Talk:Mathematics/Archive 6

message: I want to say that, even though in some sense I reverted it, I found Gububbu's version not particularly worse than the current one--while it was hardly complete, at least it avoided the sin of excessive ambition in "defining" math. But then Rick stepped in with a clearly unacceptable version, which was immediately vandalized. So rather than try to split the difference I reverted back before the latest outbreak of hostilities, hoping things would then be discussed according to procedure.
Let me explain my objections to Rick's version, in the hope that we can start to converge a little. I do not agree that mathematics is "the most certain [...] knowledge that we possess". For example, I am more certain of my own existence than I am of any mathematical proposition. Now, it could be said that that's my knowledge rather than ours, but nevertheless Rick's phrasing comes far too close to an assertion of apodeictic certainty. That topic could be discussed further down in the article together with objections to the concept; it should not occur unchallenged in the introduction.
The other objection is the bit about "using the method of deductive reasoning from definitions and axioms". Of course that is an important part of mathematics, but the phrasing suggests that it's the whole of mathematics, thereby excluding empiricism from mathematical epistemology. --Trovatore 19:01, 19 October 2005 (UTC)
replies: text: Let me just add that this version, by The Anome, is really pretty good. Includes pretty much everything, and describes common methodologies without prescribing them. --Trovatore 22:14, 19 October 2005 (UTC)
replies: text:  Part of the revert wars was me reverting twice Gubbubu's version. Sorry for that. I don't have much against that text itself, I just hoped for some more discussion here rather than pushing one's version by brute force. By the way, isn't it overblown to put those "original research" and "neutrality disputed" templates just because we fail to use a dictionary definition and instead the text says that math is the study of space, change, etc? How about removing the templates? Oleg Alexandrov (talk) 23:54, 19 October 2005 (UTC)
replies: text: I would be for removing the templates. I think Gubbubu just got a little hotheaded. Hopefully he'll cool off and remove them soon; otherwise we can see if anyone else wants to defend them here. --Trovatore 00:02, 20 October 2005 (UTC)
thread_title: Recent revert wars

message: # My 100× reverted version contained mostly all disputed "definitons" of maths. What you have done was deleting a scientific definition from the article, and I think that is uneacceptable. You can debate that Webster's dictionary says truth or foolness, but you can't debate that Webster says that what it says. So editors reverted my version outraged our NPOV policy. Please send me the necessary apologetical letters with the  donations. 
# Unlike you, I haven't deleted your work, your thougts from the article. I only moved down the recent "definition" with some row. But your reverts deleted important tings. I think your method was a bit impolite. Please in the future 1). READ, 2). THINK, 3). ASK/TALK, then 4). ACT  before starting revert wars, in this order, especially when you reverting a logged-in, unanonim user's acts.
# I said I haven't dleted anything. But I could do that without any talks and debates! Namely, the recent "definition" of maths ("study of structure, change" and what else) has no scientific resources (see Wikipedia:Cite sources) and then 1). it must be a serious pov, or/and 2) it must be Wikipedia:Original research! So I think anyone who debate this definition, cpuld delete it, only with a remark in the summary (no resource pov, original research deleted).
# So please Trovatore, don1t delete pov/orig. res. templates, on no accounts. I think three of our policies shouldn't be injured. That is too much. Gubbubu 11:20, 20 October 2005 (UTC)
thread_title:  Gubbubu's remarks 

message: Apparently we should rethink our article and add a section on philosophical views of mathematics and applications to say the least and _then_ try at the intro again. --MarSch 12:35, 20 October 2005 (UTC)
replies: text: Whatever. :) Just let us not rush to edit the article without much consultation. That only leads to frustration on all sides. Oleg Alexandrov (talk) 13:58, 20 October 2005 (UTC)
thread_title:  intros summarize articles 

message: The current introduction seems fine to me.  Sorry if I got a little hot under the collar yesterday.  I just got back from a conference in which I learned that most high school geometry courses will no longer cover proof because it isn't on the high stakes "no child" test.  Sigh. Rick Norwood 14:04, 20 October 2005 (UTC)
replies: text: what's a "no child" test??? --MarSch 11:23, 21 October 2005 (UTC)
replies: text:  No Child Left Behind, President George W. Bush's education initiative. I don't know how good it is, but it made a lot of conservatives mad, and that is always a good thing. Oleg Alexandrov (talk) 14:09, 21 October 2005 (UTC)
thread_title:  the current intro 

