Talk:Mathematics/Archive 12

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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.

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

It appears Math and physics in fact are unified should we mention it?

Alright, here we go... Light and energy transmit patterns that we can measure (detect with our organs).

To measure is to calculate (create) distinctions, to be distinct then, is to be NOT EQUAL, to any other distinct-pattern (red, is not equal to blue). Now create is a verb, and therefore a function. Our eyes and ears gather information, distinct visual forms and detectable forms of energy through our ears, neurons, synapses etc. from the patterns of energy in the environment.

Therefore our organs measure (enumerate) the forms of energy(light, etc) in the environment. This would mean that math is actually the study of patterns of light and energy. An abstract concept, actually exists as data in our minds, as a form of stored energy. Therefore an abstract concept is stored as and is a form of stored energy.

Agree, disagree? If so explain and demonstrate how this is wrong. BeExcellent2every1 (talk) 06:58, 20 November 2007 (UTC)

BeExcellent2every1 (talk) 06:58, 20 November 2007 (UTC)

It's just wrong. It's against Wikipedia:No original research, also. Charles Matthews (talk) 08:28, 20 November 2007 (UTC)

You haven't explained how it is wrong. I just said that if you're going to make a CLAIM that you KNOW the STATEMENT is WRONG, then what do you KNOW about the STATEMENT that is WRONG. How do you know it is wrong? You must be able to point out the flaw for your claim to be valid, if you say the definitions are invalid, then which word, and which definition. Where exactly, which words, are wrong? so I can find which definition is incorrect. Otherwise you're claim is invalid, you must show your work, which words or statements are incorrect, otherwise you are making no intelligible claim.BeExcellent2every1 (talk) 08:58, 20 November 2007 (UTC)

Even if you were correct, this talk page is the wrong venue for such ideas. In fact, there really isn't any place (on wikipedia) where such discussion is appropriate. Such speculation violates our most basic policies, as Charles pointed out. —Cronholm¹⁴⁴ 09:45, 20 November 2007 (UTC)

I understand no-original research, I was just wondering if anyone had discovered that little fact. Apparently not. "Even if you were correct" the fact that you said this, means you dont know. So please accept that you don't know, and your claim to my first paragaphs incorrectness is invalid.BeExcellent2every1 (talk) 10:08, 20 November 2007 (UTC)

Cronholm¹⁴⁴ did not claim that you were incorrect. Within the realm of Wikipedia, the verifiability requirement means the burden of evidence (not proof, but evidence) falls on the person wanting to include the information. So if you'd like to discuss some sources, (for example, whether or not a source does a good job explaining the idea, or whether or not a source would be considered reliable) this is the place to do that, but it is not the place to discuss whether the idea is correct. --Smiller933 (talk) 15:00, 20 November 2007 (UTC)

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)

you're right, their should be a "is" after the change. repeating the word mathematics is redundant. Also there shouldn't be an "and" before change. the sentence should be, "Mathematics is the body of knowledge centered on concepts such as quantity, structure, space, change, and is also the academic discipline that studies them." Lou Dofoye (talk) 03:00, 7 February 2008 (UTC)Lou Dofoye

I respectfully disagree. By the same token, one should also change

Arthur had smuggled in beer, nuts, and crisps, and hidden the contraband in the closet

into

Arthur had smuggled in beer, nuts, crisps, and had hidden the contraband in the closet.

That is not an improvement, however. --Lambiam 06:29, 7 February 2008 (UTC)

It is fine because the "and change" shows the termination of the list of "concepts". However, I think the following sentence is more accurate and succinct:

"Mathematics is the science of quantity, structure, space, and change."

Calling something a "science" automatically implies that it is both a body of knowledge and an academic discipline.To alleviate confusion with natural and social sciences, you could also write:

"Mathematics is the formal science of quantity, structure, space, and change."

Check the articles on science and formal science for more information. Aetherealize (talk) 09:33, 20 February 2008 (UTC)

Does anyone have a problem with the above as the first sentence, or think that the current one is better? Aetherealize (talk) 23:53, 25 February 2008 (UTC)

Just calling it "a science" is clearly not acceptable, as that term is largely identified today with "natural science". A problem with using "formal science" is that this is not a well-known and generally understood concept. Our article Formal science does not do a good job of explaining the notion either; formulations like "A formal science is a theoretical study" and "The formal sciences are built up of theoretical symbols and rules" make me shudder. While the present first sentence is decidedly inelegant, I think its message is clearer. --Lambiam 11:29, 26 February 2008 (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)

Lambiam, I felt I should point out that you sort of used a formula improperly in your argument that mathematics is more than just formulas. (". . . the misconception that Mathematics = lots of formulas.") However, I agree with your main point. Also, the picture is ugly. - Chris Klein —Preceding unsigned comment added by 131.215.172.198 (talk) 08:40, 7 November 2007 (UTC)

Images for applied mathematics

Mathematical physics

Analytical mechanics

Mathematical fluid dynamics

Mathematical economics

Financial mathematics

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)

As a maths graduate from the UK, I would suggest people used mathematics wherever possible to avoid this kind of argument. My own opinion is that maths is the correct spelling, but then I'm biased. SpaceLem 17:41, 8 November 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)

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 misunderstanding 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)

Its confusing to pop to this page without the lead explaining why. Its NOT obvious to someone from the opposite side of the Atlantic.
I'm not sure calling them alternate labels means much. People will enter math or maths wanting the information in this article.
math & maths ARE used as equivalents to mathematics. Entering "math" or "maths" in m-w.com and you get: "mathematics."
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 presence 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 incompleteness of the objectionable phrase. Anyone who ends up at the article has the Disambiguation 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 colloquialisms 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. Essentially all differences come down to predicted effects on the readers, negative and positive (including 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 take 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, starting 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 judgement 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)

In the UK, you would say "I'm a maths teacher", or "I teach maths". SpaceLem 17:52, 8 November 2007 (UTC)

Usage is always relevant. Darn, I swore I wasn't going to get drawn in to this discussion. "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 (hypothetically) disoriented 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 much easier. Full discussion is instead taken up in section 1. --Thomasmeeks 18:11, 28 October 2007 (UTC)

Beauty is in the eye of the beholder. Your objection to "math" and "maths" baffles me. More information is better than less, and the mention in the article is about 1/1000 as long as the discussion about it here. Rick Norwood 12:20, 29 October 2007 (UTC)

That's why I did not refer to "beauty," although it is relevant to refer to properties associated with beauty that can be expected to result in a more beautiful Edit. If the "more information" provided is unnecessary, distracts from the article content, & misleads (as my numbered points above have argued above repeatedly), that does not make it better. The question is not whether the information should be included at all but whether it should be deferred to section 1 where the objections to its misleading & distracting incompleteness are removed. --Thomasmeeks —Preceding comment was added at 12:56, 29 October 2007 (UTC) (Proofing edit Thomasmeeks 13:19, 29 October 2007 (UTC))

More information is certainly not always preferable to less. Rick, be serious; that remark is absurd on its face. Yes, beauty is subjective and I make no bones about my objection to the parenthetical being subjective. But subjectively, I really do think it's hideous and ought to go. I won't act unilaterally on that perception, but I will state it, so that if enough other people agree, then we can get rid of it. --Trovatore 17:10, 29 October 2007 (UTC)

Disambiguation text at top of article: Edit conflict

This is a subsection, since apparently one of the disputants thinks that it is related to the "Maths vs. Math" section immediately above. The following Disambiguation text at tht top of the article was restored:

For different uses of similar terms, see Mathematics (disambiguation) and Math (disambiguation).

