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Archive 5 | ← | Archive 9 | Archive 10 | Archive 11 | Archive 12 | Archive 13 | → | Archive 15 |
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Agne 05:52, 26 September 2006 (UTC)
I have made a request regarding this issue here. -- ScienceApologist 21:03, 26 September 2006 (UTC)
The word discipline in the definition of mathematics invokes evokes some very negative connotations that reinforce the perception that mathematics is not fun.
The word discipline has, among others, these senses (from various dictionaries):
And if the above is not enough, there is BDSM.
-- Jtir 14:57, 30 September 2006 (UTC)
Discipline (definition 2): a branch of knowledge, typically one studied in higher education : sociology is a fairly new discipline. Stephen B Streater 17:23, 30 September 2006 (UTC)
This is, of course, a subject that keeps coming up. I think the current opening paragraph captures what the quoted definitions have in common, and the question of whether math is a science is too controversial for us to use the word "science" in the opening paragraph.
The quoted definitions take one (or both) of two approaches. One approach is to give some kind of list of the topics studied by mathematics. This is, I think, how non-mathematicians think of mathematics. Note that astronomy was once considered mathematics but is now considered a science. Any such list is necessarily incomplete, but our list seems to me as good as any, and is reflected throughout the article as well as in other articles. I opposed the "list" approach, but when I was outvoted, I helped to make the list consistent throughout.
It seems clear to me, as a professional mathematician, that the other approach is correct, and that mathematics is that body of knowledge discovered by deductive reasoning. Science, in contrast, is that body of knowledge discovered by inductive reasoning based on careful observation and measurement. But, again, I was outvoted, and am happy that deductive reasoning at least gets a mention in the opening paragraph. Rick Norwood 13:17, 2 October 2006 (UTC)
I prefer discipline and I'm opposed to science, simply because it's not agreed this is the case (evidenced in the monster of a footnote you have had to include, an entire section in this article and the science article), not because I have an opinion either way. Is branch of knowledge really better than discipline?
I think most people refer to these .. things .. as an academic discipline as opposed to a branch of knowledge (google agrees with me when I googled those two terms), though either seem to be in use so I'm not totally opposed to the latter being used here. Not that my own limited experience counts for much, but I've found that branch of knowledge tends to be reserved for more specialised topics within a discipline.
I don't think it's possible to mix up academic discipline and BDSM given the context of the article. If you're really concerned about this, a simple wikilink as I've done here and the addition of the word academic would more than suffice. Most words have more than one meaning, we'd never be able to avoid them all, but at least this way we remove the possible ambiguity and stick to the apparent norm for describing subjects/fields of study/etc while the academic discipline article goes into more detail if necessary for the user, including using the term branch of knowledge. darkliight [πalk] 06:47, 3 October 2006 (UTC)
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)
I have moved almost all of the inline references to a separate References section, fixed a few {{cite}} templates, and added one new reference on the Fields Medal. For most of the ones that I moved, the inline citations are now either an author's name, or a quote with the author's name. This approach is nice because it puts the references in one place and it removes clutter from the body of the article (esp. clutter due to the {{cite}} templates, which, although they are very flexible, take up a lot of space). It is also easy to cite a work multiple times. The order and naming of the end sections follow Wikipedia:Guide_to_layout#Standard_appendices. The Earliest Uses of Various Mathematical Symbols is a fantastic reference, which could probably be cited more than once in the article, but I haven't decided what "author" I should attribute it to. -- Jtir 21:12, 2 October 2006 (UTC)
The new lead sentence contains all the mathematical concepts that I could identify in the first and third sentences of the original, adds some others (notably theorem and proof), and organizes them in a logical sequence.
The second sentence distinguishes between pure and applied -- it needs to be extended.
The third sentence concerning the evolution of math in the new lead is not changed from the original. It needs a brief transition from the definition of applied.
