Talk:Mathematics

Template:WP1.0 The main page for discussing math-related issues on Wikipedia is Wikipedia talk:WikiProject Mathematics.

Archives
Chronological archives
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
Information subpages
Conceptions of mathematics Notable theorems and conjectures Jokes, anecdotes, puzzles, games, riddles Source material
Discussion subpages
New Editor FAQ

Pictures

This is just a suggestion but could we try to find better pictures for differentail equations (and possibly differential geometry) in "Fields in mathematics" since these two don't look as asthetically pleasing as the others. Algebra man 13:18, 20 June 2007 (UTC)

Cubes

"Mathematics has since the time of ancient Greece, been a set of variances of agreed scale to calculate the number of singular item of use to the commercial environment, even the Romans had no use for 0, nothing or not worth anything. Why then is there a need today for any other type of mathematics, well no longer are we limited by the use of the human brain for our ability to recall knowledge, we have at our control the ability to program a system of electrical impulses to enable a Knowledge retrieval and calculation system called a computer via a system of knowledge retrieval information pods called the internet, to store unique pieces of Knowledge relating to unique areas at unique times. It is this unique singular ability that will take us to another system of calculation, “compound mathematics”. This is the ability to use the unique singular knowledge about any unique area of space at any unique singularity of time, to justify the next event in that unique area of space in the next singularity of time. It is the interaction of the compound effect of the changes caused to these unique areas of space by other unique areas of space over a series of singularities of time that along side the basic principal of physics will become a fresh approach to Calculate the evolvement of knowledge. So how do I justify this claim, for many years I have been trying to justify the ability, to fit a cube in a square. Infact my entire life has been trying to achieve this impossibility. Yet, Albert Einstein tells us in one of the greatest scientific human achievements of all time “The splitting of the atom” that Energy is Equal to the mass of light squared."

Perhaps if I was an academic person I could understand the basis of this equation better, but I am not an academic. I consider myself a practical person and earn my living not from theoretical theories but my ability to turn ideas into actual practical useful objects. It is this practical perspective of the laws of nature that have given me so much trouble with Mr Einstein Equation. A mass by dictionary definition must be, Lump – a body of matter that forms a whole but none definable shape. Collection – a collection of many individual parts. Great unspecified Quantity – a large but unspecified number or Quantity. Physics physical quantity – the property of an object that is a measure of it inertia, the amount of matter it contains, and its influence in a gravitational field. Symbol m. The problem I have is how you can put a mass in a square. A dictionary definition of a mathematical square

“the produce of multiplying a number or term by itself”.

In the practical world I live in any number multiplied by itself must produce an area, and because it has no third dimension. This area cannot even have a surface, because to create a surface you require three dimensions. How does a non-academic practical person, tell a world of academic physics masters. That the most famous equation in the World, E=Mc2 is fine if you are looking to justify the “current situation”. But this must lock you into the present situation where you have only one fixed set of variance. Somewhere between a super nova spewing massive amounts of matter from a magician’s hat, to a matter gobbling black hole putting it back into the magician’s hat, but unable to explain “WHY”. Hence a singularity. “ONE EVENT”. So how can we take the singularity of this one event to another horizon. simply by taking energy to the point its velocity is equal to the mass of light cubed. you will not only discover your missing "dark matter" but find a path through the wormhole of your current impass. To understand more go to Spacetime @ talk page of cubedmass. --Thor 14:54, 1 July 2007 (UTC)

First, please add new material at the bottom of the page. That is where people look for it. I've moved your comments here.

I think most of your problems are linguistic rather than scientific or mathematical. For example, in E = mc^2, the "square" has nothing to do with the geometric figure called a "square" but rather uses the second definition of the word, a number multiplied by itself. You seem to think that the only situation in which we might multiply numbers is to find area, but that is not the case. For example, if I multiply the number of hours I work each day by the number of days I work each week, I arrive at the number of hours I work each week. But there is no area involved -- no-one is claiming that hours can be an area. Rick Norwood 15:09, 1 July 2007 (UTC)

I thank you for your help and comment I also understand that in the singular how you have arrived at the number of hour worked in a given period of time. but to work that number of hours in that period of time energy must have been transfered from your effort to your product.

