of mathematics and the Philosophy of science, where Popper and Lakatos could be discussed at the required technical level. --Jtir 12:48, 5 October 2006 (UTC)
replies: text:  Well, the nice thing with naming it Phiosophy of Mathematics, is that we could have a main article link to that page and briefly summarize the issues. However, issues about philosophy of math and psychology of mathematics, certainly need to be on this page! --Vesal 21:55, 5 October 2006 (UTC)

text: Yes, the math is not redicible to logic part is quite bad, but it is directly from Popper, see /Sources and the most important limitative results that he referse to are Tarski's indefinability theorem and Gödel's incompleteness theorem I believe... --Vesal 21:09, 5 October 2006 (UTC)

text: Good thing I put a disclaimer, I think I am wrong... Well, I'm certainly wrong about the views being similar to that of Popper, since Einstein's essay is from 1921. But it is a complex issue. Currently, we can leave it be, as I have changed the footnote already. On the other hand, we have now three references to the unreasonable effectiveness. --Vesal 22:22, 5 October 2006 (UTC)
thread_title:  Mathematics as Science, Philosophy of Mathematics 

message: I've written a sample gallery into the sandbox. The Picture_tutorial illustrates some other options. --Jtir 14:34, 6 October 2006 (UTC)
replies: text: Here is another sample. This one has a vertical format and is implemented with an infobox. Infoboxes are much more flexible than <gallery> tags. The Numerical analysis article uses infoboxes. The Fields of mathematics section would benefit from vertical layout of the images. The images could also be annotated more fully. --Jtir 19:13, 6 October 2006 (UTC)
thread_title:  sample gallery in sandbox 

message: Text alignment can be controlled.  I have centered some captions and left-aligned others. The alignment may need some tweaking. Further, they eliminate clutter -- namely the small resize icon that indicates the image is a thumbnail. In some cases the result has been a smaller box, which saves screen space. Also they support titles above the boxes if editors feel those would be desirable.
Another advantage to infoboxes is that images and captions can be stacked more densely, as this sandbox example shows.
User:Fredrik raised these issues (which I am paraphrasing):
#Using infoboxes is inconsistent.
#Infoboxes are complex.
#They interfere with custom style sheets.
*Actually, I was increasing consistency.
*I agree that they are more complex (I know, because I just got through trying to get them to display correctly and then tediously editing six of them without breaking anything.), but they also are more capable.
*I don't know if the last is true. However, most readers of the encyclopedia probably don't know how to edit custom stylesheets, so they deserve to see an attractive layout without them.
The six blocks of images illustrating fields of mathematics waste screen space at each side and have poor integration with the article.  What does a picture of Rubik's Cube captioned Abstract algebra tell a reader? Further, it is far more conventional to put that info along the sides.  Now they divide the article.
I converted the panel illustrating number systems into a vertical infobox and it looks fantastic.
Before, it was hard to see where one system ended and the next began.
* Now they are easy to see.
I rv'ed it when I realized that doing the same thing with the remaining panels would end up with panels running far past the text they are supposed to illustrate.  I like the images, but there are too many of them for side panels.  I am now thinking they might be better collected in a separate gallery section with more informative captions.
--Jtir 17:35, 7 October 2006 (UTC)
replies: text: Image syntax is easy to understand, and very logical.  Making all images into a table is just pointless.  And like above, even you say they look alike, and the image syntax has the advantage of working with custom style sheets.  Can you find any other articles that use this infobox structure instead of the image syntax? I can't. And the resize icon is not just clutter, it's there for a purpose: it's saying that you can click on the image to see it larger. —Mets501 (talk) 18:23, 7 October 2006 (UTC)
replies: text: Every image is already clickable, so what does that icon add?  The Lord of the Rings does not have that icon and clicking on the image brings up a larger image. It is redundant and therefore clutter. Or am I missing something? --Jtir 18:59, 7 October 2006 (UTC)
replies: text:  "Image syntax is easy to understand, and very logical.":  Now I realize what I have been missing. This is all about keeping things simple for the editors. That is certainly desirable, since editors of any skill level may edit the WP. It would make things even simpler if there were no style boxes at all. :-) And I also just realized the examples I have been citing are automatically generated from templates. Editors can see the complexity after expansion, but they don't have to know how to create it in detail.  However they still have to edit after expansion, as this edit of the FA shows. --Jtir 19:30, 7 October 2006 (UTC)
replies: text: I'm sure simplicity for editors is an important consideration, but there is also the issue of having a consistent style. The infobox style is for infoboxes, and the image style is for images. Mixing them around goes against the point of having the styles in the first place. It is true that the displays in the fields of mathematics section are an anomaly - they are not simply images or infoboxes. The best description of them probably is navigation boxes with images. At any rate, they shouldn't be used as a model for other images in the article, and if there are problems with the image style, then the style should be discussed, not simply discarded in this article. JPD (talk) 14:44, 9 October 2006 (UTC)
thread_title:  Why infoboxes are better than inline images. 