I used bulleted clauses after realizing the sentence would be unreadable otherwise. The new structure is highly adaptable and can be extended ad infinitum, if needed. The phrase relating mathematics to knowledge and science is also flexible and it could even be removed without modifying the rest of the definition. I didn't wikify it because it is too hard to edit complex sentences that are fully wikified and I expect there will changes. :-)
-- Jtir 17:39, 3 October 2006 (UTC)
I'm very impressed with this article, especially the illustrations. But the first sentence is really awkward. Of the definitions cited above, I'm most impressed with Britannica ("Science of structure, order, and relation that has evolved from counting, measuring, and describing the shapes of objects.") Yes, I have read the above discussion and I have already learned that it is difficult to give good definitions on wikipedia, where you have to accommodate every minority view. That is a pity, because this article is really beautiful. (well done!) -- Vesal 21:02, 3 October 2006 (UTC)
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)
So anyway, this is what I will do, I will create the subpages, and since it is your discussion that I will be summarizing, I would ask you guys to look them over. If you find them helpful, we could put them on more prominent position. I will begin with the /FAQ and then the topical subpages:
-- Vesal 21:50, 3 October 2006 (UTC)
I started the FAQ, see what you think. Since this is a core article of wikipeda, there might be future drives to improve quality and I think a FAQ is useful to avoid having the same "Is math a science debates" all over again. I personally would state in the lead that math is a science, but the purpose of the FAQ is to give the answer quickly to people like me. -- Vesal 15:54, 4 October 2006 (UTC)
What is the point of this, if you are not going to go back through the archives to find all the discussions about the intro, etc? If the subpage is only going to contain the recent discussion, it may as well be on this page. JPD ( talk) 10:26, 5 October 2006 (UTC)
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:
Very much in line with the todo list. -- Vesal 23:27, 4 October 2006 (UTC)
I wouldn't object to this section being incorporated into a philosophy of mathematics section, but I don't think that it is POV use something like "mathematics as science" as a heading for a section discussing the different views on whether/how maths is (a) science. On that topic, now that Poppers views on the matter have been clarified, the mention of Lakatos' work doesn't quite fit in. I am not sure whether it should be removed or reworded. I am also not sure why the Einstein footnote is needed. As the text suggests, the Einstein quote supports the view that pure maths is not science if you take a partiuclar view of what science is. The text doesn't suggest any more than this, and the footnote doesnt' seem to clarify much anyway. JPD ( talk) 10:45, 5 October 2006 (UTC)
It is not entirely clear what the new paragraph means in its assertion that mathematics is not "reducible" to logic. I suppose it has something to do with undecidable questions such as the continuum hypothesis. I know there are some people who claim that we can replace logic by either experiment (if a computer can't find a counterexample to the Riemann Hypothesis, then it must be true) or intuition (the Riemann Hypothesis must be true because it is beautiful) but as several people have observed, comments on the subject in this article should be a) basic and b) referenced. Rick Norwood 13:37, 5 October 2006 (UTC)
About the footnote on Einstein... Yes, it is very badly written, I tried quite hard, but it is very difficult to explain a long essay in a few words with my bad english. The problem is that the quotation is out of context. When Einstein is arguing that a pure branch of mathematics like geometry really depends on the physical world, I find it unethical to cite him as saying quite the opposite. Disclaimer! I might be wrong about what Einstein is arguing for in the essay, but I did read all of it, and it sure seemed the point was that pure math is a science. In fact, very similar to the views of Popper. --
Vesal 21:24, 5 October 2006 (UTC)
I have created three more Talk subpages and put links to them in the Talk page infobox:
They have already been set up with a brief descriptive header and populated with a least one entry. You may use that entry as a prototype for more entries.