message: I haven't been given a clear answer who says that "maths is the study of structure, change and patterns"? Where this definition came from? Please answer, I esp. beg MarSch to answer me. Gubbubu 16:30, 20 October 2005 (UTC)
replies: text: Well, you haven't said why you think that the article is NPOV, or original research. The only thing I could find is a complaint that no sources are mentioned. That is true, you do have a point here, and perhaps the best way to get a definition is to distill something from the definitions given in a couple of recent dictionaries. However, we don't go around and slap  and  on every article which does not cite its sources. -- Jitse Niesen (talk) 17:12, 20 October 2005 (UTC)

text: I for one am a pure mathematician, not a math ed specialist (which doesn't mean I don't take my teaching seriously, just that it's not my area of research), and I certainly don't "reject the importance of proof", though I may not give it the unique epistemological status that you do. What I reject is overly prescriptive and restrictive epistemology that excludes attempts such as Woodin's to answer questions like the real truth value of the continuum hypothesis. --Trovatore 23:15, 20 October 2005 (UTC)

text: Well, you can put it that way if you want to, but I don't know that the development of the theory was particularly axiomatic. I think he does think of it as an axiom now, rather after the fact. --Trovatore 23:32, 20 October 2005 (UTC)

text: The major disciplines within mathematics first arose out of the need to do calculations in commerce, to measure land, and to predict astronomical events. These three needs can be roughly related to the broad subdivision of mathematics into the study of structure, space, and change (i.e. algebra, geometry and analysis).
I don't see these ideas as particularly POV or OR.
And by the way the lead should summarize the rest of the article. So, making substantive changes in the lead without changing the rest of the article is backwards. Paul August ☎ 00:19, 21 October 2005 (UTC)

text: It seems I don't need to explain myself anymore, since you all've done so for me :) Thanks. Gubbubu, you are welcome to constructive criticism or even non-constructive, but those templates seem not to have any support besides you, so I've removed them. They bear no relation to reality. --MarSch 11:30, 21 October 2005 (UTC)
thread_title:  Why templates been removed??? 

message: It was at 173K so most is now in /Archive4. I'm fairly happy with it now. It reads well. I think the 'common misconceptions' section might merit a page of its own. Charles Matthews 13:04, 21 October 2005 (UTC)
replies: text: It's easy enough to see where it comes from: quantity = analysis, structure = algebra, space = geometry, plus change = differential calculus.  Or for the OED arrangement = combinatorics, which is in a sense better because less redundant and more in tune with compsci. So this is all just using lay words for things that undeniably are mathematics. Charles Matthews 07:26, 22 October 2005 (UTC)
thread_title: This page

message: : It seems I don't need to explain myself anymore, since you all've done so for me :) Thanks. Gubbubu, you are welcome to constructive criticism or even non-constructive, but those templates seem not to have any support besides you, so I've removed them. They bear no relation to reality. --MarSch 11:30, 21 October 2005 (UTC)
replies: text: Yes it seems to be you need to explain your deletion. Sorry, I put back templates. Gubbubu 15:23, 21 October 2005 (UTC)
thread_title:  Ask for Marsch 

message: Mathematics is often defined as the study of certain topics, such as quantity, structure, space, and change. Another view, held by many mathematicians, is that mathematics is the body of knowledge justified by deductive reasoning, starting from axioms and definitions.
# First of all, you mustn't delete alternative "definitions", especially from peer-reviewed sources. this is awful! We will censoring ALL scientific writings of definition of Maths????? Gubbubu 15:38, 21 October 2005 (UTC)
replies: text: Could you calm down on this issue? You've made your point. Often defined: this doesn't say rightly defined. It just means we start with one common view, before moving onto another. The rest of the article does plenty to support that first sentence; it does not say that the definition is correct. In fact I don't suppose the article now does define mathematics. Giving any narrow definition would be wrong, I think. Charles Matthews 15:48, 21 October 2005 (UTC)
thread_title:  Gubbubu's critics on recent "definition" 