message: Under "things math is not", I'd like to see a comparison with algorithms. Is the difference the capacity of algorithms to save state?
A high school student (many I'm sure) recently asked, "What's this stuff good for". How about a page on the applications of high school math? 
Will Brown  12 October 2006
There's not much wrt history, specifically contribution of eg al gorizme or whatever his name was, that is the arab contribution... Also deals with categorising, rather than actually talking about the content, simple things like place value and the representation '0'... is this on purpose? I am sure you guys have talked about this... I was just curious --Fidocancan 12:25, 29 October 2006 (UTC)
replies: text: I can't remember any specific discussions about that; more on whether maths was to be called a "science" or a "discipline" :-). The problem is that there is so much to say that you must make a selection, and even then can only touch on the topics. What we have tried to do is identify the major topics and refer to other articles dealing with the topic in more detail. So the section on History refers to the article History of mathematics, and as you will see that is by itself so rich that it is essentially impossible to give a balanced summary in the present article that would specifically name al-Khwarizmi. History of mathematics further refers to History of mathematical notation which refers to History of the Hindu-Arabic numeral system. Important as this has been to the development of mathematics, many other things not mentioned directly in the text are equally important to the whole subject. We are open to all suggestions for improvements, though.  --LambiamTalk 15:26, 29 October 2006 (UTC)
thread_title: Possible Additions:

message: The page classifies discrete mathematics as a relatively new discipline.  In so far as it is concerned with computer science this is true but discrete mathematics itself (contrasted to more continuous settings like topology or calculus) is hardly new.  Some of the earlier purely combinatorial works are attributed to Bhaskara (1114- circa 1185) and Gerson (1288-1344).  Combinatorics falls neatly into the category of discrete mathematics so these counter examples serve to debunk the idea that discrete mathematics is new.  May of the principal results are in fact significantly older than calculus. [ED Forgot Spell check]
—The preceding unsigned comment was added by 68.48.143.71 (talk • contribs) 01:57, November 1, 2006 (UTC).
in the Discrete Math section, the word 'soluable' is used where it seems the word 'solvable' was meant. Pulseczar 03:43, 25 January 2007 (UTC)
thread_title: Discrete Mathematics

message: I know this was discussed above but unfortunately I wasn't around to participate. It is very misleading to describe mathematics as " the academic discipline that …". Mathematics is not just an academic discipline. Academics is in no way a defining property of mathematics. Mathematics and mathematicians, existed before the existence of formal academic institutions, exist now outside of them, and would continue to exist without them.  For now I've returned the lead to the original "discipline".  "Body of knowledge" would also be acceptable to me. Even science used in the broad sense would be better than "academic discipline". Paul August ☎ 06:03, 2 November 2006 (UTC)
replies: text: I haven't read back over the discussion, but I think it was added because of a concern that people might confuse it with ... bondage. While I don't mind the sentence without the word academic in it, I never thought it was a problem with it in there either. Now I'm a bit curious, what does academic really mean in this context? darkliight[πalk] 08:53, 2 November 2006 (UTC)
replies: text: See Academic discipline. The fact that maths is an academic discipline now does not imply it has always been so – although the notion of it being academic has a long background. The discussion about "discipline" is still on this page. Personally I prefer "study", which is the noun that was used until early June. Objection: it excludes the use of mathematics. OK, make it "branch of knowledge". No, too static. And so on and on. This may be one of these cases where for every choice there is a majority who prefers another choice.  --LambiamTalk 09:42, 2 November 2006 (UTC)
replies: text:  Hmm. I always felt that an academic discipline was something that could be studied at a college or university level (as Academic discipline suggests), but that just because something could be studied outside of those environments it should not be excluded as an academic discipline. I'm not arguing one way or the other here, I'm just trying to get a good sense of the what the words really mean. darkliight[πalk] 10:03, 2 November 2006 (UTC)

text: Well, if one won't do, let's try three. Of the three I put in, I like Peirce best; but I'm a Hilbertian. Septentrionalis 19:27, 2 November 2006 (UTC)
thread_title:  "academic discipline"? 