The objective is to collect material that can be used to broaden the scope of the article. It is not to redo the work of wikipedians, which is what I was doing until Vesal set me straight. :-)
Would a subpage called "Mathematical Creativity, Intuition, and Aesthetics" be of interest? (I could probably find some quotes by Poincaré, Polya, or Einstein in this area.) -- Jtir 18:12, 5 October 2006 (UTC)
Some of the subpages are not for discussion, they are for collecting and organizing information. Editors may add information to them or correct them, but there is no discussion on them. Here are two hints:
-- Jtir 15:13, 6 October 2006 (UTC)
Maybe the argumentative parts of "mathematics as science" could be entirely ditched in favor of a portrait gallery of famous mathematicians, philosophers and artists with a quotations on mathematics. In particular on what they think mathematics is. So the idea is a slight extreme of what has already be suggested, that we don't define mathematics. But what do you think about the idea of basically only pictures and quotations instead of "Some mathematicians think...". A good place to collect them is of course the /Conceptions_of_mathematics page, even if we don't do pictures and quotes, it would still be very nice to have opinions from maybe Hardy on math for math's on sake etc, maybe like "A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas." stolen from the G. H. Hardy page. -- Vesal 23:05, 5 October 2006 (UTC)
I've written a sample gallery into the sandbox. The Picture_tutorial illustrates some other options. -- Jtir 14:34, 6 October 2006 (UTC)
The movie Good Will Hunting is an example of mathematics in popular culture. I was thinking of developing an infobox featuring it. The use of low-resolution images is OK, according to the copyright boxes for these images.
My reasons are:
NB:
The
Good Will Hunting article refers to the problem as an equation: "...wondering who could have solved the equation."
At another point the article reads: "...astonished assistant staring at the correctly solved theorem."
The
Parseval's theorem article does not mention the movie.
Any comments or suggestions? -- Jtir 20:34, 6 October 2006 (UTC)
Mathematics is also a thing that each and every single one of us do every single day. For example, when you are drinking water, your arm makes an angle. When a person lays down on a bed, this person makes a straight line. And if you pay attention of what a person is doing, he or she would see that Mathematic in there. Franck Jr. Colas, 18:26, May 14, 2007.
For example:
:{| style="border:1px solid #ddd; text-align:center; margin: auto;" cellspacing="15" | [[Image:Pythagorean.svg|96px]] || [[Image:Taylorsine.svg|96px]] || [[Image:Osculating_circle.svg|96px]] || [[Image:Torus.png|96px]] || [[Image:Koch curve.png|96px]] |- |[[Geometry]] || [[Trigonometry]] || [[Differential geometry]] || [[Topology]] || [[Fractal geometry]] |}
which looks like:
BTW, WP:MOS#Images is a guideline. -- Jtir 16:18, 7 October 2006 (UTC)
<!-- Infobox --> {| cellpadding=3px cellspacing=0px class="wikitable" style="float:right; border:1px solid; margin-left: 1em" |colspan=2 align=center style="margin: 10px; border-top:1px solid"|[[Image:Adi Shankara.jpg|center|200px]] |- !style="background:#f90; border-bottom:1px solid" align=center colspan=2|Adi Shankara |- |align=center style="border-top:1px solid"|Dates:||style="border-top:1px solid"|c. [[788]] to [[820]] [[AD]] <ref name="Dates"> There is some debate regarding this issue. {{cite book | last = Tapasyananda | first = Swami | year = 2002 | title = Sankara-Dig-Vijaya | pages= xv-xxiv }}
What you've pasted is part of an infobox, not an image with a caption. You'll notice that all the images throughout that FA use the Image: syntax. darkliight [πalk] 17:02, 7 October 2006 (UTC)
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):
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.
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)
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)
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)
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)
Mathematics is certainly an academic discipline, but it is clearly more than that. The implication of the former lead was that mathematics was restricted to being an academic discipline, which is just not true. Paul August ☎ 18:42, 2 November 2006 (UTC)
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)
Actually, a lot of this article is horribly pretentious and not useful, nor understandable by a person interested in looking at the various fields of mathematics. The subject is hard as it is, why deter people from it by just stating that everyone who studies it has their head stuck up their asses? BTW, I was the one who removed it, and I think the "misconceptions" part should be taken too. —The preceding unsigned comment was added by 216.165.37.30 ( talk • contribs) 03:16, November 16, 2006 (UTC).