Edit summary of orginal Edit; Disambig at top: "For other meanings of 'mathematics" or "math'," --> "For different uses of similar terms,. . ".: more concise, accurate ("uses" vs. "meanings"), less distracting

The revert-Edit that it replaced was:

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

Edit summary; Undid revision by ... Please stop this nonsense

The last comment seems to violate Wikipedia:Talk page guidelines#Behavior that is unacceptable, Wikipedia:Neutral point of view, and Wikipedia:Assume good faith guidelines. There is nothing in the Edit summary to support its assertion, and the the Edit summary of what was reverted was ignored without good reason. --Thomasmeeks 03:40, 30 October 2007 (UTC)

I'm not opposed to the disambig text being changed, but I don't think that "For different uses of similar terms" is very clear. Ben 04:33, 30 October 2007 (UTC)

On further thinking, is it possible to combine the the disambig text with the "maths and math" text problem discussed above? Is something like:

Maths and math are colloquialisms of mathematics and redirect here. For other meanings of "mathematics" or "math", see Mathematics (disambiguation) and Math (disambiguation).

possible? Ben 04:38, 30 October 2007 (UTC)

I was indeed annoyed, after such earlier edits as these: [1], [2], and [3]. They introduce pointless complications; in particular, there is no point in disambiguating maths because it is not used with a secondary meaning in Wikipedia articles, so what are the other uses? Also, having more than one wikilink in a line on a dab page is in contravention of the guidelines. I see no plausible argument for replacing the standard wording for dablinks, used everywhere else, by an ad-hoc wording that is in my opinion rather unclear (what are "similar terms"?). In the BOLD–revert–discuss paradigm, if your bold edit gets reverted you don't reapply it, but discuss first. What particularly irked me was this comment made shortly after the edit creating the situation referred to, which suggests to me that there is an agenda behind the otherwise pointless edits, to wit to gain an advantage in the teapot debate. --Lambiam 11:00, 30 October 2007 (UTC)

0T. I do appreciate the gentle opening and close of Ben's Edit summary for the 2nd revert of my Edit and invitation for further discussion ("Revert for now. ... Can we wait and see what happens on the talk page?"). On the middle portion, see below.

1T. A general comment first. Things go better all around with a mutual, thorough, & unsparing application of the principle of charity. "Unsparing," b/c the principle can be used to peel away charitable (roughly, truth-maximizing) interpretations to reveal remaining points at issue. It includes a willingness to abandon (a) defective formulations (possible, yea, even in my case) when they are shown to be such and (b) interpretations of an Edit that fail to comprehend in what sense(s) the editor might have a valid point.

2T. The Edit of Lambiam ("L." for short) above begins by expressing annoyance resulting at 3 earlier Edits of someone else (me), 2 of them earlier or later reverted by 1 person (L.), and 2 of them on a disambiguation page, the same Edit but with a more complete Edit summary in the 2nd case. I did see a problem with the remaining Edit (pointed out by L.) & tried to avoid the repeating the mistake. But the earlier Edits do not exculpate multiple violations of WP guidelines (referred to at the top) in the "Edit summary" reverting a later Edit by that same person (me). Toward the end above, L. again expresses annoyance at an earlier Edit summary of mine, which names no one but refers to what I identified as a problem in the Edit it replaced. I regret that L. is also annoyed at that. Like L., I do have an agenda: to improve the article.

3T. Lambian asserts that "having more than one wikilink in a line on a [Disambig note] is in contravention" of WP guidelines, for which the link is Wikipedia:Disambiguation. If there were such a guideline, it would be absurd. (Why cavil at "1 line" but not 1 line + 1 word on another line?) There is no such guideline to my knowledge.

4T. Lambiam's Edit above has a link to Wikipedia:Disambiguation. But the link in no way supports a "standard" wording that does not concisely or precisely describe the Disambiguation.

5T. The greater conciseness of the 1st Disamb above is of course why "more concise" was used in the accompanying top "Edit summary" above.

6T. The imprecision of the 2nd Disambig above (referred in the 1st "Edit summary" at the top) is in its use of 'meaning' which suggests a "definition," the first dictionary-definition of 'meaning'. But the other terms on the Mathematics (disambiguation) are

Mathematics (producer), a hip-hop producer.
Mathematics (album), an album by the band The Servant.
Mathematics (song), a song by Mos Def
Mathematics Magazine, a publication of the Mathematical Association of America.

These are better described, not as "meanings," but as "uses" as multiple similar examples on Wikipedia:Disambiguation#Disambiguation links illustrate. Similarly for Math (disambiguation). That is why the assertion was made for the first "Edit summary" above that it was more precise.

7T. "Mathematics" and "math" are "similar terms," including spelling and a common dictionary reference for the 2 terms. Within each of the Disambig pages, there are also multiple similar terms or articles describing different uses.

8T. Ben's suggested alternative I believe comes closer to being a disambiguation itself, rather than referring as briefly as convenient to a Disambig page.

9T. I believe that the Edit summary at the top stands up well against all of the criticisms above raised against the corresponding Edit. --Thomasmeeks 21:28, 31 October 2007 (UTC) (2 minor typos fixed Thomasmeeks 19:33, 1 November 2007 (UTC))

I do not think that "maths" is a colloquialism. For example, in schools in Britain one will find the word "maths" used extensively on formal documents such as timetables, school reports et cetera. It is by far the most common term found in the media. Finally it is used in formal publications by the government, such as [4]. It is an abbreviation, but used in Britain as a slightly less formal synonym. I can not comment on the usage of "maths" in the rest of the world (it use is not confined to Britain) or of that of "math". Thehalfone 06:04, 6 November 2007 (UTC)

Probably "abbreviation" is a better word than "colloquialism" for the American use of "math", as well. I still don't see that it belongs in the lead. --Trovatore 08:08, 6 November 2007 (UTC)

I take it that the above 2 comments are related to Ben's suggestion above for this subsection referring to "colloquial" in the Disambig. It is both a colloquialism and an abbreviation (called a "shortened form" in my unabridged dictionary). Should either be mentioned? Arguably neither should, because it just adds unnecessary detail ("clutter") to the Disambig. --Thomasmeeks 14:24, 6 November 2007 (UTC) (minor typo fixed. Thomasmeeks 21:08, 6 November 2007 (UTC))

The above proposed Edit (1st indent at the top), has been reverted once apiece by 2 different editors, who suggested that it was "unclear." I have used plain words to express a plain meaning in the Edit. I have shown above the relevant sense in which the Edit is plain. One editor called the words "ad hoc." I have shown in what relevant senses the wording is standard, less misleading, and more informative than the alternative. I believe that these advantages trump the "ad hoc" label.