This must as you have stated occured over time and the energy you have used to create your product will have to be replaced or you cannot work further periods of time. My though is how does this energy transfer through time. in your use of singular mathmatics you have explained how you have used unique amount of energy in a unique period of time to create a unique product in a unique area of space. this i see as singular or squared area. What i want to create is a interaction between the singularity of a unique energy used at a unique space and time and its effect on the total amount of available energy over the total amount of available space in the next unique moment in time. Because energy can,t be lost it can only be changed. i know this cannot be done using singular or squared energy to mass ratio because although this justifies the current unique spacetime it can,t take you to the next unique spacetime because it has no means of interacting with other units of unique spacetime. to do this you need a compound or cubed energy to mass ratio it is that will create the interaction to create the next unique unit of spacetime.--Thor 18:14, 1 July 2007 (UTC)

The energy expended in answering your question comes ultimately from the source Einstein described in his famous equation. In the sun, gravity causes fusion which releases energy which reaches the earth in the form of sunlight. The sunlight falling on plants is converted into chemical energy by photosynthesis. When I eat those plants, the chemical energy is converted into a form that can be used by my muscles to allow me to type on a keyboard and answer your questions.

The energy to mass ratio is not squared. Rather it is itself a square, the square of c. This is, however, a purely arithmetic square, not a geometric square.

You seem to assume that the time dimension is quantized rather than continuous. This is still an open question. As you observe, the assumption that time is quantized leads to serious problems. It may be that time is continuous. Rick Norwood 22:45, 1 July 2007 (UTC)

again i must thank you for your comments. the main problem, i have no academic knowledge (although i'm tryin to learn/understand it). so my ability to comunicate in the type of academic language curently understood will not be possiable. However i hope you will hummer my quantized rather than constinuous vision of time, because that is what it is. because i'm not academic i perceive in my practical Knowledge as a quantified chain of events not a continous chain of events. Einstiens relativity along with newtons "equal and opposite" and the many other rules or laws of physics have built up into our knowledge of the subject. you will find in general that the rules or laws that our individual knowledge of physics understands is the rules and laws as individuals we will agree with or disagree with. This in turn will devide us into groups that agree or disagree with therectical propositions. but every individual or group will base there view on the level of knowledge at there disposal. I will know try to my comunicate my views,Sorry i have to go back latter--Thor 16:09, 2 July 2007 (UTC)

The purpose of this page is to discuss improvements to our encyclopedia article on Mathematics. Wikipedia is not a forum for general discussion. If you have specific questions on scientific topics, you can ask such questions at the Science section of our reference desk. Thank you.  --Lambiam^Talk 08:35, 3 July 2007 (UTC)

Many thanks for your comments,I honestly wish my ability to comunicate was better but I understand better than most in "conceptual fact" but my beleif is still nobody will ever understand the dicipline of the ability to use mathematics with your academic perception of only one understanding of 0 plus the ability to use + or - to take towards or away from the concept of answer you seek but I wish you well and will continue to follow. cubedmass 13.07 07

First Sentence

I believe there should be an "is" after "change" in the first sentence. ". . .change, and is also. . ." Otherwise, "the academic discipline" is also one of the subjects of "Mathematics" along with quantity, structure, space, and change. I'm not an English teacher, so someone else will have to make this change.

The present first sentence is short for:

"Mathematics is the body of knowledge centered on concepts such as quantity, structure, space, and change,

and

mathematics is also the academic discipline that studies them."

In an English sentence like that, you can leave out the repetition of "mathematics is" after "and" without change of meaning. Although potentially ambiguous, I think the risk of an actual misinterpretation is small.  --Lambiam^Talk 10:15, 6 July 2007 (UTC)

Mathematics concept collage

Recently the image Mathematics concept collage was added to the article. Personally I'm less than enthusiastic about the image, because it reflects and propagates the misconception that Mathematics = lots of formulas. I don't see any added value. But perhaps others are happy with it and I'm just alone in my grumpiness. So I don't want to remove it straightaway without inviting some opinions.  --Lambiam^Talk 14:26, 7 July 2007 (UTC)

I don't mind the image. If several people dislike it, it should go. I moved it a little further down the page. Rick Norwood 14:28, 7 July 2007 (UTC)

I don't like it much. The images in the navigation boxes further down do a much better job of expressing the richness of mathematics, in my view. It might be more appropriate for an article on high school mathematics, or perhaps mathematics education. -- Avenue 15:27, 7 July 2007 (UTC)

I agree with Avenue. It doesn't seem to take a broad enough view of mathematics. JPD (talk) 18:51, 8 July 2007 (UTC)

I also dislike the image, for similar reasons to Lambiam, Avenue, and JPD. EdwardLockhart 08:06, 9 July 2007 (UTC)

I dislike it too. I've removed it. --Zundark 08:18, 9 July 2007 (UTC)

Good. Paul August ☎ 22:56, 9 July 2007 (UTC)