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)
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)
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)
Why is this article partially locked? Charles (Kznf) 21:35, 29 January 2007 (UTC)
Probably because someone, likely a high school student or University student was vandalizing the page. I'm not sure, but it seems like the kind of thing that would happen...
Trocisp 17:44, 30 January 2007 (UTC)
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)
Oh wait, its under the picture, never mind =P. Talcite 02:44, 5 February 2007 (UTC)
The article asserts that fallible intuitions have led to mistaken "theorems" often in the history of Mathematics. This may be, but the link provided does not seem to support the assertion very well. Most of the examples at the other end of the link are simple algebraic errors, not mistakes of the kind Newton, Descartes or Euler might have stumbled into for lack of sufficient rigor. I have not edited the article, but if you want to edit it in the matter, feel free. Tbtkorg 17:11, 28 February 2007 (UTC)
This is not quite what I'm looking for, since most people would naively agree that in the plane given a point and a line there is one and only one parallel to the line through the point. This can't be proven, but it is generally accepted. I'm looking for a statement that was asserted by mathematicians, and given a falacious proof, which later turned out to be mathematically (rather than metamathematically) incorrect. Of course, there have been lots of "proofs" that, for example, pi is rational, but no real mathematician accepts these. Can the record of mathematics in establishing truth really be that good? Rick Norwood 12:55, 17 March 2007 (UTC)
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)
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)
I disagree. For most terms in wiki - we do add the [edit] Etymology of the word, as well as possible variants.
Sardonicone 04:59, 7 March 2007 (UTC)
If it's fairly close to standard practice with other articles, I fail to see how it really affects this one as well.
However if there's a concensus to remove it, I'll refrain from adding it back in. Sardonicone 05:07, 7 March 2007 (UTC)
Being from North America, it was not my intent to start up any sort of Dialect war. I can see how that could happen though, which is why I'll be glad to concede that point pending a sort of consensus on the issue.
Apologies if I offended anyone. Sardonicone 05:20, 7 March 2007 (UTC)
The brief note on math/maths stood without bothering anybody for years. If either side is offended because the other side comes first, I suggest that they have way too much spare time on their hands. Rick Norwood 19:37, 7 March 2007 (UTC)
I've made it shorter. Is that better? I grew up with "math" -- "The guy who taught us math, who never took a bath, acquired a certain measure of renown..." -- but I find "maths" charming, like schoolgirls in neckties. Rick Norwood 20:11, 7 March 2007 (UTC)
"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 :)
This article contains many sections without any references. I tagged those sections with {{ unreferenced}}-- Sefringle 03:45, 23 March 2007 (UTC)
According to wiki policy, if something is so well known that it doesn't "need" a reference, then it is also so well known that it is easy to provide a reference, so provide one. Why not? I'll start. Rick Norwood 12:58, 23 March 2007 (UTC)
I took care of two. Are there others? Rick Norwood 13:32, 23 March 2007 (UTC)
But inline references are handy, and answered a question that somebody went to the trouble to ask. Rick Norwood 00:29, 24 March 2007 (UTC)
Also note the comment in the discussion of whether or not this should be a Featured Article where someone faults the paucity of inline references. Rick Norwood 21:08, 29 March 2007 (UTC)
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)
Marsch made the edit "fixme: explain what that equation has to do with the picture". I undid the edit. The picture is clearly a plot of the function z(x,y) with the color determined by the z value at every point (x,y). Eighty 05:58, 25 April 2007 (UTC)
I'm not sure if this is where the following belongs. I rather suspect that it is not. But I don't know where it actually does belong.
Wikipedia is suppossed to be a general encyclopedia. Why then, do so many articles on mathematics related subjects require a strong background in mathematics in order to understand them? Is it truly impossible to write an article on a mathematics subject that is comprehensible to the general public -and- useful to someone who requires more in depth information - particularly is it truly impossible given that we can benefit from Wikipedia not being paper?- 198.97.67.56 16:10, 20 April 2007 (UTC)
Rick Norwood 15:16, 22 April 2007 (UTC)
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)
This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 5 | ← | Archive 9 | Archive 10 | Archive 11 | Archive 12 | Archive 13 | → | Archive 15 |
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)
I have made a request regarding this issue here. -- ScienceApologist 21:03, 26 September 2006 (UTC)
The word discipline in the definition of mathematics invokes evokes some very negative connotations that reinforce the perception that mathematics is not fun.