message: Does anyone know what page I should go to in order to learn about the history of Arabic numberals and how they came to be the main symbols of mathematics? -- Thearticulator 21:18, 25 October 2005 (UTC)
replies: text: Nothing could be simpler.  The title of the article is "Arabic numerals" (note spelling).  For more info, try "Numerals" and "Base ten". Rick Norwood 01:01, 26 October 2005 (UTC)
thread_title: Arabic Numberals

message: I read some of the article, the introduction and the history, and quite frankly I did not like it very much. It seems like a lot of original research. Can't you say that mathematics was invented (my view is that it was invented)? At least mention prominent mathematicians in the history sectoin, or the first person one might call a mathematician? The introduction seems very dense and doesn't sit well with me. Both definitions seem very forced. Check out this article and maybe it will help give some perspective on your dispute Math Invented or Discovered?. The history part seems sort of rambling about "abstraction" and things like that, and to me looks like it has suffered a long battle. I think at the heart of your problems are very deep philosophical issues, some of which philosophers have probably already sorted that out to your satisfaction, you just don't know yet, some of which you might agree or disagree on, some of which are just "who knows?". Personally, I would just say "Mathematics is the study of numbers" and leave it at that for this article. Leave it up to the reader whether they feel like reading into it or not. You should also check out Philosophy of mathematics. If you ask both people who disagree you might find they simply have a different outlook, and can maybe agree to disagree. If you look on the Internet, people have all sorts of opinions when you ask "What is math?," but everyone would agree that it is a study of numbers. I don't know if this is sufficient for this article (I found one article by a math professor that said saying math was the study of numbers was like saying zoology is the study of giraffes--he went on to say nobody really knows.), but try a different approach. There are many many different views. The last one I got was from here and it has lots of other views.--Ben 09:38, 2 November 2005 (UTC)
replies: text: Mathematics is the study of numbers; I don't think any competent judge could accept that. Charles Matthews 09:47, 2 November 2005 (UTC)
replies: text: Oh sorry, I didn't realize that you guys are having a contest :P Never mind then. (and ya missed my point too). --Ben 11:53, 2 November 2005 (UTC)

text: I don't think anyone missed your point, Ben, but just to be sure -- your point seems to have been that the introduction should be simpler.  I tend to agree.  But the question of whether mathematics is "numbers" (where does that leave geometry?) or "truth discovered by deductive reasoning" (the Sherlock Holmes approach) has not been settled by the philosophers, who also do not agree on whether mathematics is discovered or invented.  An honest introduction to the subject has to present both points of view. Rick Norwood 13:04, 2 November 2005 (UTC)
replies: text: "Numbers and shapes" then. That was just an example. I'd say why weigh in on whether it is "truth discovered by deductive reasoning" or not. Leave it up for the reader to decide, or put it on the Philosophy of mathematics page. Anyway, the first part of the intro, while I think it's awkward, doesn't negate the second, it doesn't say whether or not what is being studied is invention or discovery or whatever, but the way it is written it seems like that's what is being said. Anyway I was only responding to the RFC and trying to help and let you know what I thought of the article. Good luck with your dispute. --Ben 13:22, 2 November 2005 (UTC)

text: Reuben Hersh, What is Mathematics, Really?, gives it 250 pages and 65 pages of notes. I actually think it would be good to cover all the bases, with respect to things he brings up, somewhere here. But not on this page. Charles Matthews 13:12, 2 November 2005 (UTC)

text: I appreciate your comments, Ben. Rick Norwood 14:22, 2 November 2005 (UTC)
thread_title: From the RFC

message: I like the suggestion of adding a few names to the article.  Archemedes, Newton, and Gauss?  Aristotle?  Any thoughts on the subject?
On another topic, I'm going to go back in and separate the theorems from the conjectures.  Frankly, having "Important theorems and conjectures" and "Famous theorems and conjuectures" looks dumb. Rick Norwood 13:10, 2 November 2005 (UTC)
replies: text: Probably does - to people who are confused as to whether celebrities are important people. Rick, there must be other edits you can make. Charles Matthews 13:12, 2 November 2005 (UTC)
replies: text: There are indeed other edits I can make, and I make them.  But this article needs work, and I am trying to help. Rick Norwood 14:24, 2 November 2005 (UTC)
thread_title:  people? 