Concerning the above discussion, if one has nothing further to add, there is no reason merely to reiterate points already made. There may be of value, however, in attempting to defeat an argument against one's own argument, which would not be reiteration. Otherwise a non-response is open to the inference that no defense is possible, which is a questionble type of "consensus" solution. An expressed plurality opposing an Edit is especially vulnerable to challenge if the supporting argument is defective.

Comments are welcome concerning the proposed Edit, whether favorable or not to the position of this writer, --Thomasmeeks —Preceding comment was added at 18:08, 8 November 2007 (UTC)

For other uses, see Mathematics (disambiguation) and Math (disambiguation) would work fine for me. (John User:Jwy talk) 21:08, 8 November 2007 (UTC)

The "standard" way to handle this would be to use:

{{redirect|Math}}

{{otherusesof}}

resulting in:

"Math" redirects here. For other uses, see Math (disambiguation).

For other uses of "Mathematics", see Mathematics (disambiguation).

This, I feel, is perfectly clear. This could be combined on one line, for example in the form as suggested several times above, by John/Jwy, or – less concisely, but perhaps clearer – in the form:

"Math" redirects here. For other uses of "Math" or "Mathematics", see Math (disambiguation) and Mathematics (disambiguation).

An explanation of the alternative formulation involving the phrase "similar terms" is provided above. Unfortunately, we cannot add this explanation to the line or lines in the article. I still feel that (without accompanying explanation) this is less clear than basically any other formulation that has been considered. --Lambiam 21:37, 8 November 2007 (UTC)

John's proposed (3rd) alterative above has the advantage of brevity but the disadvamtage of possibly raising the distracting question of "Other uses of what?" The proposed Edit at the top avoids raising this question in clear enough terms.

Lambiam's 1st ("standard") alterative is not currently used for the article, presumably b/c what is there is better.

Lambiam's 2nd alternative above is an improvement over the current Edit by replacing "meanings" with "uses," as suggested at (6T) above. But it has the problem of telling those who search for "math" that they have beem redirected to "Mathematics," which they cam see for themselves and of which they are so informed by the little math#note right under the article title just for them. There is no reason to think that anyone else would care to be so informed. So, the first sentence ("Math" redirects here.) is doubly unnecessary, except to explain the second sentence. The proposed Edit does the same thing in one line and one sentence. (7T) above explicitly addresses the assertion that the phrase "similar terms" in unclear, the first sentence of which points out what should make assertion of unclarity unpersuasive. For that reason, I simply do not believe most people would find that phrase at all unclear in context. I realize that the following objection could be made: "If is it clear, why did you have to point to those things that make it clear?" My answer is, "because those things seem to have been overlooked in the assertion of unclarity." My prediction is that most people would regard the proposed Edit at the top as clear and favor it for its brevity. And, to the contrary, for those opposed. Additional comments are welcome, pro or con. --Thomasmeeks 02:26, 9 November 2007 (UTC)

From responses above, there seems to be a recognition of problems with the Current Disambig (CD) at the top of the article:

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

starting with use of the word "meanings," The phrase "For other meanings of ,,, math" misleadingly suggests that "Math" is the title of the ariicle. The question is what to do about it. The lack of concisensss is a distractng drawback of (CD). There would surely be wide agreement that a good reason for a Disbambig is to inform readers of where to find links distinguishing "different uses of similar" terms. The proposed Edit for example tells everyone who searched for "mathematics" or "math" where to look if they were suprised or disappointed to end up at the "Mathematics" article. So does (CD) but more verbosely and misleadingly.

A personal note: why spend all this anergy on such a small matter? I'm referring not merely to myself but everyone else who has read or contributed to this subsection and section that precedes it. Part of the answer may be that the subject (math) is considered important enough to make the lead as good as it can be. First impressions, for good or ill, can make a difference. That's worth discussion if it thare is a prospect for improving the article. It would be nice if there were a template that solved every problem beforehand. In the absence of that, reasoned discussion of relevant alterives might be second-best. What I have found offputting about (CD) is its awkwardness and length in trying to explain not one but 2 terms and Disambig links. It is not spam, but it may result in a similar reaction. Comments welcome. --Thomasmeeks 17:36, 10 November 2007 (UTC) (Minor typos fixed. Thomasmeeks 21:43, 10 November 2007 (UTC))

Request for comment on Disambiguation text for "Mathematics"

This section is a request for comment on the current Disambiguation text (labelled CD) below) at the top of Mathematics:

CD: For other meanings of "mathematics" or "math", see Mathematics (disambiguation) and Math (disambiguation).}}

Proposals have been made in the previous subsection (Talk:Mathematics#Disambiguation text at top of article: Edit conflict) with accompanying comments, pro and con. The proposals are labelled for convenience below.

D1: For different uses of similar terms, see Mathematics (disambiguation) and Math (disambiguation).

D2: Maths and math are colloquialisms of mathematics and redirect here. For other meanings of "mathematics" or "math", see Mathematics (disambiguation) and Math (disambiguation).

D3: For other uses, see Mathematics (disambiguation) and Math (disambiguation)

D4: "Math" redirects here. For other uses of "Math" or "Mathematics", see Math (disambiguation) and Mathematics (disambiguation).

D5: "Math" redirects here. For other uses, see Math (disambiguation). (together two lines)

For other uses of "Mathematics", see Mathematics (disambiguation).

Issues about the proposals relate to clarity, accuracy and conciseness. There seems to be an impasse in discussion of the previous section, which additional comments below might alleviate. Please indicate (and sign) which of the alternatives below is top-ranked in your judgment, with or without reasons. (Ties are permitted for equally top-ranked akternatives under "Other".) This "straw poll" will end in a week.

Top-ranked:

CD:

Minor Support: I have no real objections to this version, other than the note in my D4 support. Ben 00:01, 21 November 2007 (UTC)

D1:

Unsurprisingly perhaps, in light of discussion in the preceding section, I believe that this one is least objectionable. --Thomasmeeks 13:48, 14 November 2007 (UTC) (Minor typos fixed above, Thomasmeeks 15:36, 14 November 2007 (UTC))

Per comments under "Other" below, I accept that D2-D4 would be an improvement over CD. --Thomasmeeks (talk) 15:02, 17 November 2007 (UTC)

Oppose: This is just not clear. The idea here is to help lost or confused readers. If some lost or confused reader ends up here then I can not possibly fathom how this message would help them back on their way, other than providing the disambiguation links. Since every other disambiguation message has those links, I can't see a reason to support this. Ben 00:01, 21 November 2007 (UTC)

Relative to the "Top-ranked:" heading, the above comment is misplaced and possibly prejudicial. I believe that D1 speaks for itself to most readers. A full response was provided in the previous subsection. See also P.S. near bottom below. --Thomasmeeks (talk) 14:40, 21 November 2007 (UTC)