Images for applied mathematics

Mathematical physics

Analytical mechanics

Mathematical fluid dynamics

Numerical analysis

Optimization

Probability

Statistics

Mathematical economics

Financial mathematics

Game theory

Mathematical biology

Cryptography

Operations research

I liked the idea of illustrating different areas of mathematics with images and thought I'd extend it to the section about applied maths. Above, I give an incomplete suggestion and I need you to fill in the gaps. Does protein folding fall under mathematical biology? This could be an alternative for fluid mechanics. Finally, the table is too wide and won't break automatically, so someone who knows how needs to fix it. —Bromskloss 15:54, 30 May 2007 (UTC)

Nice work, Bromskloss. I've gone ahead and added a shortened version of the the above to the article. Paul August ☎ 13:48, 20 June 2007 (UTC)

I replaced the ugly Image:Trapetsmetoden.png (see right) with Image:Finite element solution.svg (see right, below). The latter is my own picture, and better illustration of numerical analysis can be found perhaps, but I'd argue it beats the original picture. Oleg Alexandrov (talk) 03:54, 16 July 2007 (UTC)

Used for calculus

Ok. Actually, I don't think the original one was that bad. Handwriting is kind of cosy :-) and you can hardly see it in the scaled-down image anyway. However, the main reason for the original image was that it is analogous to the one used for calculus. —Bromskloss 14:55, 22 July 2007 (UTC)

I call for others to share their opinion on this. I think we are better off with the original image (numerical integration) than the current (finite element), for three reasons:

• More fundamental to numerical analysis
• Analogous to calculus illustration
• The current one is very similar to the optimization illustration

—Bromskloss 05:17, 10 August 2007 (UTC)

New numerical integration picture

.

Then how about using the "new numerical integration" picture on the right, instead? My only concern is that the hand-drawn picture is ugly. Oleg Alexandrov (talk) 15:33, 10 August 2007 (UTC)

I think it is best to view the three images in context. So we have:

Original:

Mathematical physics	Mathematical fluid dynamics	Numerical analysis	Optimization	Probability	Statistics	Financial mathematics	Game theory

Current:

Mathematical physics	Mathematical fluid dynamics	Numerical analysis	Optimization	Probability	Statistics	Financial mathematics	Game theory

Proposed:

Mathematical physics	Mathematical fluid dynamics	Numerical analysis	Optimization	Probability	Statistics	Financial mathematics	Game theory

So far I like the original best. (Oleg: there is just no accounting for taste ;-) I think the handwritten drawing looks informal but not ugly. For me the "beauty" of a diagram is one that communicates well — so I hope all of the blackboard drawings I've done were beautiful, though handwritten. It also helps to remind (or even inform!) that mathematics (for a little while longer at least) is done by people not machines. Paul August ☎ 16:42, 10 August 2007 (UTC)

I also prefer "original". I can see the charm of hand-drawn diagrams but that's not the most important for me. The "current" diagram does not yell out numerical analysis to me. I don't like the "proposed" diagram at this size; I'm not sure what the problem is but the red and blue curves are hard to distinguish and the dash lines look odd when shrunk so much.

I notice only now that there is also a "game theory" image. That disappears behind the right edge of the window on my laptop (screen size 1024 x 768). Should we distribute the images over two rows for poor people like me with small screens? -- Jitse Niesen (talk) 04:23, 11 August 2007 (UTC)

Apart from the charm of diagrams and such clumsily drawn on napkins (but how did the stars get there? were they pasted on?), can someone explain how the "original" image illustrates the "Trapezium rule" other than in a quite confusing way, what with the steps up and down? Or if it does not illustrate that rule, then what does it represent? Maybe we should also consider other candidates, for example an illustration of finding zeros using the regula falsi or Newton's method.  --Lambiam 05:12, 11 August 2007 (UTC)

Indeed, is the hand-drawn picture an accurate representation of the trapezium rule? Oleg Alexandrov (talk) 06:04, 11 August 2007 (UTC)

Secant method

Regula falsi

Newton's method

On the right are some other numerical pictures, following Lambiam's suggestion. They won't scale well either to the small size.

If agreed that the illustration of the trapezoidal rule without the staircase which Jitse says has the curves too close (I agree) is a better picture, I can make a version of it to look better small (disclaimer: I made the original, although I hope I am not driven by selfish interests here :) If the hand-drawn picture is agreed to be a better illustration, it can be recreated in SVG easily. Oleg Alexandrov (talk) 06:25, 11 August 2007 (UTC)

For an image illustrating the trapezoidal rule I'd recommend to have equidistant "sampling". The following function has been engineered to have a few relatively but not excessively large deviations from the linear approximations when sampled at integral x, for x = 0 to 5:

0.05x⁶ − 0.762x⁵ + 4.229x⁴ − 10.188x³ + 9.116x² + .638x + 0.66.