message: I object in the strongest possible terms to the repeated attempts to push CH on this page. You could poll all the Fields Medallists and all the Wolf Prize winners in mathematics about its importance. I think you'd only get one vote; and Paul Cohen presumably would reckon the matter was settled. This page needs perspective. The matter has been discussed above. Charles Matthews 14:20, 2 November 2005 (UTC)
thread_title: Continuum Hypothesis

message: "Originally the collective name of geometry, arithmetic, and certain physical sciences (as astronomy and optics) involving geometric 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 to include those branches of physical and other research which consist in the application of this abstract science to concrete data."
Given this, our introductory paragraph doesn't seem so bad.  In my personal opinion, mathematics is knowledge obtained by deductive reasoning from first principles and science is knowledge gained induction from careful observation and measurement.  But that is neither here nor there.  We are bound by what the primary sources say. Rick Norwood 16:56, 6 November 2005 (UTC)
thread_title:  The OED definition of mathematics. 

message: You and I agree that something should be said about the amount of mathematical activity over the last hundred years.  Oleg Alexandrov said, "I would concider accepting something in the spirit but not letter of this sentence."  Would you attempt a sentence on this subject. Rick Norwood 23:57, 6 November 2005 (UTC)
replies: text: To be honest I sort of thought Charles had a point with the comparison with Literature; I hadn't looked at it that way before. --Trovatore 00:08, 7 November 2005 (UTC)
replies: text: Let's attempt a section on 'Mathematics as a profession' to accommodate this. Qua profession, mathematician has seen enormous growth, and no question. (By the way, despite what Oleg wrote above, User:Axel Boldt and User:Michael Hardy were in my view the important pioneers here in the mathematics sections.) Charles Matthews 10:52, 7 November 2005 (UTC)
thread_title:  Request to Trovatore 

message: I had resolved to let things settle down, and a consensus be reached, before inserting "number, shape, structure, and change" everywhere a similar list appears as a definition of mathematics.  But somebody has changed the first sentence unilaterally, which got me to thinking (always dangerous).
Most authorities define science according to method rather than subject matter.  For example, from the Oxford American Dictionary "a branch of study requiring systematic study... ."  On the other hand, most authorities define mathematics according to subject matter.  For example, "The science of number, quantity, and space".
But every mathematician can think of ways of studying number, quantity, and space that are not mathematics, numerology for example, and can also think of areas of mathematics, logic and set theory for example, that are not about number or quantity or space.
So, how about this:
:Mathematics is usually defined as the study of such subjects as number, shape, structure, and change.  Many professional mathematicians, however, use mathematics to describe any study in which theorems are deduced from axioms and definitions, including such areas as mathematical logic and set theory.
Then we can use the "number, shape, structure, and change" ruberic throughout the rest of the article.
Comments? Rick Norwood 21:19, 13 November 2005 (UTC)
replies: text: I think the introduction the way it is now sounds better while saying the same thing. Oh, and I reverted the anon change you mention above. I like the "often" part which the anon removed.  Oleg Alexandrov (talk) 23:02, 13 November 2005 (UTC)

text: I would think we should indeed put "quantity, structure, space, and change" everywhere for consistency, but one should look carefully around the place those occur, to see if they match with what is in there. But let us see if there are other opinions too. Oleg Alexandrov (talk) 23:46, 13 November 2005 (UTC)
replies: text: Well, I've waited more than a week, and you are the only person to offer an opinion on "quantity, structure, space, and change" v. "number, shape, structure, and change", so I will defer to you, and to tradition, and go with the former.  I only know of a couple of places that need changing, so I'll do that now. Rick Norwood 20:26, 17 November 2005 (UTC)

text: That was rather fun.  It is surprising how easily the various topics fall into place under the headings "quantity, structure, space, and change".  Now all of the definitions of mathematics on the page agree, and the topics are covered in the same order in each subsection.  Form follows function.  Rick Norwood 21:25, 17 November 2005 (UTC)
thread_title:  number, shape, structure, and change 