D2:

Neutral: I only floated the idea of moving the colloquialism stuff into the disambiguation as an alternative to removing it completely, per the discussion going on above this one. I have no strong feelings for it. Ben 00:01, 21 November 2007 (UTC)

D3:

Oppose: This is just too short, maybe even an ambiguous disambiguation. :) Ben 00:01, 21 November 2007 (UTC)

D4:

Support: I prefer this over CD since it's apparently convention to note a redirect in the disambiguation. A small caveat, I think that and should be changed to or (or vice versa), and I think uses should be changed to meanings as in CD. Ben 00:01, 21 November 2007 (UTC)

D5:

Minor support: I believe this is how the Wikipedia guidelines specify this should be done (though I could be confused!), so I wouldn't oppose it - but spreading this over two lines? Ugh. Ben 00:01, 21 November 2007 (UTC)

Other (please indicate)):

I like CD just fine, and find this whole fuss a waste of time. Rick Norwood 16:45, 13 November 2007 (UTC)

D1 is confusing, and D2 is an unnecessary and avoidable complication, compared to CD. The others are fine. --Lambiam 21:15, 14 November 2007 (UTC)

This discussion is a waste of time. The only improvement would be a technical solution assuring that only the relevant disambiguation page is offered for "Mathematics" or "Math", and none is offered for "Maths". For instance, whenever an article "X (Disambiguation)" exists, the server could add the disambiguation link automatically to the article "X". This could be decided before doing a redirect. This technical solution may not be worth implementing. In this case/in the meantime all proposed solutions are fine. --Hans Adler 21:25, 14 November 2007 (UTC)

Responding to RfC. Keep it simple since readers are only interested in locating the disamb. link , so: D1.Labongo 15:10, 16 November 2007 (UTC)

D1 is the simplest except it ought to say math(s) to cover both terms as 'math' is not used in many countries. Fainites ^barley 19:36, 16 November 2007 (UTC)

- The point is not that some countries use math, some maths. The point of a disambiguation page is that math has other meanings and maths apparently has only one meaning. The is no page maths (disambiguation).

Rick Norwood (talk) 16:06, 20 November 2007 (UTC)

As to the last sentence of the introduction for this subsection (above the "Top-ranked:" line), a week has elapsed for this "straw poll with comments" in an effort to break the apparent impasse of the preceding subsection at Talk:Mathematics#Disambiguation text at top of article: Edit conflict and locate a possible consensus as to proposed Disambigs. The last Edit by a "new discussant" (for this subsection) was 4 days ago. A ranking of the current and proposed Disambig texts from highest to lowest consensus (as nearly as I can determine is from the above 6 "votes" cast) is:

~~D1 preferred by 3 & accepted by 1 as good as other Ds~~

~~D3: accepted by 1 as good as other Ds & by 1 as good as D2-D5~~

~~D4: accepted by 1 as good as other Ds & by 1 as good as D2-D5~~

~~D5: accepted by 1 as good as other Ds & by 1 as good as D2-D5~~

~~D2: accepted by 1 as good as other Ds~~

~~CD: preferred by 1.~~

Currently D1 has the widest acceptance with a "majority" of "votes" in a large field of proposed alternatives. Moreover, "voters" have had a chance to inspect detailed discussion of the preceding subsection. Prudence might be advisable at this point.

I propose that if the above top-ranking of D1 is maintained for another week, it be used as a substitute for CD in the article. In the meanwhile, additional comments and/or "votes" on (de)merits of the alternatives are welcome. (Editors new to this subsection might wish to consult the preceding subsection for more detailed discussion.)

It is appropriate to recognize that not everyone might agree with D1 to replace CD (not to mention that the result could overturned). But there might still be acceptance of the process in this section for resolving the impasse of the preceding subsection. If there are no further comments in that time, I'd further propose that this section be deleted as suggested in Wikipedia:Requests for comment#Example use of RFCxxx Template (to be reposted if anyone sees fit now or later). --Thomasmeeks (talk) 17:56, 20 November 2007 (UTC) (See discussion below.)

I don't quite recognize the votes in the above tally. Maybe I have a different interpretation of "as good as". You don't seem to take account of objections, in which you might include the editor who wrote in an edit summary: "The new version doesn't make sense".[5] I must say it is slightly curious that the two outside commenters prefer D1 because it "is the simplest", while clearly D3 is simpler. I don't know what this says about how serious we should take their opinions. ~~Also, these two users appear to be both editing pages as disparate as Lavvu and Talk:OPV AIDS hypothesis, and somehow manage never to be editing at the same time; perhaps they share their computer.~~ --Lambiam 20:15, 20 November 2007 (UTC)

Thank you, Lambiam. Let me attempt to respond. This subsection is a request for comment to locate where the largest consensus was. Anyone was free to comment or not in this subsection, including those from who commented in the previous subsection. I counted above only those who chose to respond in this subsection. I do not think that all earlier comments of someone necessarily carry over to later discussion, much less a following subsection. (That user of course is free to determine whether or not to comment here.) The discussion of the previous subsection was extended. Nothing in the above tally was assumed either way as to how a user who responded in an earlier subsection would respond if that user did not in fact respond in this subsection. It appeared to me that Rick Norwood preferred CD, that Hans Adler ranked D1-D4 equally over CD, and that Lambiam ranked D3-D5 over CD & D1. Lambiam, I believe, raises interesting prima facie points about the 2 "votes" for D1, in light of which I'd say, "Let the voting/comments continue above or below and I'll strike out the provvisional result above. I hope that there would be continued effort to find s consensus. An attempt to improve the article by transparently fair means remains the only objective here. (talk) 23:11, 20 November 2007 (UTC)

P.S. I must say, I continue to be astonished at the reassertions that those entering "Math" would find D1 about "Math" and "Mathematics" unclear (& presumably without motivation to go to the respective Disambiguation pages), with or without the extended discussion of the previous section. --Thomasmeeks (talk) 00:50, 21 November 2007 (UTC)

P.P.S. There is this to be said for D1 being "simple" (but not too much so). It is more concise than any alternative except D3. D3 is shorter but question-begging: "other uses" in D3 wrongly suggests that the term "math" that follows has already been used in the article, so it is not simplest in the relevant sense of avoiding unnecessary quetions. Hence, there is some validity in both comments of the "outsiders" as to simplicity of D1. (Incidentallyy if we are going to start not counting "votes" that we think don't quite compute, I don't think that that should stop with the "outsiders.") --Thomasmeeks (talk) 21:56, 29 November 2007 (UTC)

I understand why math redirects here, and I still find D1 unclear. I imagine a confused reader would be worse off. What are these similar terms you mention? Why would I care about other uses of them? Ben 07:58, 21 November 2007 (UTC)

So, "math" redirecting to Mathematics is clear but D1 is unclear? Again, I'm astonished at such an assertion. The "similar terms" are "mathematics" & "math," mentioned in an obvious context in D1 (& commented on in (7T) of the previous subsection). Again, I believe that few readers would be puzzled, despite contrary expressions above. I do agree that anyone who accepts the above argument would likely instead "vote for" some other alternative. --Thomasmeeks (talk) 14:40, 21 November 2007 (UTC)