 --Lambiam 20:30, 11 August 2007 (UTC)

Nice job, that should be easy enough to plot. What we did not agree on is whether there should be a staircase or trapezoids when discretizing (I'd argue for the latter). Oleg Alexandrov (talk) 00:34, 12 August 2007 (UTC)

If it was called the staircase rule I'd probably argue for staircases, but it ain't.  --Lambiam 02:21, 12 August 2007 (UTC)

But it doesn't resemble the non-numerical image, and it would be nice if it did. —Bromskloss 07:29, 20 August 2007 (UTC)

(de-indenting) I think the hand-drawn picture is a fair representation of the trapezium rule. It it based on the fact that the trapezium has the same area as the hexagon. My hand-drawing-with-ASCII-symbols skills are not up to the challenge, but perhaps the following will clarify what I mean.

               _
    /|        | |
   / |        | |
  /  |  =    _| |   
 |   |      |   | 
 |___|      |___|

However, I didn't recognize the picture as illustrating the trapezium rule. I thought it was approximation by a piecewise constant function, as in nearest neighbor interpolation, or perhaps integration by the midpoint rule. There is nothing in the picture that says it's the trapezium rule; where did you get that idea? -- Jitse Niesen (talk) 02:44, 12 August 2007 (UTC)

I don't know. :) I guess from comparison with the other picture. The point is still the same, to we want trapeziums or a staircase? In the meantime I tweaked the trapezium rule picture to make it look better small, see to the right (96px, as in the gallery above). Again, the ugly picture can me made svg too, the issue is of staircase vs trapezium. Oleg Alexandrov (talk) 03:30, 12 August 2007 (UTC)

The name of the image is Image:Trapetsmetoden.png, and trapetsmetoden is Swedish for "the trapezium method". The article on the Swedish Wikipedia actually contains ASCII art, with a staircase, of arguably greater sophistication than displayed by Jitse.  --Lambiam 06:12, 12 August 2007 (UTC)

Apparently the discussion here died out. I replaced my finite element picture with the trapezoidal rule seen on the right. Again, if people prefer the straircase figure, let me know, and I can recreate it in SVG. Oleg Alexandrov (talk) 01:55, 18 August 2007 (UTC)

More images

Purely a question of aesthetics. Preferences? Suggestions? --Cronholm¹⁴⁴ 03:01, 19 August 2007 (UTC)

I prefer the left one. —Bromskloss 15:11, 11 September 2007 (UTC)

The left one makes the overlap more obvious — the gradients are only distracting. ⇌Elektron 16:53, 11 September 2007 (UTC)

I think the one on the right is prettier, while the one on the left might be clearer. For a survey article, I favor using the prettier one (which is indeed in use now). Suggested improvement: don't lighten the border around the left circle in the overlap area. Right now, both images look like two colored lenses, with the right lens above the left one. Removing the visual cue for Z-order will help lead the viewer to see this as a symmetrical relationship. --Ben Kovitz 14:53, 17 October 2007 (UTC)

GA status reviewed

This article has been reviewed as part of Wikipedia:WikiProject Good articles/Project quality task force. I believe the article currently meets the criteria and should remain listed as a Good article. The article history has been updated to reflect this review. Regards, OhanaUnited^{Talk page} 21:44, 8 September 2007 (UTC)

Abstract Algebra image

Why is the abstract algebra image a Rubik's Cube? —Preceding unsigned comment added by 151.63.84.14 (talk) 17:34, 17 September 2007 (UTC)

Abstract algebra studies algebraic structures, such as groups, and Rubik's Cube provides a tangible representation of a group: Rubik's Cube group.  --Lambiam 19:45, 17 September 2007 (UTC)

Maths vs. Math

The current introduction reads "Mathematics (colloquially, maths or math)" and I highly disagree with the placement of "maths" in front of "math". Math is the better spelling, and should come first. I believe this point is extremely important and worthy of debate. Please change this or argue about why it should not be changed. —Preceding unsigned comment added by 129.173.121.142 (talk) 20:52, 18 September 2007 (UTC)

If you're that worried about which of the two comes first, change the order. I can't see that it actually matters. --Mark H Wilkinson ^{(t, c)} 21:38, 18 September 2007 (UTC)

I don't care which comes first, but you are on very shaky ground if you argue that one form is "better" than the other - they are just different conventions. I believe that "maths" is the norm for English speakers outside of North America. Certainly "maths" is the norm in England - saying "math" here would make you sound very ... um ... American. Gandalf61 06:40, 19 September 2007 (UTC)