message: Automated theorem proving has some value as evinced by the existence and value of formal verification. The assertion that they will generate nothing of value therefore has to be qualified. "Widely recognized esthetic value" is a reasonable formulation of such a qualification.--CSTAR 23:01, 20 November 2005 (UTC)
replies: text: I understand your point, and it is not worth getting in a fight over, but to say that automated theorem proving has not generated anything of esthetic value is to suggest that it has generated things of practical value.  I'm a big believer in the esthetic value of mathematics, but I thought in this context the adjective sounded a bit snobby to me. Rick Norwood 01:13, 21 November 2005 (UTC)
replies: text: Automated theorem proving has roiled the theory of hypergeometric series,   where new identities can be found at will. Aesthetically, the new identities are similar to the old, hand-derived ones.  Are the newer identities "less beautiful"? The analogy is that of using a computer to multiply numbers: it has allowed the level of abstraction to jump up a notch. In at least this area, automated theorem proving actually has resulted in new and aesthetically pleasing identities (and I know this contradicts my earlier statements). linas 15:33, 5 December 2005 (UTC)
thread_title:  Aesthetic value 

message: would you like to publish this article? -- Zondor 22:13, 27 November 2005 (UTC)
thread_title:  publication 

message: I think the following could be more accurate with the changes I indicate--I am writing as an anthropologist who did field research in New Guinea among technically neolithic people, whose number system I saw first hand.  Another anthropologist studied it in detail later. The Oksapmin people I lived with didn't count seasons and didn't recognize years because it was the equatorial tropics. They did count objects, however; but not abstractions. You could ask how many times were you angry today, and they would be able to give numerical values to it. But I doubt that it happened every day. (This is just an impression.)
:The evolution of mathematics might be seen to be an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction was probably that of numbers. The realization that two apples and two oranges do have something in common, namely that they fill the hands of exactly one person, was a breakthrough in human thought. In addition to recognizing how to count concrete objects, prehistoric peoples also recognized how to count abstract quantities, like time -- days, seasons, years.
I would change it this way:
:::The evolution of mathematics might be seen to be an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction was probably that of numbers. The realization that two apples and two oranges do have quantity in common, for example, that they both correspond to "two" fingers, was a breakthrough in human thought. In addition to recognizing how to count concrete objects, prehistoric peoples probably also recognized how to count abstract quantities, like time -- days, seasons, years. Addition was also likely in prehistory, where, e.g., three men coming up a hill could be called "three" men or "one-two" men. --samivel 22:33, 27 November 2005 (UTC)
replies: text: I don't like your suggested change, but I appreciate your thoughtfullness in discussing it instead of just making it.  First, it is dangerous to extrapolate from neolithic peoples today to prehistoric peoples.  Second, this is too technical for a general article.  An article on "neolithic mathematics" might be nice.  There are some references you could use in the article Pythagorean theorem. Rick Norwood 23:15, 27 November 2005 (UTC)

text: Agree with Rick. Let us keep it simple. An article on neolithic mathematics would be nice. Oleg Alexandrov (talk) 23:50, 27 November 2005 (UTC)
thread_title:  Prehistoric math 

message: I tried to add the following category entry:
 Mathematics
But I got a spam filter message when I tried to save the page.  I went to the spam blacklist, and comcast.net (my ISP) wasn't listed.  Does anyone know what is going on?  
If someone could add this to the article for me, I'd appreciate it.  Please note the blank space right before the word Mathematics.  Thank you.  Go for it! 13:40, 4 January 2006 (UTC)
replies: text: I don't see a need to add  Mathematics to the mathematics article. :Category:Mathematics is already in :Category:Top 10, so that should be enough. There is a rule somewhere about not overcategorizing things; an article should not show both in a category and in a subcategory of that cateogory. Oleg Alexandrov (talk) 20:05, 4 January 2006 (UTC)
thread_title:  I was blocked from the Mathematics article by a spam filter! 

