Talk:Mathematics

Lead paragraph (sorry)

"Mathematics as profession" does not at all treat the right topic. "Renowned Math prizes" would be a more appropriate title. — Preceding unsigned comment added by 85.224.152.237 (talk) 20:20, 6 April 2013 (UTC)

I agree with the fact that the content of "Mathematics as profession" has nothing to do with it's title. "Math Prizes" or "Math Awards" would a more appropriate title for that content. Anyway, would be a good thing to have a section titled "Mathematics as profession" or something similar to deal with the professional jobs where mathematicians apply their knowledge. MickMurillo (talk) 21:21, 3 May 2013 (UTC)

The philosophy of mathematics, the branch of philosophy that studies mathematical assumptions, foundations, and implications, is one of the biggest branches of philosophy in the world. This branch never stops growing, from Thales, a great mathematician from Ancient Greece, to V. N. Bhat, a small mathematician from India, they have all added what little they could. Every idea and theory has helped this art grow. Every year mathematicians discover something new that helps us understand mathematics a little better. The mathematicians don't MAKE or ADD to the subject, they DISCOVER something that is already there. This is the crux of the matter, you cannot make something in math, everything is just there. There can, however, be another way to interpret the art. The Arabic numerals, which were actually made in India but were carried to England by Arabic Traders, are known as the language of math. However, if you lived in Babylon in prehistoric times, you would have a whole different way to express mathematics. The Arabic numerals aren't math, they are just a way to interpret the art. However that means that mathematics cannot be defined because there is no definite way to express it. From the plastic ladybugs used by teachers in 2nd grade to help you add and subtract, to the Arabic numerals used around the world, they are just different languages used to express math, just like all the different languages in the world that are used to express people. Math is a never ending problem, that can be used to solve problems. Just like you can never count to infinity using a language of math, you can never be finished with math. There will always be a new theory to try or a new method that explains another one of life's great questions. -- Professor Captiosus — Preceding unsigned comment added by Professor Captiosus (talk • contribs) 17:29, 20 January 2013 (UTC)

Given the warning in the article pseudo-code about changing the opening, I decided to bring my proposal here, since the way it currently reads is awkward, in my opinion. I propose:

Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of abstract objects and the logical relationships among such objects. Mathematics encompasses topics including quantity, structure, space,and change, although it has no generally accepted definition.

...for the following reasons: 1) Mathematical entities, as represented by symbolic notation, are abstract. They are well defined for the purposes of an axiomatic system, and the rules and operations between mathematical objects are logical in character. I'm sure there is no objection here. 2) The topics listed are not well defined, and while math is used to study things like structure and change, it is NOT the study of naturally occurring structure or change, but the study of abstract representations of such. That is to say, the quantum zeno effect negates the direct correspondence with reality of infinitesimal calculus. Topology deals with abstract surfaces ect. 3) The "and more" is amateurish and doesn't do anything to inform a reader about what mathematics actually is. 4) I don't even know what is meant by "the abstract study of subjects" - the verb study is surely only undertaken by a physical human or physical computer, an abstract object cannot "study" anything as far as I know. The word "subjects" is too ambiguous and probably incorrect. In colloquial parlance "subjects" can mean topics of learning in school or whatnot, but "fields" or "disciplines" works better if I understand the connotation correctly. In any event, Math is the the discipline that makes use of well-defined abstract objects and manipulates them by logical rules and operations. One might even include "rigorous" before "study" in my proposed intro, but it's not particularly important. What I see as important is to do away with "abstract study" because nobody even knows what abstract study is. Either everything that could conceivably studied is abstract or nothing is. My point is that I could see dog feces on my shoe and look at it carefully and in my brain associate dog feces with my previous understanding of dog feces, and the structure of the smear on my shoe could be "structure", and by the current lead paragraph I would be doing math. To me, a definition that excludes nothing is a poor definition. -Fcb981(talk:contribs) 00:56, 29 August 2012 (UTC)

This is, as you might guess, a discussion that has been held many times before. The conflict is between what non-mathematical sources say mathematics is and what mathematicians say mathematics is. While I agree with you, non-mathematical sources such as dictionaries and encyclopedias say mathematics is the study of numbers and shapes. Wikipedia reflects sources, not truth. Sigh! Rick Norwood (talk) 17:21, 29 August 2012 (UTC)

Fcb981, I sympathize with your complaints about the opening quasi-definition: "abstract study" is weird, the mathematical study of dynamics is awfully static and certainly different from how change is studied in the natural sciences, etc. I'd like to see a better definition. However, here are the three big reasons favoring the current definition:

(1) The breakdown of math into major topics corresponds to the structure of the article, at least the subheadings under "Pure mathematics". A good lead should summarize the body of the article; see WP:LEAD.

(2) The definition of mathematics is highly controversial. Please see Definitions of mathematics for a sampling of leading definitions and the unresolved conflict between them. There is not even a consensus among mathematicians on how to define mathematics; see Mura, Robert (Dec 1993). "Images of Mathematics Held by University Teachers of Mathematical Sciences". Educational Studies in Mathematics 25 (4): 375–385. . For this reason, it's not appropriate for us to give a proper definition that draws a clear boundary between what is and is not mathematics; we settle for a rough distinction that leaves the boundary indeterminate.

