Talk:Mathematics

Early Zero

The Olmecs in Mexico developed the Zero before the Indus Valley civilzation (India). There should be a mention of them and of course the Great Mayas. —Preceding unsigned comment added by 128.196.165.102 (talk • contribs) 22:24, June 13, 2008 (UTC)

Definition

Wanted to change the definition to make it grammatically clear (a "body of knowledge" can't "study" anything). I was thinking something like `Mathematics is the body of knowledge and academic discipline arising from the study of such concepts as quantity, structure, space, and change.' but I can't change it. Not sure about "arise" either, hopefully another author will think of something better. —Preceding unsigned comment added by 150.203.114.44 (talk) 15:45, 8 October 2008 (UTC)

OK, you do sort of have a point here, I think. Be aware that much blood has been spilled over this sentence; changes to it have to be made delicately. Maybe something like mathematics is the body of knowledge comprising the study...? --Trovatore (talk) 19:15, 8 October 2008 (UTC)

I feel very uncomfortable with the words "body of knowledge", though I am sure that the idea behind is good; in my opinion mathematics is "techniques, methods, models" in relation to the real world (including human mind) and its (scientific) description.Jorgen W (talk) 01:35, 7 November 2008 (UTC)

I don't completely understand. You don't think the knowledge that we've discovered using those techniques, etc, is part of mathematics? Or you don't think it constitutes knowledge at all? --Trovatore (talk) 02:55, 7 November 2008 (UTC)

I didn't say that the knowledge using those techniques isn't part of maths: on the contrary, I'm just saying that mathematics is also techniques, methods, models, arguably (a naive point of view), maths is "motion-movement", transformation of natural phenomena into abstract and wider structures; the term body of knowledge sounds a bit more "static" or just symbolic (sort of meta-language used as a tool by natural scientists). Furthermore, let's compare the heading of Physics and Science. :) --Jorgen W (talk) 01:18, 9 November 2008 (UTC)

Right, it's those things as well, I agree. I sort of prefer the version that said mathematics was a discipline. But unfortunately some people read that word and automatically think bondage and ... or some such thing. Someone asked the question once, if mathematics is a discipline does it hurt much?. We obviously can't use science because a significant point of view denies that it is a science (though personally I say it is). So it's tricky. All in all I'd be happy to go back to discipline; what do others think? --Trovatore (talk) 02:04, 9 November 2008 (UTC)

Oh, wait a minute; it says now that it's a discipline, and a supporting body of knowledge, and it's said that for a while. I hadn't bothered to check. So now I'm really confused as to what it is you don't like -- your techniques etc are subsumed in discipline, and you agreed that the "body of knowledge" was also part of mathematics. --Trovatore (talk) 10:12, 10 November 2008 (UTC)

Shouldn't this, somewhere in the lead, call Mathematics a hard science and an exact science. If we can't attribute those characteristics to math, then what?  :) Student7 (talk) 02:10, 28 January 2009 (UTC)

Both of those names have just a tinge of a dig taken at the social sciences. I don't see that that's helpful here. --Trovatore (talk) 02:15, 28 January 2009 (UTC)

Jorgen, I share your opinion about math. However, our opinions about math, no matter how well-reasoned or even true, are not relevant on Wikipedia. All we do here is summarize information from reliable, published sources: see WP:OR. Most other reference works define mathematics as something like the study of quantity, form, structure, pattern, etc. Philosophically inclined folks like to try to invent a super-rigorous definition that aims to capture all of that, usually under something like "drawing necessary conclusions". Posting that sort of definition would take a side in a debate (see WP:NPOV). Let's just do a good job summarizing the main, non-side-taking definitions. (And, hey, please argue for your definition in scholarly forums! I'd like to see that POV much more widely recognized.) --Ben Kovitz (talk) 04:24, 29 January 2009 (UTC)

Here are some definitions:

from the 1933 OED: "the abstract science which investigates deductively the conclusions implicit in the elementary conceptions of spatial and numerical relations, and which includes as its main divisions geometry, arithmetic, and algebra."

from the 2000 American Heritage Dictionary: "The study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols."

from Random House: "the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically."

from one of those Webster's dictionaries: "That science, or class of sciences, which treats of the exact relations existing between quantities or magnitudes, and of the methods by which, in accordance with these relations, quantities sought are deducible from other quantities known or supposed; the science of spatial and quantitative relations."

from WordNet: "a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement."

from the American Heritage New Dictionary of Cultural Literacy: "The study of numbers, equations, functions, and geometric shapes (see geometry) and their relationships."

Since we're writing an encyclopedia, we can have a more in-depth definition. We can surely do better than any of the above. But we shouldn't violate the basic idea: math is the science that studies certain things: quantity, structure, pattern, relation, <argue for stuff here>, etc. (Replace "science that studies" with "study of" if you're worried about people who construe the word "science" narrowly; but I think that's unnecessary.) --Ben Kovitz (talk) 04:43, 29 January 2009 (UTC)

--Ben Kovitz (talk) 04:43, 29 January 2009 (UTC)

I am astonished at the lack of rigour in most of the above defintions of mathematics. I hope that you see that something along the lines of "The application of logic to axiomatically defined systems" is much more appropriate.

Maths Graduate, UK

Awards and Prizes in Mathematics

This should include the William Lowell Putnam Mathematical Competition for college undergraduates in the US and Canada. —Preceding unsigned comment added by 166.82.218.97 (talk • contribs)

Vectors generalized to vecor spaces?