message: I looked through Mathematics looking for a link to a page about computer applications and libraries for mathematics (hoping to get from there to a page about the PARI math library).
I couldn't see a relevant link, but maybe no article or category exists to link to quite as I've defined it; I did at least find :Category:Computer arithmetic, a link to which would be a good start. Not sure though whether it should go under 'Change', 'Applied mathematics' or 'Mathematics and other fields'. Hv 17:49, 11 January 2006 (UTC)
replies: text: Update: finally found the page I was looking for under PARI-GP computer algebra system, categorised under :Category:Computer algebra systems. Hv 18:30, 11 January 2006 (UTC)
thread_title:  Request for link to mathematical computing 

message: What exactly does this sentence mean:
: attempts to circumvent the usual criteria for publication of mathematical papers in a learned journal after peer review, with assumptions of bias
I can't quite figure it out. Does it mean that the person who is attempting the circumvention is assuming that the journal's editors are biased? Or something else? Could it be made clearer please? Dmharvey 21:45, 24 January 2006 (UTC)
replies: text: I think it means what you suggest it means.  Pseudomathematicians may claim that they don't publish in standard journals because standard journals are biased against them.  -lethe talk 22:16, 24 January 2006 (UTC)
replies: text: It would be a big help if you told us where the quoted phrase appears. Rick Norwood 22:02, 24 January 2006 (UTC)
replies: text: It's there, in the article. -lethe talk 22:16, 24 January 2006 (UTC)
replies: text: OK thanks guys. Hopefully it's clearer now. Dmharvey 23:03, 24 January 2006 (UTC)

text: I assumed it was somewhere in the article.  I was hoping to learn which section it was in. Rick Norwood 18:58, 25 January 2006 (UTC)
thread_title:  could someone please clarify.... 

message: What do people think of Rick's recent edit to this article. I can't make up my mind if this info is worth including or not? Oleg Alexandrov (talk) 01:11, 10 February 2006 (UTC)
replies: text: Keep, but as a statment with a citation, rather than as a quote (I hsoudl earn how to do footnotes...) Tompw 23:26, 10 February 2006 (UTC)
thread_title:  Recent edits to this article 

message: I was surprised but pleased to discover that Mathematics is now a good article.  Somehow, even though I visit this article every day, I missed that.  In any case, now that the article is proposed for the article improvement drive I've been reading over it to see what remains to be done.
The first thing, which I think would kill any chance of a move to excellence, is that fact that the new picture, while very nice, covers up some of the words.  This is something I don't know how to fix. 
Second, there has been a gradual drift in the first two paragraphs, which I think now need polish.  Here is how they currently reads:
::"Mathematics is often defined as the study of topics such as quantity, structure, space, and change. Another view, held by many mathematicians, is that mathematics is the body of knowledge justified by deductive reasoning, starting from axioms and definitions.
::"Mathematics, in nearly every society, is used in fields such as the natural sciences, engineering, measuring land, predicting astronomical events, medicine, accounting, and economics. Some of these fields often give rise to and make use of new mathematical discoveries. Mathematical study often involves discovering and cataloging patterns, without regard for application.
"Mathematics is often defined as..."  No.  I am fairly sure that mathematics is defined that way only in Wikipedia, and nowhere else.  How about "Mathematics can be defined as ..."
"Mathematics, in nearly every society...such as...some of these...often give rise...often involves..."
I understand the use of qualifiers to avoid dogmatic statements, but one "nearly", one "some" and two "often"s is too much weaselwording.  How about "Mathematics is used throughout the world in fields such as science, engineering, surveying, astronomy, medicine, and economics.  These fields both inspire and make use of new discoveries in applied mathematics.  Pure mathematics is also widely studied for its own sake, without any particular application in view."
Comments? Rick Norwood 21:25, 15 March 2006 (UTC)
replies: text: That would definitely be an improvement, in my opinion. I'd remove astronomy from the list, because it is part of science. Furthermore, I don't quite like how you sneak in the applied vs pure distinction at the end; it smacks of using a term before it is defined (but perhaps it will be clear to the reader anyway). Unfortunately, if one removes "applied" and "pure", the word "mathematics" appears twice next to eachother. -- Jitse Niesen (talk) 23:56, 15 March 2006 (UTC)
thread_title:  Good 

message: The picture still covers up some of the words.  Does anyone here know how to fix this? Rick Norwood 22:03, 17 March 2006 (UTC)
replies: text: What are you refering to?—Daelin @ 2006–03–18 10:08Z
When viewed on my browser, the picture covers up the last two letters of the word "medicine".  Rick Norwood 02:19, 19 March 2006 (UTC)