message: I see an anon has taken the plunge and removed the controversial "What mathematics is not", as was discussed on here recently. Before some reactionary leaps to revert the change, I'll point out that I completely agree with this deletion. How does everyone else feel? Soo 22:57, 15 November 2006 (UTC)
replies: text: I agree, and have said so repeatedly. I wouldn't mind getting rid of the "misconceptions" section along with it. --  Trovatore 22:59, 15 November 2006 (UTC)

text: I disagree because many people who are not familiar with what mathematics is really all about would be MOST helped by the delineations between mathematics and accountancy, mathematics and numerology, etc.  That's my objection to the "not useful" argument.  As for the "pretentious" argument, I'm unclear about what the anon editor thinks this section is "pretending" to do.  capitalist 04:34, 16 November 2006 (UTC)

text: There are many things mathematics is not: arm wrestling, butterfly collecting, change ringing, .... We can't possibly list everything mathematics is not, and the idea (as I understood it) was to take away some common misconceptions. So we need at most one section, say "misconceptions", rather than "is not" + "misconceptions". I'm not sorry to see "is not" go, because it wasn't good. "Misconceptions" is also not very good, and, I'm afraid, in fact OR, so I won't mourn its demise either. I can see the potential value of a well-written section, but this is not it.  --LambiamTalk 07:31, 16 November 2006 (UTC)
replies: text: I agree that there should only be one section and that it should be titled "Misconceptions".  I never liked the "What Mathematics is not" title because it seemed kind of in the reader's face.  I would like to see the deleted information on accountancy, theorom solving and numerology appear in the "Misconceptions" section however.  capitalist 05:14, 18 November 2006 (UTC)
replies: text: I can agree in principle that a well-written "Misconceptions" section could, in theory, have (extremely modest but) positive value to the article, taken in isolation. But trying to keep it well-written would be a continuing annoyance that I think would tip it over into the negative. The things are pure POV bait, not worth the trouble. Deep-six it now and leave it out. --Trovatore 05:24, 18 November 2006 (UTC)
replies: text: Actually, I take the first part of it back. I can't imagine such a section being well-written. I think they're not just POV bait; they're pretty much ineherently POV. Salt and burn its bones. --Trovatore 05:37, 18 November 2006 (UTC)
replies: text: Smells like consensus... Soo 22:35, 20 November 2006 (UTC)
replies: text: Bah!  I'm going to lunch. ;-)   capitalist 03:57, 22 November 2006 (UTC)
thread_title:  What mathematics is not 

message: The drive to get this article to featured status seems to have stalled in recent months. I will try to push things along over the next few months but I don't have enough knowledge of the subject (or time) to do everything myself. Anyone willing to get one of Wikipedia's most important (and most read) articles to Featuredhood, say "aye". Soo 22:35, 20 November 2006 (UTC)
replies: text: I'll do my best to help, but it'll be easier if someone could tell us what to do. I think it's a great article, but it's kind of difficult for a new-comer to determine its needs? Snailwalker | talk 13:23, 15 December 2006 (UTC)
replies: text: The to-do list at the top would be a pretty good place to start. The hard bit is sourcing everything. Soo 18:46, 15 December 2006 (UTC)
thread_title:  Featuredness 

message: Multi-dimensional Math
While this is part of THE LIGHT; The Rainbow of Truth collection of research ideas attributed to the philosophy of Thinking in Colour, it is also the logical development of Alfred North Whitehead and his observation that "There are no whole truths; all truths are half-truths. It is trying to treat them as whole truths that plays the devil".
In the realm of Mathematics we appear focused in the world of  concrete reality, whereby in the world of abstracts and mult-dimensional representations we have different answers.  American school redefines mathematical paradigm
The simple reality that in the absolute concrete world, 1+1 = 11, and in the pure abstract world, 1+1=1, case example, the cities of Port Arthur and Fort William were united and formed the city of Thunder Bay, Ontario.  Here the addition of concepts remains the same, only that the concept is larger.
The addition of variables can have different values if the value of each integer has sub-values.  One bag of marbles plus one bad of marbles equals 200 marbles.  The complexity of the variables has changed in this particular example; multi-dimensional math.
--Son of Maryann Rosso and Arthur Natale Squitti 22:54, 29 December 2006 (UTC)
replies: text: Heehee, top trolling sir. Soo 23:54, 29 December 2006 (UTC)
thread_title:  Multi-dimensional Math 

message: I can't find a topic for an important branch of lower mathematics: that which is often called commercial math or business math. It is a practical subject, emphasizing simple arithmetic, percentages, and fractions, but also covering things such as banking transactions (writing checks, for example), purchase orders and invoices, consumer and business loans, etc. All of these things have a mathematical component, or at least a computational one, and they are very widely taught in commercial courses around the world. Does this subject have an article? If not, should it? What should it be called? Lou Sander 20:18, 13 January 2007 (UTC)
replies: text: You may want to post this at Wikipedia talk:WikiProject Mathematics where most math discussion takes place. Oleg Alexandrov (talk) 21:24, 13 January 2007 (UTC)
replies: text: It's called arithmetic. Rick Norwood 13:41, 30 January 2007 (UTC)
replies: text: Oh, bravo!  :o)  capitalist 04:16, 3 February 2007 (UTC)
thread_title:  Commercial / Business Math 

message: Why is this article partially locked? Charles (Kznf) 21:35, 29 January 2007 (UTC)
thread_title:  locked? 