The word discipline has, among others, these senses (from various dictionaries):
And if the above is not enough, there is BDSM.
-- Jtir 14:57, 30 September 2006 (UTC)
Discipline (definition 2): a branch of knowledge, typically one studied in higher education : sociology is a fairly new discipline. Stephen B Streater 17:23, 30 September 2006 (UTC)
This is, of course, a subject that keeps coming up. I think the current opening paragraph captures what the quoted definitions have in common, and the question of whether math is a science is too controversial for us to use the word "science" in the opening paragraph.
The quoted definitions take one (or both) of two approaches. One approach is to give some kind of list of the topics studied by mathematics. This is, I think, how non-mathematicians think of mathematics. Note that astronomy was once considered mathematics but is now considered a science. Any such list is necessarily incomplete, but our list seems to me as good as any, and is reflected throughout the article as well as in other articles. I opposed the "list" approach, but when I was outvoted, I helped to make the list consistent throughout.
It seems clear to me, as a professional mathematician, that the other approach is correct, and that mathematics is that body of knowledge discovered by deductive reasoning. Science, in contrast, is that body of knowledge discovered by inductive reasoning based on careful observation and measurement. But, again, I was outvoted, and am happy that deductive reasoning at least gets a mention in the opening paragraph. Rick Norwood 13:17, 2 October 2006 (UTC)
I prefer discipline and I'm opposed to science, simply because it's not agreed this is the case (evidenced in the monster of a footnote you have had to include, an entire section in this article and the science article), not because I have an opinion either way. Is branch of knowledge really better than discipline?
I think most people refer to these .. things .. as an academic discipline as opposed to a branch of knowledge (google agrees with me when I googled those two terms), though either seem to be in use so I'm not totally opposed to the latter being used here. Not that my own limited experience counts for much, but I've found that branch of knowledge tends to be reserved for more specialised topics within a discipline.
I don't think it's possible to mix up academic discipline and BDSM given the context of the article. If you're really concerned about this, a simple wikilink as I've done here and the addition of the word academic would more than suffice. Most words have more than one meaning, we'd never be able to avoid them all, but at least this way we remove the possible ambiguity and stick to the apparent norm for describing subjects/fields of study/etc while the academic discipline article goes into more detail if necessary for the user, including using the term branch of knowledge. darkliight [πalk] 06:47, 3 October 2006 (UTC)
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)
I have moved almost all of the inline references to a separate References section, fixed a few {{cite}} templates, and added one new reference on the Fields Medal. For most of the ones that I moved, the inline citations are now either an author's name, or a quote with the author's name. This approach is nice because it puts the references in one place and it removes clutter from the body of the article (esp. clutter due to the {{cite}} templates, which, although they are very flexible, take up a lot of space). It is also easy to cite a work multiple times. The order and naming of the end sections follow Wikipedia:Guide_to_layout#Standard_appendices. The Earliest Uses of Various Mathematical Symbols is a fantastic reference, which could probably be cited more than once in the article, but I haven't decided what "author" I should attribute it to. -- Jtir 21:12, 2 October 2006 (UTC)
The new lead sentence contains all the mathematical concepts that I could identify in the first and third sentences of the original, adds some others (notably theorem and proof), and organizes them in a logical sequence.
The second sentence distinguishes between pure and applied -- it needs to be extended.
The third sentence concerning the evolution of math in the new lead is not changed from the original. It needs a brief transition from the definition of applied.