text: I think you must be using a horribly broken browser like Netscape 4 or IE 4, or you've scaled your font up enormously.  What you seem to be describing is not something that can be caused by the page's markup, and I cannot reproduce it in the three browsers I use.  Upgrade or downgrade to something that works, or change your default theme in "my preferences".—Daelin @ 2006–03–21 06:21Z
I'm using Internet Explorer.  Is that a bad thing?  I tried to find the version number but it didn't seem to want to tell me.  Does no one else see part of the word "medicine" covered up by the picture? Rick Norwood 13:52, 21 March 2006 (UTC)

text: I think you'll find that the obstructed word will change if you change the width of your browser window.  You'll find the version number under Help->About Internet Explorer in tiny light grey lettering.  IE has a number of serious problems, but only IE4 is actually technically broken, and unable to properly render floats according to any interpretation of the standard. The page will render properly in IE2, IE3, IE5, and IE6.  —Daelin @ 2006–03–21 19:17Z
Thanks.  It says version 6.0.2900 and then some more stuff.  Rick Norwood 21:43, 21 March 2006 (UTC)
thread_title:  Can someone help with the picture? 

message: I have renamed the "References" section to "Further reading". After looking at the works listed there, and reviewing who added each work when, I doubt whether any of these were actually used in the writing of this article. The section was originally (Nov 25 2001) called "Further reading", was renamed "Bibliography" (Dec 13 2003) and only recently renamed "References" (Dec 16 2005). Four of the entries have annotations (e.g. "Boyer …  A concise history of mathematics from the Concept of Number to contemporary Mathematics), which also supports my guess that they were added as further reading rather than used as references.
Thus, as the article now stands it has no references section. That is a problem which we should fix. If any of the current works actually were used as references (or can be cited as references for any of the assertions in the article), they should be moved to the new section. Also any contributors to this article should list any other such references actually used. And of course any editor can try to find appropriate references for various parts of the article.
In addition we should also review the "Further reading" section (i've copied it below for easy reference).  There are a lot of books on mathematics, is the current list the "right" one? Are there works we want to add? (For example, the original list contained: "Mathematical Society of Japan: Encyclopedic Dictionary of Mathematics, 2nd ed., MIT Press, Cambridge, Mass., 1993. Definitions, theorems and references." which got deleted somewhere along the way.) — or delete? (we don't want everybody just adding all their favorite math books).
Paul August ☎ 20:28, 23 March 2006 (UTC)
replies: text: This is probably a good idea. What I've done myself is create my own bibliography subpage. We could create a common one for mathematics as a subpage of the project page. We can discuss this further at the project talk page. Paul August ☎ 21:26, 23 March 2006 (UTC)

text: In general I think it's unnecessary to distinguish cited from uncited works in a refs section. I don't ever recall seeing this done in a journal article. Occasionally WP articles have references that are not only uncited, but not even directly on-topic to the article; these might reasonably go in a separate section, assuming they're to be kept at all. --Trovatore 21:03, 23 March 2006 (UTC)
replies: text: Common WP practice regarding this is not yet very mature. But many would say that it is intellectually dishonest to list a work as a reference if it has not actually been used as such. Paul August ☎ 21:26, 23 March 2006 (UTC)
replies: text: This has me a bit concerned. My understanding of references is "this is where you can find such and such", not necessarily "this is where I found it". Have I really misunderstood this? Where would I put, say, Hallett's book referenced at limitation of size, a book I don't actually own, but is clearly the correct place to look? It seems really pedantic to me to give the section a different name for this reason. --Trovatore 22:56, 23 March 2006 (UTC)
replies: text: How do you "know" this is where you can find such and such unless you've looked there yourself? For me a reference is "this is where I know it can be found because I've seen it there". Paul August ☎ 00:20, 24 March 2006 (UTC)
replies: text: Well, I have browsed the book, but that was a long time ago. In any case it's mentioned in the abstract of another paper disputing what the author says is Hallett's thesis that Cantorian set theory was "a theory of limitation of size from the beginning". --Trovatore 00:40, 24 March 2006 (UTC)