I still say we should simply remove the parenthetical remark about the colloquial names. What does it add to the article? What information does it convey that the reader doesn't already know? Just stick to "mathematics", which is the appropriate form for the formal register used in an encyclopedia article. --Trovatore 15:15, 19 September 2007 (UTC)

For one thing, Maths and Math both redirect to Mathematics, so the parenthetical remark offers an immediate explanation to the reader redirected here of the why of that redirection. I would not assume that all readers already know that these forms are common colloquial abbreviations of the word "mathematics".  --Lambiam 17:14, 19 September 2007 (UTC)

so so cool jennifer —Preceding unsigned comment added by Babygurl 305 (talk • contribs) 14:12, 1 October 2007 (UTC)

1AT. If it is a redirect, it is not needed, b/c obvious. Wikipedia:What Wikipedia is not#Wikipedia is not a dictionary, so the inclusion of the terms is unnecessary and to that degree arguably unencyclopedic, if they were colloquialisms[].

2AT. None of my 3 standard dictionaries list then as a colloquialisms. Rather, they are alternative labels.

3AT. Should the article be suggesting in the lead sentence that the bolded terms math & maths should be used as equivalent? Only if it is meant to suggest that they are equivalent terms, say in the U.S. and in Great Britain. I doubt that there is one standard encyclopedic source that so indicates for either, much less both. In that respect, it does not satisfy WP:VERIFY policy. Rather, it is an invitation to misuse or nisunderstanding as to regional differences, b/c of American & British parochialism.

4AT. If it is to be mentioned at all, the British-U.S. differences should be noted so as not to mislead, as it is in section 1. Why not keep the first sentence clean and simple and save the parochialism for sect. 1? --Thomasmeeks 02:07, 17 October 2007 (UTC)

1. Its confusing to pop to this page without the lead explaining why. Its NOT obvious to someone from the opposite side of the Atlantic.
2. I'm not sure calling them alternate labels means much. People will enter math or maths wanting the information in this article.
3. math & maths ARE used as equivalents to mathematics. Entering "math" or "maths" in m-w.com and you get: "mathematics."
4. What are people going to be mislead about? In any event, I think any possibility of misleading are minimal compared to the confusion someone coming on the page by surprise.

I think it useful to have math and maths in the lead to explain why the user ended up on the page. If they want to know the etymology, it can be found below. I plan to switch the lead back. (John User:Jwy talk) 02:55, 17 October 2007 (UTC)

I think it's really unlikely that there are very many users who type either of those terms into the search box and are surprised where they wind up (likewise for internal links). I don't question the accuracy, which was what you referred to in your edit summary, just the value. It's aesthetically hideous, so for it to be there there ought to be a compelling reason, and I just don't see it. --Trovatore 03:22, 17 October 2007 (UTC)

The phrase "(colloquially, maths or math)" strikes me as pedantic. I don't think a native English speaker would be confused by the redirect. However, a great many Americans don't know that "maths" is the British version of "math". So, even though I don't like it, I think it's OK to keep the phrase. Also, I just checked refrigerator and indeed it mentions "fridge" in a parenthetical comment in the lead. Television includes lots of colloquialisms. So I think we are actually being consistent with the rest of Wikipedia here, without becoming a dictionary. --Ben Kovitz 14:44, 17 October 2007 (UTC)

Well, I withdraw my point (2AT) above. My standard dictionaries don't seem to mention any colloquialisms.

1BT. Still, "(colloquially, maths or math)" is unnecessary there. In the Lead, the phrase lacks the context provided in sect. 1 on regional differences, thus arguably violating WP guideline to WP:LEAD#establish context. Including that context in the Lead would bog the Lead down. A N. American might wrongly conclude they the terms were equivalent in use there, when they are not. That is misleading. Similarly for a Brit. Inclusion there is unnecessary except on the assumptions the few readers unfamiliar with the connection of mathematics to math(s) would not be able to figure it out from the Redirect. So, not only is its presemce there arguably pedantic but patronizing and misleading. Finally, mathematics is a scholarly subject. Shouldn't the lead indicate that, rather than not try to bulwark against extremely rare contingencies by writing down to its audience?

On Jwy's points, I regret that I was unclear, concerning which let me try to do better:

1CT. Assuming away common knowledge is arguably a formula for overwriting.

2CT. Point (2) above neglects the misleading inoompleteness of the objectionable phrase. Anyone who ends up at the article has the Disabiguation at the top & sect. 1 to help out. I believe that the hypothetical person of concern is a virtual singularity.

3CT. The objectionable terms are not equivalent within each geographic region, the failure of which to mention is misleading.