I used bulleted clauses after realizing the sentence would be unreadable otherwise. The new structure is highly adaptable and can be extended ad infinitum, if needed. The phrase relating mathematics to knowledge and science is also flexible and it could even be removed without modifying the rest of the definition. I didn't wikify it because it is too hard to edit complex sentences that are fully wikified and I expect there will changes. :-)
-- Jtir 17:39, 3 October 2006 (UTC)
I'm very impressed with this article, especially the illustrations. But the first sentence is really awkward. Of the definitions cited above, I'm most impressed with Britannica ("Science of structure, order, and relation that has evolved from counting, measuring, and describing the shapes of objects.") Yes, I have read the above discussion and I have already learned that it is difficult to give good definitions on wikipedia, where you have to accommodate every minority view. That is a pity, because this article is really beautiful. (well done!) -- Vesal 21:02, 3 October 2006 (UTC)
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)
So anyway, this is what I will do, I will create the subpages, and since it is your discussion that I will be summarizing, I would ask you guys to look them over. If you find them helpful, we could put them on more prominent position. I will begin with the /FAQ and then the topical subpages:
-- Vesal 21:50, 3 October 2006 (UTC)
I started the FAQ, see what you think. Since this is a core article of wikipeda, there might be future drives to improve quality and I think a FAQ is useful to avoid having the same "Is math a science debates" all over again. I personally would state in the lead that math is a science, but the purpose of the FAQ is to give the answer quickly to people like me. -- Vesal 15:54, 4 October 2006 (UTC)
What is the point of this, if you are not going to go back through the archives to find all the discussions about the intro, etc? If the subpage is only going to contain the recent discussion, it may as well be on this page. JPD ( talk) 10:26, 5 October 2006 (UTC)
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:
Very much in line with the todo list. -- Vesal 23:27, 4 October 2006 (UTC)
I wouldn't object to this section being incorporated into a philosophy of mathematics section, but I don't think that it is POV use something like "mathematics as science" as a heading for a section discussing the different views on whether/how maths is (a) science. On that topic, now that Poppers views on the matter have been clarified, the mention of Lakatos' work doesn't quite fit in. I am not sure whether it should be removed or reworded. I am also not sure why the Einstein footnote is needed. As the text suggests, the Einstein quote supports the view that pure maths is not science if you take a partiuclar view of what science is. The text doesn't suggest any more than this, and the footnote doesnt' seem to clarify much anyway. JPD ( talk) 10:45, 5 October 2006 (UTC)
It is not entirely clear what the new paragraph means in its assertion that mathematics is not "reducible" to logic. I suppose it has something to do with undecidable questions such as the continuum hypothesis. I know there are some people who claim that we can replace logic by either experiment (if a computer can't find a counterexample to the Riemann Hypothesis, then it must be true) or intuition (the Riemann Hypothesis must be true because it is beautiful) but as several people have observed, comments on the subject in this article should be a) basic and b) referenced. Rick Norwood 13:37, 5 October 2006 (UTC)
About the footnote on Einstein... Yes, it is very badly written, I tried quite hard, but it is very difficult to explain a long essay in a few words with my bad english. The problem is that the quotation is out of context. When Einstein is arguing that a pure branch of mathematics like geometry really depends on the physical world, I find it unethical to cite him as saying quite the opposite. Disclaimer! I might be wrong about what Einstein is arguing for in the essay, but I did read all of it, and it sure seemed the point was that pure math is a science. In fact, very similar to the views of Popper. --
Vesal 21:24, 5 October 2006 (UTC)
I have created three more Talk subpages and put links to them in the Talk page infobox:
They have already been set up with a brief descriptive header and populated with a least one entry. You may use that entry as a prototype for more entries.