text: Um, I think that's just not true about what journals allow. Nobody ever complained about that in my papers. I typically use the BibTeX \nocite command once or twice, to mention a work that the reader may need to understand the background of the question, but which I don't find necessary to cite in any particular line. --Trovatore 21:29, 23 March 2006 (UTC)

text: Ok, I've started a "References" section, and moved Klein there. Paul August ☎ 00:20, 24 March 2006 (UTC)

text: Yes I agree about Kelly and Herstein, only general works should be listed here. Rick, you've given your opinion on some works to add (all of which seem ok to me), do you have an opinion about the works already listed?  Paul August ☎ 00:20, 24 March 2006 (UTC)

text: I have not read any of the books currently listed as "Further reading" so I really don't know if they are outstanding or not.  Another book I used in this article, though I used it more heavily in the History of Mathematics article, is An Introduction to the History of Mathematics by Howard Eves.  I don't know how it compares to the History of Mathematics listed above, but I like it. Rick Norwood 13:37, 24 March 2006 (UTC)
thread_title: "References" and "Further reading" sections

message: In my contributions to this article, I used information from the book by Kline, so it is a genuine "Reference".  Other works cited in the text inclued Newton's Principia, Wigner's  Unreasonable effectiveness..., and Hardy's Apology.  Whether they were actually used or not I do not know.
:Ok, I've started a "References" section, and moved Klein there. Paul August ☎ 00:20, 24 March 2006 (UTC)
thread_title: What works should be listed as References? 

message: As for "Further reading", that section should point only to major works about mathematics in general.  For example, much as I love Kelly and Herstein, they should be listed in Topology and Modern Algebra, not here.  Essential works of general interest that come to mind are Men of Mathematics by Bell, The Encyclopedic Dictionary of Mathematics, The World of Mathematics by Newman, The Mathematical Tourist by Peterson, Journey through Genius by Dunham, Godel, Escher, Bach by Hofstadter, Elements by Euclid, and Writing Mathematics Well by Gillman.  Anything on this list that does not belong?  What should be added? Rick Norwood 22:50, 23 March 2006 (UTC)
replies: text: Yes I agree about Kelly and Herstein, only general works should be listed here. Rick, you've given your opinion on some works to add (all of which seem ok to me), do you have an opinion about the works already listed?  Paul August ☎ 00:20, 24 March 2006 (UTC)

text: I have not read any of the books currently listed as "Further reading" so I really don't know if they are outstanding or not.  Another book I used in this article, though I used it more heavily in the History of Mathematics article, is An Introduction to the History of Mathematics by Howard Eves.  I don't know how it compares to the History of Mathematics listed above, but I like it. Rick Norwood 13:37, 24 March 2006 (UTC)
thread_title: What works should be listed as "Further reading"? 

message: We should append a new section to the article that discusses the contributions great mathematical thinkers like Euler, Gauss, Archimedes, and Newton have made and how those contributions further advanced mathematics thought. - Christopher 20:55, 29 March 2006 (UTC)
replies: text: I do not think that is import on the mathematics page, because we have a history of mathematical ideas but maybe on the mathematician page it might work. Besides how did those guys advance mathematical thought? No one was able to pass Archimedes. Timothy Clemans 20:59, 29 March 2006 (UTC)
thread_title: Include contributions men have made to mathematics?

message: This seemed like the best place to get people's attention about the article PDE Surfaces, written by Zer0 cache. I suspect that it's promoting research, but I can't be sure. It would be appreciated if other editors can check this out. I've also left a small query at PDE surfaces talk page. MP   (talk) 11:28, 11 April 2006 (UTC)
replies: text: I've copied this to Wikipedia talk:WikiProject Mathematics which is really the propper place. --Salix alba (talk) 14:19, 15 April 2006 (UTC)
thread_title:  Not sure where to put this 

message: There are a few maths articles looking for reviewers in Wikipedia:Good articles/Nominations.  Some of them are quite specialised and I suspect that it would be a while before anyone got around to reviewing them so I thought I would point it out here in case anyone wanted to look.  --Richard Clegg 16:18, 24 April 2006 (UTC)
thread_title:  Good article nominations