4CT. See (4CT) immediately above. --Thomasmeeks 20:20, 17 October 2007 (UTC)

Thomas, it sounds like we agree in our distaste for the phrase. Let's see if I can answer your objections, though, since, after reading all of the above and thinking about it, I came to the opposite conclusion.

• Is there a concise way to say that "maths" is British and "math" is common in the United States? I agree that we are perilously close to overwriting here, so an especially concise wording would be best. Or, in favor of keeping the phrase and not explaining the regions in the lead: Is it not fairly common on Wikipedia for introductions to mention alternate terms in use in different geographical regions, without spelling out these regions? For examples, see Dosa, Hing. Hero sandwich locates the main phrase to New York but doesn't tell which regions use the alternate terms. This seems encyclopedic to me without stepping into dictionary-land or regional-glossary-land.
• Indeed, assuming away common knowledge is terrible, but I'm quite sure that a majority of Americans don't know that mathematics is called "maths" elsewhere. (I didn't know that hing is called "giant fennel" until a moment ago.;))
• Isn't it commonplace and proper on Wikipedia to list common informal synonyms in the lead, especially when it's likely that many people haven't heard them? (Refrigerator, Television, etc. You can probably find more.) This combined with the previous point is what swung me to favor keeping the phrase.
• Regarding establishing context, I believe that principle refers to the conceptual context of the whole topic, not the geographic context of the term, e.g. "abstract algebra" in the article Group (mathematics).

--Ben Kovitz 21:38, 17 October 2007 (UTC)

Just because there are lots of other articles that do it doesn't necessarily mean it's a good thing to do. But to be honest, I don't care as much if refrigerator is written in a distracted and distracting style. Who cares? It's just about refrigerators. I don't think we should have that tone here.

It may be that there are lots of Americans who don't know the word "maths", but I don't think we should be particularly at pains to teach it to them in this article, and certainly not in the lead. It's not a mathematical issue. --Trovatore 22:15, 17 October 2007 (UTC)

1DT. Ben Kovitz's 1sr point above is to recomment a concise statement of U.S./British use of math/maths in the Lead rather than simply deferring it to section 1, presumably b/c different colloguialisms in the 2 different national areas are too interesting and important to defer and are worth repeating. This despite the presumable minuscule fraction of potential readers unaware that math or maths refers to mathematics. If that is not overwriting, it would be hard to cite an example. Asserted analogies cited are Dosa, Hing. Hero sandwich Refrigerator, Television, "etc.," but significantly not scholarly subjects (for one good reason, they do not appear in WP or other broad scholarly-discipline articles). The lack of parallel is unpersuasive.

2DT. Is it so important nations learn each others colloquialisms in the Lead?

3DT. On WP:LEAD#Establish_context, the link recommends "supplying the set of circumstances or facts that surround it," the U.S./British use of math/maths in the Lead would do that but at the cost of overwriting noted in (1A). The current "(colloquially, maths or math)" lacks context. Examples that cite synonyms within a country are not parallel, nor are examples offered for the purpose of providing colorful alternatives. Why create a problem in the Lead that sect. 1 avoids?--Thomasmeeks 04:18, 18 October 2007 (UTC)

I'm not convinced:

• The phrase is short and to the point, perhaps misleading - but misleading only in its brevity. It IS the lead, the full explanation follows for those who might get it wrong. I agree adding a fuller explanation in the lead would make it awkward (although I'd be happy to be proved wrong).
• I still think it helps establish a navigation context for a user who was redirected.
• In addition, including the phrase as is allows a reasonably smooth way of providing the two (very common) alternatives terms early so they may appear in bold, consistent with WP:LEAD#Bold title.
• While I agree we can assume common knowledge, cross-Atlantic linguistic awareness cannot be assumed (especially my fellow Americans' awareness of Britishisms).
• And finally, we must remember the target audience of this article is not just academics.

I think these items are enough to justify a slight awkwardness. (John User:Jwy talk) 07:22, 18 October 2007 (UTC)

John & others, I have relabelled my points above for ease of reference & Strikethrough where appropriate. Let me try to address the above points. Essantially all differences come down to predicted effects on the readers, negative and positive (indluding future reviewers of this article).

1ET. "(colloquially, maths or math)": Short, to the point, and misleading -- not only in its brevity but its placement -- in the lead. Additionally it is likely to be offputting to readers on each side of the ponds (Atlantic & Pacific), b/c it seems to patronize & b/c it informs without informing sufficiently to avoid the suggestion that math & maths are to be used equivalently in each country, when most readers will know that for their country the terms should not be so used. What they might well infer is sloppy editing (discussed in more detail at 1AT, 3AT, 4AT). That is offputting and should not happen in the lead, which should rather "invite a reading of the full article." Why read further if the 1st line seems amateurish (even if it is less so than it seems)?