The objective is to collect material that can be used to broaden the scope of the article. It is not to redo the work of wikipedians, which is what I was doing until Vesal set me straight. :-)
Would a subpage called "Mathematical Creativity, Intuition, and Aesthetics" be of interest? (I could probably find some quotes by Poincaré, Polya, or Einstein in this area.) -- Jtir 18:12, 5 October 2006 (UTC)
Some of the subpages are not for discussion, they are for collecting and organizing information. Editors may add information to them or correct them, but there is no discussion on them. Here are two hints:
-- Jtir 15:13, 6 October 2006 (UTC)
Maybe the argumentative parts of "mathematics as science" could be entirely ditched in favor of a portrait gallery of famous mathematicians, philosophers and artists with a quotations on mathematics. In particular on what they think mathematics is. So the idea is a slight extreme of what has already be suggested, that we don't define mathematics. But what do you think about the idea of basically only pictures and quotations instead of "Some mathematicians think...". A good place to collect them is of course the /Conceptions_of_mathematics page, even if we don't do pictures and quotes, it would still be very nice to have opinions from maybe Hardy on math for math's on sake etc, maybe like "A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas." stolen from the G. H. Hardy page. -- Vesal 23:05, 5 October 2006 (UTC)
I've written a sample gallery into the sandbox. The Picture_tutorial illustrates some other options. -- Jtir 14:34, 6 October 2006 (UTC)
The movie Good Will Hunting is an example of mathematics in popular culture. I was thinking of developing an infobox featuring it. The use of low-resolution images is OK, according to the copyright boxes for these images.
My reasons are:
NB:
The
Good Will Hunting article refers to the problem as an equation: "...wondering who could have solved the equation."
At another point the article reads: "...astonished assistant staring at the correctly solved theorem."
The
Parseval's theorem article does not mention the movie.
Any comments or suggestions? -- Jtir 20:34, 6 October 2006 (UTC)
Mathematics is also a thing that each and every single one of us do every single day. For example, when you are drinking water, your arm makes an angle. When a person lays down on a bed, this person makes a straight line. And if you pay attention of what a person is doing, he or she would see that Mathematic in there. Franck Jr. Colas, 18:26, May 14, 2007.
For example:
:{| style="border:1px solid #ddd; text-align:center; margin: auto;" cellspacing="15" | [[Image:Pythagorean.svg|96px]] || [[Image:Taylorsine.svg|96px]] || [[Image:Osculating_circle.svg|96px]] || [[Image:Torus.png|96px]] || [[Image:Koch curve.png|96px]] |- |[[Geometry]] || [[Trigonometry]] || [[Differential geometry]] || [[Topology]] || [[Fractal geometry]] |}
which looks like:
BTW, WP:MOS#Images is a guideline. -- Jtir 16:18, 7 October 2006 (UTC)
<!-- Infobox --> {| cellpadding=3px cellspacing=0px class="wikitable" style="float:right; border:1px solid; margin-left: 1em" |colspan=2 align=center style="margin: 10px; border-top:1px solid"|[[Image:Adi Shankara.jpg|center|200px]] |- !style="background:#f90; border-bottom:1px solid" align=center colspan=2|Adi Shankara |- |align=center style="border-top:1px solid"|Dates:||style="border-top:1px solid"|c. [[788]] to [[820]] [[AD]] <ref name="Dates"> There is some debate regarding this issue. {{cite book | last = Tapasyananda | first = Swami | year = 2002 | title = Sankara-Dig-Vijaya | pages= xv-xxiv }}
What you've pasted is part of an infobox, not an image with a caption. You'll notice that all the images throughout that FA use the Image: syntax. darkliight [πalk] 17:02, 7 October 2006 (UTC)
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):
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.
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)
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)
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)
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)
Mathematics is certainly an academic discipline, but it is clearly more than that. The implication of the former lead was that mathematics was restricted to being an academic discipline, which is just not true. Paul August ☎ 18:42, 2 November 2006 (UTC)
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)
Actually, a lot of this article is horribly pretentious and not useful, nor understandable by a person interested in looking at the various fields of mathematics. The subject is hard as it is, why deter people from it by just stating that everyone who studies it has their head stuck up their asses? BTW, I was the one who removed it, and I think the "misconceptions" part should be taken too. —The preceding unsigned comment was added by 216.165.37.30 ( talk • contribs) 03:16, November 16, 2006 (UTC).