An important concept here is that of vectors, generalized to vector spaces,

What does that mean? Vector spaces aren't generalized vectors. You can't just string words mathematicians use and call yourself a mathematician!! —Preceding unsigned comment added by 141.211.62.162 (talk) 14:22, 9 December 2008 (UTC)

If you know what a vector space is, it is obvious that what is meant is the generalization from vectors to elements of a vector space; so need to be insulting. Still, it should be changed. Phoenix1177 (talk) 10:58, 27 January 2009 (UTC)

Mathematics as a science in the lead

The lead seems to imply that Mathematics is definitely a science, whereas the Mathematics#Mathematics as science goes into a lot of depth and contains many essentially contrary views, including one by Einstein. I don't think that the lead is handling this correctly right now. I also wonder at the quote in the second sentence being disconnected from the following paragraph- it seems to me that those should be in one paragraph, probably the quote should be moved down.- (User) Wolfkeeper (Talk) 18:50, 30 January 2009 (UTC)

I thought this spelled out the semantic confusion pretty clearly:

Carl Friedrich Gauss referred to mathematics as "the Queen of the Sciences". In the original Latin Regina Scientiarum, as well as in German Königin der Wissenschaften, the word corresponding to science means (field of) knowledge. Indeed, this is also the original meaning in English, and there is no doubt that mathematics is in this sense a science. The specialization restricting the meaning to natural science is of later date.

Actually, I am not aware that the older meaning of "science" has passed out of use. I believe that it's still the primary sense of the word. A quick look at http://dictionary.reference.com/browse/science reveals:

"1. a branch of knowledge or study dealing with a body of facts or truths systematically arranged and showing the operation of general laws: the mathematical sciences." (Random House, 2006)

"1. Knowledge; knowledge of principles and causes; ascertained truth of facts. ... 2. Accumulated and established knowledge, which has been systematized and formulated with reference to the discovery of general truths or the operation of general laws; knowledge classified and made available in work, life, or the search for truth; comprehensive, profound, or philosophical knowledge." ("Webster's" Revised Unabridged, 1998)

Some of the definitions do limit themselves to the natural sciences, though, like the American Heritage definition. If you'd like to try wording things so the reader does not get confused by the semantic confusion around the word "science", please have a go! --Ben Kovitz (talk) 01:57, 1 February 2009 (UTC)

move structure below space and change?

I think the "structure" section, being a more advanced topic would work better under the "space" and "change" section. I want to hear other's thoughts and opinions before making the change. Kevin Baas^talk 17:26, 13 February 2009 (UTC)

I think it's a good idea. Abstract algebra is abstracted from more-"concrete" ideas, so I think a lay reader will have an easier time following the sequence that you propose. Your sequence might even provide a nice way to work in a reference to the Erlangen program. --Ben Kovitz (talk) 03:56, 14 February 2009 (UTC)

Here there be tygers! The "quantity, structure, space, and change" rubric is the result of a long hard fight between the "mathematics is a subject" contingent and the "mathematics is a method" contingent. (I want the article to say "Mathematics is that body of knowledge discovered by deduction, just as science is that body of knowledge discovered by induction," but I lost the fight and the current lede was a compromise.) The "quantity, structure, space, and change" definition now appears not just here but across the mathematics portal. If you change it here, you should change it everywhere, and be prepared to fight every inch of the way. I would suggest not even starting unless you have at least six months with nothing better to do. Rick Norwood (talk) 17:25, 14 February 2009 (UTC)

Have you read the proposed idea carefully? It's not proposing to change the definition, it's proposing to change the order of some of the sections later in the article. --Ben Kovitz (talk) 18:09, 14 February 2009 (UTC)

I understood that. But if you change the order of the subsections, shouldn't you change the order in the lede to reflect that? And if you change the order in the lede, shouldn't you change the order in all the other articles that list those topics in that order?

The order does not seem that important to me, because I don't believe that definition of mathematics for a minute. (Where does game theory fit? How about probability and statistics? How about mathematical economics, which John Nash won a Nobel prize for?) But that definition follows a number of standard dictionary definitions, or is, rather, an expansion of them. Most dictionaries limit mathematics to the study of numbers and shapes.)

But if you do start to make structural changes in the article, just be aware that this article is closely watched. Rick Norwood (talk) 21:55, 14 February 2009 (UTC)

Here goes... Kevin Baas^talk 16:47, 17 February 2009 (UTC)

btw, i visualize mathematics. thats what i see when i do it: quantity, space, and change. that's how math is done. that's what it's used to describe. etc. etc. etc. space + change = structure (hence analytic geometry, etc.) (perhaps you can add in quantity to count sets and all that.) but there is no way to derive change from quantity, space, and structure. you take out the change and you break it - there are things it can't do anymore. (like adaptive control, feedback, nonlinear dynamics, etc. you know, the really cool stuff.) so unless you seek to regulate calculus or violate set theory in your basic definition of mathematics (oh, the irony!), i would say the foundations of mathematics, if one is to name just three, are quantity, space, and change. just my opinion. and frankly, i'd hate to see how critics of that see mathematics - it'd be like a world without color. Frozen in time, as it were, in a neat little box. Kevin Baas^talk 17:07, 17 February 2009 (UTC)

While it has nothing to do with the page, I see mathematics as only dealing with structure, and I don't find it to be a world without colour; nor do I follow how not viewing quantity, space, and change as foundational would violate anything, Category Theory is foundtional and is entirely structural. Maybe I'm missing the point of what you're saying. At any rate, if the order is being changed to facilitate simplicity, then your suggestion makes sense; if it is being changed to better illuminate the foundational philosophy of mathematics, then I whole heartedly disagree with you. Phoenix1177 (talk) 06:04, 18 February 2009 (UTC)