2ET. Confusing & patronizing readers and overwriting come closer to insult than help, despite good intentions, esp. given the Redirect note that would appear at the top and the Disambiguation note there, both of which provide "navigation context" without introducing misleading context (on which see 3AT).

3ET. "Math(s)" as "smooth transition" in the lead? Not if the above 2 points apply. WP:LEAD#Bold title does say the bolded term "may include variations." "May" is not "must," esp. for colloquialisms otherwise absent from enclopedia articles on scholarly subjects. Their use in the article lead suggests an attempt to appeal by "dumbing down," which readers are unlikely to appreciate and could well misunderstand.

4ET. "Cross-Atlantic linguistic awareness" not only cannot be assumed. It should not be assumed. That is the argument for omitting "math(s)" in the lead as likely to cause confusion and misunderstanding, as discussed in detail at (3AT, 1BT), and deferring it to sect. 1 where it does not do all that bad stuff.

5ET. The audience for the article may include quite young people. World Book is written for them. It is noted for good writing and does not include "math(s)" in the corresponding article. More immediately, the lead should be written to entice and inform, not drive away by overwriting, misleading, or confusing in a way made unnecessary by coverage in section 1. --Thomasmeeks 16:29, 18 October 2007 (UTC)

Responding to Jwy: I certainly don't assume that everyone will know both "math" and "maths"; what I can't figure out is why we should care whether they know them. That isn't a mathematical issue, and this isn't a linguistics article. It would be different if there were two different full, formal names for the subject; then we would have to treat the issue up front, because we would have to choose one of them for the title of the article. But these are essentially just two different abbreviations; if we stick to the correct formal name it's the same in all dialects. --Trovatore 16:34, 18 October 2007 (UTC)

It's teapot tempest time in Wikipedia. Rick Norwood 17:22, 18 October 2007 (UTC)

Seemingly, yes, but if this page can teke care of some "little" things by appealing to such norms as provided in Wiki policies & guidelines and appeals to good sense in their apps. for making cumulative progress on the article. On the other hand, if discussions get stalled in editors talking past each other, progress on the article may get stalled as well. I believe that the above very long discussion illustrates both possibilities. It also illustrates how hard it is, even with the best of intentions to make positions as clear and compelling as may be necessary to make progress & the necessity of close reasoning for bridging differences. Fortunately there are ways of settling disputed points, startinng with this page. It should not be a matter of picking sides but working toward the common end of article improvement. If anyone (else) wants to add to the discussion, please consider doing so. There is always the WP:RfC option, but resolving the matter on this page seems preferable. --Thomasmeeks 17:31, 19 October 2007 (UTC)

I couldn't care less about "policies" in this connection. I'm not interested in wonking a micro-issue like this. I simply state my opinion that the parenthetical is ugly, and my reasons for believing that it's unnecessary. If people agree with me, we can get rid of it; if not, I'm not going to fight about it. --Trovatore 17:48, 19 October 2007 (UTC)

I agree - it's ugly and unnecessary. EdwardLockhart 11:18, 20 October 2007 (UTC)

It's harmless -- well, mostly harmless. The usage is ubiquitous. Do you say, "I am teaching a mathematics class." or "I'm teaching math."? Rick Norwood 13:34, 21 October 2007 (UTC)

There is no doubt that it's ubiquitous; that's not the point. It's not formal writing. We're not chatting with our friends here; we're writing encyclopedia articles, and a certain tone is expected. If we were to actually use the word "math" or "maths" in the article, it would detract from the appearance of seriousness.

Of course the current parenthetical remark isn't use, it's mention, so I don't object to it on those grounds. But I still think it's ugly and unnecessary. It isn't "harmless" because it's ugly; this is an aesthetic judgment on my part with which you may agree or disagree. It's unnecessary because it's not relevant to the subject matter. --Trovatore 18:45, 21 October 2007 (UTC)

Usage is always relevant. Darn, I swore I wasn't going to get drawn in to this duscussion. "The guy who taught us math, who never took a bath, acquired a certain measure of renown..." Rick Norwood 21:19, 22 October 2007 (UTC)

Hmm? No, usage is not always relevant. This article is not about English usage; it's about mathematics. --Trovatore 21:21, 22 October 2007 (UTC)

One can agree that usage is always relevant in a dictionary, but see above (1A & following, after 17:14, 19 September 2007 Edit) that Wikipedia:What Wikipedia is not#Wikipedia is not a dictionary as to its relevance in the present discussion. Thomasmeeks 12:52, 25 October 2007 (UTC)

On the Wikipedia:Redirect page, under the heading What needs to be done on pages that are targets of redirects?, we find:

Normally, we try to make sure that all "inbound redirects" are mentioned in the first couple of paragraphs of the article.