(3) As Rick Norwood said, Wikipedia is a summary of sources, not truth for which there is no consensus in previously published, reliable sources. Lacking a consensus among mathematicians, we've opted for a definition similar to that of other general reference works, but tuned a bit to the body of the article. The current definition has its flaws, but it's certainly well-sourced (except for "change").

These reasons don't mean that the current opening can't or shouldn't be greatly improved. They're obstacles that need to be overcome in order to reach that improvement. Here are three things that you can do. First, edit the body of the article to the point where it calls for rewriting the definition; see WP:LEADFOLLOWSBODY. The body of the article is begging for all kinds of improvement, and those would likely do as much or more to get across the nature of mathematics than rewriting the definition. Second, find a way to word the new definition so it doesn't take one side in the conflict over definitions. Your current proposal takes one side, or at least opposes some of the leading definitions. And third, find good sources to support the new definition. The reasons you gave above refer to the nature of mathematics, not to sources.

The reasons you gave regarding clarity are well taken, though. I just changed "subjects" to "topics". Of course, this is only a small improvement. It might also be possible to improve the "abstract" part without first overcoming the obstacles described above. —Ben Kovitz (talk) 21:03, 10 September 2012 (UTC)

Well...does seem to be written by mathematicians and not writers.  :-) In addition to starting with a single awkward sentence (instead of a well formed paragraph), it then goes on to provide a laundry list of quotes about math from famous people. I feel that the field is so broad and there's no "Joe Math" who started it, so a good lead on the topic should probably avoid naming any specific mathematicians as best possible. I'm also about the "holy trinity of paragraphs" so I'd say paragraph one would go approximately like this (solve for X)

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the abstract study of topics including quantity,[2] structure,[3] space,[2] and change.[4][5] While the term has been around since X[?], there is no generally accepted definition of everything it encompasses [7][8], and practicing Mathematicians analyze many other properties [6]. Though often pursued for its own sake, many of today's scientists rely heavily on applied mathematics for their work—and practical uses for what began as pure mathematics are frequently discovered.[17]

For what would be the third paragraph, start with a variant of Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.[11] and finish with a couple more sentences about applications. The second paragraph is whatever's left when the quotes are cut—basically expanding on the definitions of the field and its sub-branches. Well, there's my "vision statement". Metaeducation (talk) 08:09, 6 January 2013 (UTC)

I agree that the laundry list of quotes should be deleted wholesale and replaced with a summary of the body of the article, per MOS:LEAD. It looks like several hours' work. Want to give it a go? I haven't felt much enthusiasm for doing this, because the body is such a poor overview of mathematics. But it would still be a fine step forward. —Ben Kovitz (talk) 13:38, 20 May 2013 (UTC)

Group theory picture

As a graduate student in group theory, I do find it a bit alarming that this picture of a rubix cube has become the cornerstone of Wikipedia's imagery on groups. Yes, the rubix cube does form a group under composition of turns, but is it a key, or even interesting example of hows a group can function? I motion that it is changed to something more relevant to the field itself (e.g. an illustration of a dihedron group might be nice as it is the lodestone of much of most introductory texts). If I am alone on this issue, I will simply retract my argument, but I do find it a tad annoying. — Preceding unsigned comment added by 76.126.169.150 (talk) 03:46, 13 January 2013 (UTC)

Pure mathematics on top section

It is just a minor change but i cant touch it.

On top section last paragraph,it said, "Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind."

It is ambiguous. A mathematician can engage in "pure mathematics" without mathematics and any application in mind. The sentence isn't exactly false but ambiguous. If i can edit i would just delete ", or mathematics for its own sake, ". If you think we must mention something like "pure mathematics often has mathematics in mind", then try split the sentence in better shape.

Also,this wiki article is trivial and important for all, extra care on wordings/semantics must be given, so it doesn't spread any misleading information.14.198.221.131 (talk) 16:34, 23 December 2012 (UTC)

Wrong link in lead paragraph

Wrong link in lead paragraph - the space link should go to Space (mathematics) not Space. — Preceding unsigned comment added by 173.79.197.180 (talk) 02:02, 27 February 2013 (UTC)

Please sign your talk page messages with four tildes (~~~~). Thanks.

I'm not sure about that. The lead says that mathematics is the "study of topics encompassing quantity, structure, space, change, and other properties." So i.m.o. in this context space is meant to be taken in the more general sense. - DVdm (talk) 09:12, 27 February 2013 (UTC)

Yes. Geometry has traditionally been defined as "the science of space", not "the science of mathematical spaces" (which are not the same as space in the ordinary sense, though partly inspired by it). —Ben Kovitz (talk) 13:21, 20 May 2013 (UTC)

system of equations

Hello, i have a problem with my homework. and i was wondering if you can help me with it. — Preceding unsigned comment added by Mickenson45 (talk • contribs) 00:41, 6 March 2013 (UTC)

No, sorry. This page is for discussing proposed improvements to the mathematics article. However you can ask at the mathematics reference desk. The operative word there is "help", not "do it for you" — first, write out what you've done so far, explain where you're stuck, and ask for help getting past that point. --Trovatore (talk) 01:18, 6 March 2013 (UTC)