Additional comments and/or "votes" for at least 1 of CD and D1-D5 above as indicated or here:

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)

I dislike that formula being used as an example of a complex number. It is complex, but it's not in the spirit of the other examples. You need to use Euler's formula to expand it, and the leading 2 is extraneous. None of other examples invite manipulation, nor do they have "extras" - there is no 3π in the real numbers category, for example. Aetherealize (talk) 09:51, 20 February 2008 (UTC)

The example on the main page has changed to include an i, seems okay by me. I also suggest we retain the 2 as it makes it clear (as we see below) reals, integers and natural numbers are a subset. (John User:Jwy talk) 19:23, 20 February 2008 (UTC)

The example is the same now as it was at 15:56, September 2, 2006. There has been no recent change. See Talk:Mathematics/Archive 10#Suggested Improvement for the discussion leading up to the present version. --Lambiam 20:08, 21 February 2008 (UTC)

As it currently stands, it looks as though it is giving 2 as an example of a complex number, i'm almost certain that it isn't a complex number. Cmdr Clarke 23:18, 11 November 2007 (UTC)

You're welcome to check out the complex numbers article for the details, but briefly, complex numbers are of the form a + bi, where a and b are real numbers, and i is a number that squares to give -1. There is nothing wrong with, or stopping us from choosing, the real numbers a = 2 and b = 0. So we can see that the real numbers are in fact a proper subset of the complex numbers. Hope that helps. Ben 23:49, 11 November 2007 (UTC)

Math isnt all correct but it is supposed to be all correct

Most math problems are corect but there are some math equasions that are incorrect.Math is suposevly all are corect but this is not true (as it states in the last sentence) —The preceding unsigned comment was added by 24.217.141.75 (talk • contribs) 03:31, November 14, 2007 – Please sign your posts!

It would help us understand your point if you give an example. Rick Norwood 13:31, 14 November 2007 (UTC)

If we're going to do this, let's move the new vote to the bottom of the page.

C1 is "unclear" because of the word "similar". Disambiguation pages deal with identical words, not similar words. What are some of these words "similar" to mathematics and math?

While there are clearly too few votes to be meaningful, I continue to support the status quo.

Rick Norwood (talk) 13:46, 21 November 2007 (UTC)

On the 1st point, see (7T) at Talk:Mathematics#Disambiguation text at top of article: Edit conflict. Disambiguation pages deal with identical terms and in some cases similar terms, e.g. Mathematics (disambiguation) and Math (disambiguation). So can disambiguation texts. On the title of this seciton, undiscussed in the text that follows, let's let the RfC remain as long as there is active comment, or objection, or the 30 days indicated at as indicated in Wikipedia:Requests for comment#Example use of RFCxxx Template. --Thomasmeeks (talk) 15:03, 21 November 2007 (UTC)

We can be quite certain that the user who ends up on this page looking for "similar" terms is in fact not looking for terms that are just similar, but for other meanings of one of the terms mathematics or math themselves. Now, although in mathematical jargon identical triangles are similar, in everyday use of English the terms identical and similar are mutually exclusive: if it is identical, it is not similar. Just search for "not similar" in any of [6], [7], [8], [9], and [10], to give but a few examples. This makes the use of "similar" here unnecessarily confusing. --Lambiam 18:12, 21 November 2007 (UTC)

This has become an absurd waste of time for everyone concerned. Rick Norwood (talk) 13:57, 22 November 2007 (UTC)

I don't see a compelling reason to change anything. Anyone encountering this message for the first time that is remotely curious will click one of the links to see what possible other meanings/uses/similarities there could be. They will then say "oh" and go about their business. Unfortunately, we end up advertising a bunch of marginal articles, but it can't be helped. --agr (talk) 16:00, 22 November 2007 (UTC)

Well I do believe that it can be helped -- by making the Disambig as short as reasonnably possible, as discussed above at Talk:Mathematics#Request for comment on Disambiguation text for "Mathematics". --Thomasmeeks (talk) 17:11, 23 November 2007 (UTC)

What is mathematics a branch of?

Is there a larger category to which mathematics belongs?

Is it a branch of science?

Is it a branch of philosophy?

The Transhumanist (talk) 19:20, 25 November 2007 (UTC)

Views vary. It is a formal science, but whether or not formal sciences are science is disputed. —Ruud 20:01, 25 November 2007 (UTC)

Assuming that by "science" you mean natural science then the answers are clearly "no" and "no". There are branches of mathematics that overlap with branches of natural science, and there are other branches that overlap with philosophy, but there are also parts of mathematics that have no connection with either natural science or philosophy. Therefore mathematics is not a branch of either natural science or of philosophy. Gandalf61 (talk) 20:18, 25 November 2007 (UTC)

Mathematics is a part of collated human knowledge and is very a important tool when used to calculate third party effect within other branch's of human knowledge. My personal opinion is

mathematic along with language ( as a means of communication both spoken and written) is part of the root and trunk of the tree of human knowledge from which the branches grow.86.146.123.97 (talk) 19:13, 29 November 2007 (UTC)

Singular noun?

The article currently describes "mathematics" as a singular noun. But surely it is uncountable isn't it? (Therefore neither singular nor plural) - ^Estoy_Aquí^{(t • c • e)} 17:20, 9 December 2007 (UTC)

It's a "mass noun construed as singular". By contrast "people" is a mass noun construed as plural. I think the text is there to warn non-native-English speakers not to use it with plural verb forms (which would not seem unreasonable a priori; I think etymologically it is plural). --Trovatore (talk) 17:54, 10 December 2007 (UTC)

I think it is more accurate to classify "people" as a count noun that, despite its singular form, acts as a plural of the word "person". --Lambiam 19:49, 10 December 2007 (UTC)

Well, you can make that argument. To my mind the only true plural of "person" is "persons"; "people" is often used in that role but is actually a separate word. But anyway, if you don't like the example, substitute "cattle". --Trovatore (talk) 19:59, 10 December 2007 (UTC)

But I can't quite let the "people" thing go, because someone whose first language is a neo-Latin language might be reading this, and they tend to get confused on this point. So: "people" used to mean something like "nation" is indeed a count noun, but "people" in the sense of "persons" is a mass noun construed as plural, like "cattle". --Trovatore (talk) 20:05, 10 December 2007 (UTC)

You can't say: "A Wagogo family had on the average three cattle"; you have to use something like "three heads of cattle". You can't count cattle but only their heads. But you can say, at least in English as I know it: "Three people are vying for the position": you can count people, that is, "people" is noun that can be modified by a numeral – except the numeral "one". If two of these contenders drop out of the race, you can only say that "one person" is left. So "person" functions as the singular of "people" here. While you can say: "Three persons are vying for the position", that is not truly idiomatic English. See also Wikipedia:Reference desk archive/Language/2006 October 2#People v. Persons and Wikipedia:Reference desk/Archives/Language/2007 October 7#People, Persons. --Lambiam 21:44, 10 December 2007 (UTC)