Mentioning "math" and "maths" in the lead section is simply a way of complying with this rule. Is there a method of gauging the injury to some editors' esthetic sensibilities so as to ascertain that the amount of pain experienced outweighs the utility of doing here what we "normally" try to do?  --Lambiam 16:29, 25 October 2007 (UTC)

Frankly I think that recommendation should be changed. There are a great many reasons for making a redirect that do not merit mentioning the term in the lead. --Trovatore 18:47, 25 October 2007 (UTC)

Still, an interesting question, even if unanswerable in any conclusive sense. But it is only also fair to note the "common sense" and "occasional exceptions" links at the top of that (and every) Guideline p. and the use of "normally" in the above quotation. Virtually every point above arguing that the phrase in question should go gives reasons as why guideline should not apply here. The paragraph immediately above the one quoted refers to Wikipedia:Guide to writing better articles#Principle of least astonishment, which arguably is violated in parochial pairing in "math" and "maths" (on which, see (1ET-4ET) above). I believe that one piece of evidence can suggest that the phrase "(colloquially, maths or math)" in the 1st sent. of the article is not useful. A Google search of "math" puts the article at #16 on hit list. Is inclusion of "math" in the 1st sent. of marginal help? Arguably not for 3 reasons: (a) virtually every searcher already knows the math-mathematics link, (b) it will be close to instantly figured by others, or (c), in the absence of (1) or (2), there is the Disambig for "math" above. Use of the term "colloguially" seems much more likely to confuse than the failure of (a-c). That leaves "maths." If its inclusion were useful, one might expect that Mathematics to be near the top as to Google hits for "maths" (like a bear finding honey). It is not only not near the top. I could not find it in the top 300 Google hits for "maths" & stopped searching beyond that. --Thomasmeeks 19:19, 25 October 2007 (UTC)

The purpose of Wikipedia is to present information about topics in a way useful to the audience, not just to follow rules and not just to "be formal." In my opinion, having math and maths mentioned early in the article - and in bold - is important to give the user context should they enter "math" or "maths." Their ubiquitous use also makes them appropriate content for the article. The aesthetics are no worse, in my opinion, than birth-death years or pronunciation guides. And information trumps aesthetics. Hopefully, we find both, but I'm not creative enough to think of something better than what is there. Those are my thoughts from the north side of the teacup. (John User:Jwy talk) 00:31, 26 October 2007 (UTC)

I just don't see the scenario as likely that a user enters "math" or "maths" into the search box, and is then surprised when an article called "Mathematics" pops up. --Trovatore 00:56, 26 October 2007 (UTC)

Many arguments above against including the questioned "math(s)" phrase above (such as (1ET-4ET) or the 19:19, 25 October 2007 Edit) are also arguments that the phrase is misleading and unnecessary, and therefore a distraction. On the contrary, I believe inclusion of the phrase itself introduces unnecessary context problems. --Thomasmeeks 22:10, 27 October 2007 (UTC)

The current Edit of Mathematics has this at the top:

For other meanings of "mathematics" and of "math" and "maths," see Mathematics (disambiguation) and Math (disambiguation).

This effectively says to any interested or (hypothitically)disorientd reader that the quoted terms are being used interchangeably & makes the phrase in the first line the article "(colloquially, maths or math)" even more redundant, which makes removal of the phrase that nuch easier. Full disussiohn is instead taken up in section 1. --Thomasmeeks 18:11, 28 October 2007 (UTC)

Example of complex number (Fields of Mathematics: Quantity)

The last example of a complex number given in this section is 2*e^(i(4*pi/3)). But doesn't this evaluate to 2 [e^(i*pi)=-1 so 2*e^(i(4*pi/3))=2*(e^(i*pi))^(4/3)=2*(-1)^(4/3)=2*1=2]? I'm not sure if the expression itself is still considered complex or what or whether or not this is worth changing. -- 86.134.205.5 22:17, 27 October 2007 (UTC)

In the complex domain you cannot use e^ab = (e^a)^b without restrictions, otherwise we would get this:

e^x = (e^2πi)^x/(2πi) = 1^x/(2πi) = 1.

To interpret something of the form e^ix, just use Euler's formula.  --Lambiam 22:34, 27 October 2007 (UTC)

Oh yeah. Thanks for the insight. --86.134.205.5 22:42, 27 October 2007 (UTC)