message: Why isn't there a link to the mathematics portal? There's a link to the chem portal under Chemistry =o. It'd also be nice to have a table on the right hand side with all the different disciplines in math, much like the way the one under political science.
Talcite 02:43, 5 February 2007 (UTC)
thread_title:  Link to the mathematics portal? 

message: I believe it would be a good idea to add a page with formulas used in mathematics.  They could be grouped into categories of different areas of math with explanations and examples of the equation.  This would be of great help for many students.--Trd89 23:16, 2 March 2007 (UTC)
replies: text: This question is better suited for Wikipedia talk:WikiProject Mathematics. —METS501 (talk) 23:37, 2 March 2007 (UTC)
thread_title:  Creation of a Mathematical Formula Page 

message: The discussion of this trivial point is now far too long and disrupts the flow. Prior to making it longer, it was irritating because it sort of sounded like "those dumb North Americans don't know that it's called maths". I say dump the whole thing; it's not worth the trouble (and wouldn't be, even if it were almost no trouble). --Trovatore 21:54, 6 March 2007 (UTC)
replies: text: I agree. We have the redirect pages for math and maths. This should be enough. This article is about mathematics, not about common short forms/abbreviations for the term mathematics in every English dialect. Ocolon 22:03, 6 March 2007 (UTC)

text: It's just way too much text for its usefulness (which is essentially zero, as everyone knows the words). --Trovatore 05:05, 7 March 2007 (UTC)

text: My biggest objection is really that it's an invitation to a completely unnecessary Yank-Brit war (whose form goes first?), or at least to annoyance on one or the other part even if we don't war about it. Given that it's so completely useless, I think we should avoid even a tiny temptation in that direction. --Trovatore 05:10, 7 March 2007 (UTC)

text: No, it hasn't been there for "years"; it was added sometime last summer or fall. And it's bothered me for that long; I just haven't been irritated enough to do anything about it, until recently when it started getting long. Personally I find "maths" grating, and am more than willing to forgo "math" too, to keep "maths" out of the first sentence. No doubt there are others who feel the same way with the roles of the two terms reversed. --Trovatore 19:46, 7 March 2007 (UTC)

text: It's less offensive than it was. I still think it's unnecessary and would be better removed entirely. --Trovatore 20:18, 7 March 2007 (UTC)
thread_title: Maths, math

message: "Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens." By by? This needs correcting. Bye :)
: I corrected it. Thanks a lot. :) — Ocolon 15:20, 12 March 2007 (UTC)
thread_title:  Typo in picture description 

message: This article contains many sections without any references. I tagged those sections with --Sefringle 03:45, 23 March 2007 (UTC)
replies: text: Just because sections do not contain inline references, it does not mean they are not referenced.  Many mathematical topics, particularly basic and general ones, such as this article, have little or no inline references, as they are not suited for this purpose.  See the ~20 references at the bottom of the page; all of them were used to write the entire article. —METS501 (talk) 04:16, 23 March 2007 (UTC)

text: No-one has suggested here that the requested references are not needed because something is well known. The statement was instead: Yes, there are references, only, they are not inline. They are in the References section. Wikipedia has no requirement that references be inline. See also Scientific citation guidelines.  --LambiamTalk 19:42, 23 March 2007 (UTC)
thread_title: references problem

message: The expression beneath the image under the heading Notation, language, and rigor doesn't seem particularly simple. These things are relative, of course, but a Mandelbrot or Julia fractal would give a better illustration. Pavium 01:27, 7 April 2007 (UTC)
replies: text: While the expression is fairly simple as they come, I don't understand what the concept is supposed to be that is being described here. For simplicity leading to complexity, a puffer train in Conway's Game of Life is illustrative – but I'm against animated images unless strictly needed, and the concept is not that complex. What are we trying to say here anyway? Is the sentence actually true?  --LambiamTalk 06:37, 7 April 2007 (UTC)