The only true plural of "person" is "persons". "People" has extra baggage. It's true that it's not completely parallel with "cattle" because of the "*three cattle" problem, though the idiomatic expression is "three head of cattle", not "three heads". --Trovatore (talk) 22:57, 10 December 2007 (UTC)

Yes I'm aware it is treated as singular, but the point I was making is that it isn't (because it is uncountable). But anyway, I see that it's gone now. - ^Estoy_Aquí^{(t • c • e)} 09:54, 15 December 2007 (UTC)

Fields of mathematics

What is the goal of the "Fields of mathematics" section? To give the reader (another) overview of the main themes of math, or to introduce her to the research subdivisions? I suggest we try for the latter, because it is not done anywhere else in the article and it would dovetail nicely with the later discussion of the misconception that no new math is being done. The goals of the section (which could be renamed "Mathematics research" or so) could be:

subsections corresponding to the major subfields, with the adult terminology (e.g. Algebra, Geometry, Analysis, Logic, etc.), as used in the American Mathematical Society's Mathematics Subject Classification, or its annual survey of new Ph.D.s granted, or some other math organization's system
gentle tie-in to how these build off and connect the historical themes of math
less technical jargon (fiber bundle comes half a paragraph after Pythagorean theorem)
major subfields identified in a sane way (group theory is a subfield of abstract algebra, not a peer of it)
major outstanding problems clearly identified.

Joshua R. Davis (talk) 21:40, 12 December 2007 (UTC)

Math as Science Section

I do not mean to bring up this dispute again, but "those in pure mathematics often feel that they are working in an area more akin to logic and that they are, hence, fundamentally philosophers.", seems odd to me. Pure mathematics is not fundamentally Philosophy. No Philosophy department offers courses in pure mathematics, nor do any math text books mention philosophy. The philosophy of mathematics on the other hand is philosophy, but it is not pure mathematics. Please realize that things like Homological Algebra are not applied in any sense, they are not immediate abstractions of anything physical, they are not philosophical, and they are not considered primarily for aesthetics. Hence, such branches of mathematics can only be called pure mathematics; and it is absurd to suppose that anyone working in such fields would think otherwise.Phoenix1177 (talk) 11:08, 1 January 2008 (UTC)

As no reply has been made to the above, I am going to remove the offending sentence. If anyone objects to this please add the sentence back and we can discuss here.Phoenix1177 (talk) 04:18, 2 January 2008 (UTC)

http://www.st-andrews.ac.uk/~slr/teach07-8.html#3 appears to be a course in pure Mathematics offered by a Philosophy department. EdwardLockhart (talk) 13:16, 2 January 2008 (UTC)

That is a course in Logic, which can be mathematical. However, all of pure mathematics is not a course in logic; especially, courses mentioning modal logic. Furthermore, branches of philosophy interact with one another, the same holds for mathematics. I can see no way in which homological algebra is relevant to epistemology; I can see how it is relevant to topology and sheafs and so on. Homological algebra is not the only theory for which this holds; I can think of no theorem in group theory, differential geometry, complex analysis, etc that has any bearing on the JTB theory of knowledge or on any other such matter. In fact, none of the above branches even has a bearing on the veracity of modal realism, which is involved with modal logic. Lastlty, philosophers attempt to generate theories correspondant to reality, thus why they are debatable; the point of epistemology is to characterize actual knowledge, not to formally define an interesting concept and call it knowledge. Mathematics on the other hand does not have a serious debate over which axioms to employ; at least not since the modern times and non-euclidean geometry. Mathematics does not care if the axioms used correspond to reality, only if the results are useful/interesting; philosophers do care if their axioms correspond, indeed, it is their goal.Phoenix1177 (talk) 06:50, 3 January 2008 (UTC)

In (Vaughan Pratt (1995). "Rational mechanics and natural mathematics". In TAPSOFT’95, LNCS 915, pp. 108–122) the author proposes Chu spaces as a solution to Descartes’ problem of mind-body interaction. The idea is that the points of a Chu space are interpreted as "body", whereas its dual points are "mind". The matrix of the Chu space then serves as the mechanism of their interaction. I'm not making this up. --Lambiam 11:15, 3 January 2008 (UTC)

I never heard of him before, I'll have to look at his work sometime. Nonetheless, this example only serves my point; he is applying an interpertation to mathematical results in order to do philosophy. This is, although not so seemingly strangely, what science does to math aswell; it adds an interpertation to it. My point is this, to make mathematics philosophically useful, you must add an interpertation. We do not have to add an interpertation to results in one area of math to be able to apply it to another. For clarity: the above bit about Chu spaces is an interpertation, we could not simply say something like, "...in every hausdorff space compact sets are closed, it follows that the Gettier problems are resolvable by adding an additional contstraint on knowledge as JTB rather than taking knowledge to be fundamental...". Of course, when it comes to things like the foundations of mathematics, things can get a little blurred; but this is a far cry from saying that pure mathematics is fundamentally philosophy; any more so than saying that a chef is fundamentally a chemist.Phoenix1177 (talk) 11:42, 3 January 2008 (UTC)

But note that Pratt proposed Chu spaces, not as a model of the problem, but as a solution. My pineal gland is still reverberating from the shock. All I can say is: Monsieur, (a+bⁿ)/n = x, donc Dieu existe – répondez! --Lambiam 13:51, 3 January 2008 (UTC)

Whatever Pratt did, does not change the issue at hand. My point was not that someone would never philosophize mathematically, but that pure mathematics is not fundamentally philosophy. It is no more true that theoretical physics is fundamentally mathematics, that writing fictional novels is fundamentally linguistics(your citing Pratt, would be like me citing Tolkien here), that philosophy is fundamentally writing fiction(although Ayn Rany used fiction), that writing novels is fundamentally mathematics(Von Neumann did this once), or any other concoction. If we submit that pure math is philosophy, we might aswell just say X is fundamentally Y, irregardless of X and Y because someone will be able to find some instance of it or a case where the lines blur.Phoenix1177 (talk) 02:13, 4 January 2008 (UTC)

By the way, I love the quote from Euler above; and I did not look at Pratt's work, so I was speculating; I apologize for that bit, but my argument still stands.Phoenix1177 (talk) 02:13, 4 January 2008 (UTC)

(reset) The contentious issue is whether contemporary mathematicians consider math a science, right? Can we find reliable sources that make definitive statements one way or the other? (The paragraph as it stands is loaded with weasel words.) Joshua R. Davis (talk) 04:01, 4 January 2008 (UTC)

Actually, the issue was if pure mathematics was fundamentally philosophy; which it said in the article before removal. However, the mathematics as science view is something I also object to. However, I did not bring this up, as it appears that the current section is a comprimise based on past arguments. I will bring up my objections now, since you have brought the matter up.