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)
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)
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)
Why is this article partially locked? Charles (Kznf) 21:35, 29 January 2007 (UTC)
Probably because someone, likely a high school student or University student was vandalizing the page. I'm not sure, but it seems like the kind of thing that would happen...
Trocisp 17:44, 30 January 2007 (UTC)
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)
Oh wait, its under the picture, never mind =P. Talcite 02:44, 5 February 2007 (UTC)
The article asserts that fallible intuitions have led to mistaken "theorems" often in the history of Mathematics. This may be, but the link provided does not seem to support the assertion very well. Most of the examples at the other end of the link are simple algebraic errors, not mistakes of the kind Newton, Descartes or Euler might have stumbled into for lack of sufficient rigor. I have not edited the article, but if you want to edit it in the matter, feel free. Tbtkorg 17:11, 28 February 2007 (UTC)
This is not quite what I'm looking for, since most people would naively agree that in the plane given a point and a line there is one and only one parallel to the line through the point. This can't be proven, but it is generally accepted. I'm looking for a statement that was asserted by mathematicians, and given a falacious proof, which later turned out to be mathematically (rather than metamathematically) incorrect. Of course, there have been lots of "proofs" that, for example, pi is rational, but no real mathematician accepts these. Can the record of mathematics in establishing truth really be that good? Rick Norwood 12:55, 17 March 2007 (UTC)
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)
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)
I disagree. For most terms in wiki - we do add the [edit] Etymology of the word, as well as possible variants.
Sardonicone 04:59, 7 March 2007 (UTC)
If it's fairly close to standard practice with other articles, I fail to see how it really affects this one as well.
However if there's a concensus to remove it, I'll refrain from adding it back in. Sardonicone 05:07, 7 March 2007 (UTC)
Being from North America, it was not my intent to start up any sort of Dialect war. I can see how that could happen though, which is why I'll be glad to concede that point pending a sort of consensus on the issue.
Apologies if I offended anyone. Sardonicone 05:20, 7 March 2007 (UTC)
The brief note on math/maths stood without bothering anybody for years. If either side is offended because the other side comes first, I suggest that they have way too much spare time on their hands. Rick Norwood 19:37, 7 March 2007 (UTC)
I've made it shorter. Is that better? I grew up with "math" -- "The guy who taught us math, who never took a bath, acquired a certain measure of renown..." -- but I find "maths" charming, like schoolgirls in neckties. Rick Norwood 20:11, 7 March 2007 (UTC)
"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 :)
This article contains many sections without any references. I tagged those sections with {{ unreferenced}}-- Sefringle 03:45, 23 March 2007 (UTC)
According to wiki policy, if something is so well known that it doesn't "need" a reference, then it is also so well known that it is easy to provide a reference, so provide one. Why not? I'll start. Rick Norwood 12:58, 23 March 2007 (UTC)
I took care of two. Are there others? Rick Norwood 13:32, 23 March 2007 (UTC)
But inline references are handy, and answered a question that somebody went to the trouble to ask. Rick Norwood 00:29, 24 March 2007 (UTC)
Also note the comment in the discussion of whether or not this should be a Featured Article where someone faults the paucity of inline references. Rick Norwood 21:08, 29 March 2007 (UTC)
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)
Marsch made the edit "fixme: explain what that equation has to do with the picture". I undid the edit. The picture is clearly a plot of the function z(x,y) with the color determined by the z value at every point (x,y). Eighty 05:58, 25 April 2007 (UTC)
I'm not sure if this is where the following belongs. I rather suspect that it is not. But I don't know where it actually does belong.
Wikipedia is suppossed to be a general encyclopedia. Why then, do so many articles on mathematics related subjects require a strong background in mathematics in order to understand them? Is it truly impossible to write an article on a mathematics subject that is comprehensible to the general public -and- useful to someone who requires more in depth information - particularly is it truly impossible given that we can benefit from Wikipedia not being paper?- 198.97.67.56 16:10, 20 April 2007 (UTC)
Rick Norwood 15:16, 22 April 2007 (UTC)
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)