text: The caption should say this. Rick Norwood 13:13, 25 April 2007 (UTC)
thread_title: Simple expression of complex concept

message: Under title Fields of mathematics - Quantity, it is written that number 2 is a complex number. Is this a mistake, or is my basic knowledge of mathematic so weak?--Yovi 15:41, 12 May 2007 (UTC)
replies: text: 2 is indeed a complex number (think of it as 2 + 0i if you like). The natural numbers are integers are quotients are real numbers are complex numbers, or speaking a little more mathematically, the natural numbers are a proper subset of the integers etc. So although 2 may be a natural number, this does not preclude it from being a complex number also. As far as I can recall, this image was made to emphasize this fact. Hope that helps, darkliight[πalk] 14:28, 12 May 2007 (UTC)
replies: text: In fact, each of the articles Integer, Rational number, Real number and Complex number explains how the concept is an extension of the previous concept (for integer: natural number), and how the conceptually simpler numbers are embedded in each extension. In particular, Complex number states this in the opening paragraph, as follows: "Real numbers may be considered to be complex numbers with an imaginary part of zero; that is, the real number a is equivalent to the complex number a+0i."  --LambiamTalk 14:38, 12 May 2007 (UTC)
replies: text: But doesn't, by definition, the complex number need it's real part and it's imaginary part of the complex number? So that number 2 can not be a complex number, but 2 - 0i is a complex number.--Yovi 15:41, 12 May 2007 (UTC)
replies: text: If you use the normal rules of algebra, then 0 × x = 0 and x + 0 = x for all x. So then 2 + 0 × i = 2 + 0 = 2.  The real answer is that the complex numbers contain an embedding of the real numbers, given by the injection mapping the real number x to the complex number (x, 0), usually written as x+0i. However, by convention, the real line is identified with the algebraically indistinguishable clone found embedded in the complex plane. Computer scientists might call this a "coercion" (implicit type conversion), but mathematicians tend not to think in terms of typed objects.  --LambiamTalk 16:50, 12 May 2007 (UTC)

text: If I can locate the number somewhere on the complex plane then it's a complex number.  The fact that it happens to lie on one of the axes doesn't make it any less so.  I may be making a simplistic interpretation of Lambiam's point above, but I think the distinction that you're making between "2" and "2+0i" is a typographical one as opposed to a mathematical one.  capitalist 02:42, 13 May 2007 (UTC)
replies: text: I think one needs to state, if it should matter, whether 2 is being viewed as an element of R or of C. If we're in R, then there is no such thing as sqrt(-(2)), while in C there is. After all, 2 is 1x1 matrix too, if one chooses to view it that way; you could interpret 2+2 as adding the doubling operator to itself to get the quadrupling operator. By default, I would view 2 as an element of C. But to simply say "2 is a complex number" overlooks the importance of context, to my mind. In fact, 2 is a numeral and it could well be acting as the "ten" of the base 3 system Z3 for all I know. Context matters--one must state with what kinds of objects one is working. JJL 03:20, 13 May 2007 (UTC)
replies: text: Shouldn't we then change the article, so that it would be clearer, "with what kind of objects one is working"? I find that number 2 very confusing. Perhaps we could change it to 2 + 0i = 2, etc.?--Yovi 21:08, 13 May 2007 (UTC)
replies: text: No, I wouldn't do that.  Its the same thing as having 2 in Natural Numbers and Integers - Integers is a superset of natural numbers just as complex numbers are a superset of reals. (John User:Jwy talk) 21:30, 13 May 2007 (UTC)
replies: text: And the only reason the naturals are a subset of the integers is that we choose to identify them with the non-negative integers. Quoting from Integer: "Taking 0 to be a natural number, the natural numbers may be considered to be integers by the embedding that maps n to [(n, 0)], where [(a,b)] denotes the equivalence class having (a, b) as a member." Even if you balk at identifying the real number 2 with the complex number 2, it is true that among the inhabitants of the complex domain there is one that, among possible other names, also goes by the moniker "2". The caption of the box in the article sets the context that makes it explicit that here by "2" the complex number of that name is meant.  --LambiamTalk 22:13, 13 May 2007 (UTC)
replies: text: It doesn't really matter whether we are choosing to identify natural numbers with subsets of larger sets, or constructing the larger sets from the natural numbers, or whatever. Put simply, the article doesn't say "2 is a complex number", it gives 2 as one of the examples of complex numbers, precisely to make the point that Yovi finds confusing - the fact that the complex numbers include numbers with a zero imaginary part that does not need to be written (or a zero real part, for that matter). JPD (talk) 14:09, 14 May 2007 (UTC)
thread_title: Is 2 a complex number?