The first paragraph of the section states that mathematics, pure, is not a science in the empirical sense. Which is good, in fact this is a common misconception and I'm happy that it is cleared up in the article. However, the sentence, " If one considers science to be strictly about the physical world, then mathematics, or at least pure mathematics, is not a science." is unusual in that Wikipedia's science article does consider science to be about the physical world, although, the last paragraph of its article seems to contradict this view nonetheless.

Also, "...others feel that to ignore its connection to the sciences is to turn a blind eye to the fact that the interface between mathematics and its applications in science and engineering has driven much development in mathematics." has little to do with mathematics being science. Observe, that it talks about mathematics connection to science, which seems to implicitly deny mathematics actually being science; I would not talk about quantum mechanics connections' to science, but of quantum mechanics as science and its connections to other parts of science. This is not all, the sentence is actually talking about mathematicians thinking that the connection between math and science should not be downplayed; the article presents this asif mathematicians were saying that math and science being the same thing should not be downplayed, which is misleading as the sentence only implies that an important connection between them exists. There are important connections for between food and parties, and these have inspired many types of foods; still I would not say that this is an argument for a chef being a host.

The next sentence seems to imply that mathematics is either science or art; or some synthesis of the two. It is none of these. Art's primary aim is aesthetics, mathematics is not. Science aims for results about the natural world, math does not. Both may inspire mathematics, and mathematics be viewed in relation to both; then again, so can cooking.

Lastly, the paragraph on awards does not belong in the section. The first sentence talks about equivalent awards in science, but then says that the Fields medal is misleadingly considered to be the Nobel prize of mathematics. While these two sentences are not contradictory, they do seem to clash. Furthermore, awards deserve their own section, and we could equally talk about the equivalent awards in acting or literature; thus, showing that science and math have awards does not relate to their relation as fields. This paragraph should be moved and the mention of science in it should be taken out.

If no one objects, or if some agree, then I will change some of these things in the next few days; I do not have time right now.Phoenix1177 (talk) 04:48, 4 January 2008 (UTC)

Let me rephrase. All of the talk here, while insightful and interesting, doesn't make an encyclopedia. Opinions should come from reliable sources. Can we find published, citable quotes by Atiyah, Serre, Smale, or others? The current article sorely lacks these, so I don't object to your removing some claims, but ideally we would be disciplined in adding new claims. Joshua R. Davis (talk) 14:11, 4 January 2008 (UTC)

Adding my two pennies: much of the on one hand... on the other hand... of this section is not about the epistemological position of mathematics per se – although confusingly presented as such – but rather about the meaning of the term science. People who understand the term science as a notion comprising all systematic accumulation of knowledge are more likely to consider mathematics a science than those who understand the concept of science as being the systematic effort to understand how nature works, with observable physical evidence as the basis of that understanding, acquired through observation of phenomena, and/or through experimentation that tries to simulate events under controlled conditions. --Lambiam 15:05, 4 January 2008 (UTC)

Nevertheless mathematics answers to the latter description just fine, provided that you don't require the objects being studied to themselves be physical. --Trovatore (talk) 17:21, 4 January 2008 (UTC)

That just underscores Lambiam's well put point: in order to decide if mathematics is a science or not, you need to define science. A definition that includes "observable physical evidence as the basis of that understanding" would seem to me to indicate the "objects" have to be "physical." If we do include mathematics as a science, it has to have an "asterisk" that explains it is "detached" from the physical world in a way distinct from other sciences. In most cases, it is not an "experimental" science, one might say. (John User:Jwy talk) 22:25, 4 January 2008 (UTC)

The evidence can be physical, without the objects being physical. And I think it is an experimental science, at bottom, though perhaps many sorts of mathematicians will often not experience it that way in practice. --Trovatore (talk) 22:35, 4 January 2008 (UTC)

WARNING: I enjoy this discussion such that I will probably get far away from the topic at hand. I think there have been books written pro and con what you say in the first sentence. And I don't think modern mathematics has much experiment involved. How do you prove with a physical experiment some hypothesis about non-Euclidean geometry? But the main point is there is something very different about mathematics and the other things we call science (whether we call math a science or not) and it has to do with its looser connection with physical reality. I don't believe I am capable of expressing it in a way appropriate for the article. . . (John User:Jwy talk) 23:54, 4 January 2008 (UTC)

Non-Euclidean geometry is not a particularly good example. Some of the clearest examples are actually large cardinal axioms, though they're a little bit complicated for quick discussion. We could take a mini analogue of LCAs -- the existence of the powerset of the naturals. Does there exist, Platonistically, a completed totality containing all sets of natural numbers?

Well, if such a thing does exist, then we can predict that lots of theories are consistent, because they have P(ω) as a model. And in turn the consistency of a theory has consequences we can observe in the physical world, such as certain computer programs not halting. To be sure, the same consequences follow from ontologically more parsimonious hypotheses -- but these hypotheses, though they assume the existence of fewer entia, are nevertheless more complicated and less motivated. Without the existence hypothesis, the latter ones appear to be "brute facts" without explanation.

Of course this discussion quickly gets very involved and very controversial; just scratching the surface here. --Trovatore (talk) 00:28, 5 January 2008 (UTC)

While interesting, what you said doesn't support the claim of mathematics being an empirical science with nonphysical objects. Most of this argument seems to be: let me show the case where it is most favorable, followed by sweeping hypothesis. If mathematics is indeed as you say, then please give me an example of an experiment that will provide physical evidence for some result from algebraic topology; how about Van Kampen's theorem.

I agree that we need more sourced material, but I didn't come here to provide it; only to remove a line about pure math being philosophy. Lastly, I don't thik the average person uses science to mean the systematic accumulation of knowledge, but uses it to refer to natural science. Although, the mentioning of this difference in usage and saying that math belongs to the first type is not a bad thing; mainly because some people tend to think mathematics is a natural science(I know many people who think that mathematics is either physics or accounting, sadly).Phoenix1177 (talk) 05:54, 5 January 2008 (UTC)

What I said does indeed support my claim. I don't claim that it has to convince you; it's an explanation of how I and some others see it. Some philosophers of mathematics who have made similar arguments (though I don't know if they'd sign on to this specific one) are Quine, Putnam, and Lakatos.

Not all of mathematics has to be empirical. Not all of physical science is empirical either; much of it is the elaboration of consequences of that which we believe to be the underlying reality, but which we can never observe phenomenally. I don't know much about algebraic topology so I can't help you there -- I'm a set theorist and naturally my examples are going to come from set theory.

As for the text you removed, frankly it was not that bad and something along those lines perhaps should be restored, though admittedly it should be sourced. It didn't say that mathematics is a philosophy, just that many pure mathematicians consider what they are doing to be part of philosophy. And it's absolutely true that many of them so consider it, or at least consider it to be on the borderline. Whether they're right or not is not the point, from the standpoint of this article. But I think they are right, and I don't think there's any contradiction between that and saying that they're doing empirical science. There are no exact demarcations between any of these things; it is quite possible for an activity to be simultaneously philosophy and science. --Trovatore (talk) 07:22, 5 January 2008 (UTC)

I removed one sentence. The sentence said that pure mathematics is considered to be fundamentally philosophy. I have never heard of anyone calling topology a branch of philosophy. I do believe that set theory and philosophy might blur, but people working on the Riemann Hypothesis would most likely not call themselves philosophers, nor consider themselves as such; or do you not include analytic number theory and complex analysis in pure mathematics?

Also, you claimed that mathematics can be viewed as an empircal science. I did not ask you to prove it to me, I do expect you to back up the claim if you make it, however. There are thousands of experiments performed in science, I know of no experiment ever done that provided physical evidence for a theorem of high mathematics.

I do not recall saying that there is a contradiction between mathematics being philosophy and science at the sametime, I said that mathematics is neither of these things. In fact, I don't see why there is such a need to classify mathematics as being some other field; mathematics is its own. It would make more sense to point out the several connections between mathematics and philosophy, science, art, etc. and let the reader draw their own conclusion.Phoenix1177 (talk) 08:06, 5 January 2008 (UTC)

I did back it up. I gave specific examples of the sorts of experiments that provide physical evidence for axioms of mathematics (axioms of course are also theorems, but what I'm interested in finding evidence for is more the axioms, though in some cases they might not seem so axiomatic in character). You are not required to be convinced, but don't claim I didn't back it up.

Whether you (or I) think that mathematics is or is not philosophy, or is or is not science, is quite beside the point here, though. You think it's neither, I think it's both, but neither of those things matters. What matters is presenting the views of informed currents of opinion.

Oh, and by the way, no, the sentence you removed did not say that pure mathematics is considered to be fundamentally philosophy. If that's how you read it then you read it wrong. --Trovatore (talk) 08:31, 5 January 2008 (UTC)

I agree with Trovatore. The sentence said made the point that pure mathematicians (it really should have been some pure mathematicians) consider themselves "fundamentally philosophers" because their work is more in line with logic than sciences. This is quite different to saying they think pure maths is a branch of philosophy, but at any rate is a claim about how mathematics is viewed, not what it actually is. JPD (talk) 12:41, 5 January 2008 (UTC)

What is mathematics?

JPD wrote: "... is a claim about how mathematics is viewed, not what it actually is."

Since mathematics is an abstraction, not a physical object, what is "is" and "how it is viewed" have the same meaning. Abstractions exist only to the extent there is a consensus about them.

The problem with mathematics seems to be that non-mathematicians almost always get it wrong, so mathematics "is" one thing to non-mathematicians (usually something like "really hard arithmetic") and "is" something else to mathematicians (often something like "axioms, definitions, theorems, and proofs"). Mathematics differs from philosophy because mathematical reasoning has led to a large, useful, and generally accepted body of knowledge, while philosophical reasoning has led to many "schools" of philosophy but little in the way of philosophical "truths" that all philosophers agree on. Until the twin primes conjecture is accepted on the basis of a very large number of experiments, mathematics is not a science.

Because Wikipedia relies on published sources, this article has to go with the best definition non-mathematicians have come up with, which is usually something like "the science of number and shape". But we also mention the view of pure mathematicians. By its very nature, this disjunction will not be resolved, unless we can convince everyone in the world to become a mathematician, which would mean the end of civilization as we know it. Rick Norwood (talk) 14:31, 5 January 2008 (UTC)

I thought we were talking about the section that discusses views of mathematics as science, in particular the paragraph about the views of mathematicians on the subject. The issue isn't a definition of mathematics, but how to convey the different views, even among mathematicians. In this context, it doesn't matter what what "is" makes any sense or whether we agree with the view being described - the question is simply whether we are accurately describing a common view. JPD (talk) 15:04, 5 January 2008 (UTC)

If I ask someone what they are and they say they are fundamentally a philosopher; I would assume that they do philosophy. If you tell me most pure mathematicians feel they are fundamentally philosophers, then I assume that they feel that pure mathematics is philosophy. I suppose you could also take it to mean that their methods are fundamentally philsophical; but I don't see how this applies to mathematics in general; my point is that if I misread it, I'm sure others did. Regardless, I'm sure some mathematicians view themselves as fundamentally mathematicians, and my whole point of contention was that the article does not mention this; I read it as portraying mathematics as being some cross between philosphy, science, and art.

Also, to Trovatore: You gave one example. One example does not establish that , "...And I think it is an experimental science". I can point to a large number of physical experiments in physics, eventhough all of physics may not be experimental. You even say non-euclidean geometry is not a good example, why is it not a good example? Suppose I just make up some axioms that are rules governing symbols, arbitrarily; it may not be interesting, but I'm sure I could make it so that it wasn't experimentaly supportable in a physical way. Perhaps, mathematics evolved the way it did because we think the way we do; being such it seems to correspond to the physical world. We could generate equally complex theories from a perspective that could not even correspond via analogy, we wouldn't because they would it would be of no interest, but we could do so vallidly.

Also, I mentioned earlier about moving the awards from that section. We could equally say that the awards in science have an equivalent in acting. All awards are given based upon merit, the paragraph has nothing to do with mathematics being science; only that mathematics has awards. As such, it doesn't belong.Phoenix1177 (talk) 20:02, 5 January 2008 (UTC)

The point of the awards paragraph is to give more evidence that math is regarded as something outside science (in that the sciences have Nobel prizes and math doesn't). This is the intent of the opening sentence. I do agree, however, that the second half of the paragraph, beginning with Hilbert's problems, is irrelevant. Joshua R. Davis (talk) 22:04, 5 January 2008 (UTC)

History of Mathematics

Earliest evidence on Mathematics is found in Africa (South Africa, Congo). But there is no mention of these countries. I don't think it is fair. —Preceding unsigned comment added by Observer8 (talk • contribs) 16:15, 8 January 2008 (UTC)

Well, this is Wikipedia, the free encyclopedia that anyone can edit. That's not an invitation to add just anything, of course, but if you have reliable sources to which you can attribute your claim, I think it would certainly be worth a mention. Do be a little careful if your sources are in some way polemical or see themselves as trailblazing -- if the claims are not accepted by the history-of-math or anthropological communities at large, they can still be mentioned, but should not be presented as accepted fact. --Trovatore (talk) 19:08, 8 January 2008 (UTC)

Please find reliable sources. If you can find a reliable source which suggest that the earliest evidence on Mathematics is found in Africa, it should be mentioned in the article. Masterpiece2000 (talk) 02:48, 16 January 2008 (UTC)

Accuracy dispute?

Why is this page in the category Accuracy disputes? I can’t seem to find what, if anything is disputed, nor what is causing it to appear in this category. GromXXVII (talk) 23:03, 18 January 2008 (UTC)

When Estoy Aquí added the {{dubious}} tag in this edit the page was automatically added to the Accuracy disputes category. Ben (talk) 01:06, 19 January 2008 (UTC)

Since the user who added it has failed to give any indication why the statement is disputed in over a month, I have removed the tag. --Lambiam 06:02, 19 January 2008 (UTC)

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