 | This subject is featured in the Outline of mathematics, which is incomplete and needs further development. That page, along with the other outlines on Wikipedia, comprise Wikipedia's Outline of Knowledge, which also serves as the table of contents or site map of Wikipedia. | | Mathematics has been listed as a level-1 vital article in Mathematics. If you can improve it, please do. This page has been rated as B-Class. | | This article is within the scope of the following WikiProjects: | | |
[edit] 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) [edit] Citation needed? Hi folks, the following has a {{fact}} tag... - Further steps needed writing or some other system for recording numbers such as tallies or the knotted strings called quipu used by the Inca to store numerical data.[citation needed]
But what needs sourcing? I'm a bit confused... - Tbsdy lives (formerly Ta bu shi da yu) talk 06:29, 12 September 2009 (UTC) - Part of the problem here is that the sentence is written rather badly, so it's hard to say exactly what needs sourcing (or what the sentence means at all, I'm afraid!) Whatever the main point is (that further steps in mathematical development required writing or other notation systems?), there needs to be a citation to a reliable source that stated this is the case. It isn't enough just that a point makes sense or is logical; it must be sourced. Ideally you'd source both the main point, AND a source stating that the Inca used quipu to store data. (I didn't add the tag btw, just my thoughts). 121.98.130.90 (talk) 02:43, 27 November 2009 (UTC)
[edit] "Mathematics is a language" Yes, mathematics is a language. but mathematics is not just a language. I would like to see the following added: "Mathematics is a language, method, and body of knowledge ... " Comments? Rick Norwood (talk) 12:56, 28 October 2009 (UTC) - I have reverted the change entirely. Do we have to go here again? If so, discuss first. --Trovatore (talk) 12:59, 28 October 2009 (UTC)
Mathematics has a language, just as every field does. But that's as much as you can say. Medical researchers use language not familiar to lay people; but that doesn't mean medicine is a language. Astronomers use language not familiar to lay people, but that doesn't mean astronomy is a language. Michael Hardy (talk) 02:53, 29 October 2009 (UTC) Michael Hardy is correct. Similarly, math has methods and perhaps contains a body of knowledge, but these are insufficient for a definition. I believe the claim that mathematics is a language has been historically supported by some who adopt a formalist view of mathematics, but this is a minority philosophical view and should not be used here. Rick Norwood, you might want to expand on this in the Definitions of mathematics article where different philosophical views are discussed. --seberle (talk) 15:20, 30 October 2009 (UTC) - The philosophy is interesting, but I want this article to be mainstream. "Mathematics is a science and study..." is better than "Mathematics is a language..." but not much better, because science is inductive and mathematics is deductive. A large number of examples can show that water flows downhill, but no number of examples can prove the twin primes conjecture. Rick Norwood (talk) 15:30, 30 October 2009 (UTC)
-
- Actually, I agree with you. I am not happy about the use of the word "science" in the opening sentence. I think "study" would be sufficient. But this has apparently been debated quite a bit in archived discussions of this page (though I don't see a clear consensus on this point—did I miss it?) and apparently this is the wording that was decided. Fortunately, there is a satisfying discussion of whether math is a "science" later in the article. --seberle (talk) 16:38, 30 October 2009 (UTC)
- I don't believe there was ever a real consensus for science. I think someone slipped that in at a point when people were tired of arguing about it. While I personally am fine with science, I think it would probably be better to put that back to the status quo ante, as it's a controversial point, and also because it's not the outcome of the long painful argument. --Trovatore (talk) 19:39, 30 October 2009 (UTC)
- Yes I think Trovatore is correct about the status of "science". I think it should probably be removed. Paul August ☎ 19:44, 30 October 2009 (UTC)
-
-
-
- I do not like including "science" for stylistic reasons. As the "Mathematics as science" section makes clear (I think), math is not a science in the sense of a natural science or experimental science, but it is a science in the original sense of a "field of knowledge" or study. But this means that "science and study" is redundant (and possibly confusing). Omitting the word science in the opening sentence does not mean Wikipedia is decreeing that math is not a science; it is just putting off the debate until another section. (A second reason for omitting science in the first sentence is that this is a debated term and should not be included in the opening definition.) If the decision is made to retain "science", please consider rewording in a way that does not sound redundant, such as "Mathematics is the science that studies ..." --seberle (talk) 15:39, 2 November 2009 (UTC)
- Well, no, the section presents differing viewpoints on the question of whether mathematics is a science in those senses. As I have expressed elsewhere, my position is that mathematics is indeed an experimental science. But the point being controversial, the first sentence should probably not appear to take a position on it. --Trovatore (talk) 20:56, 2 November 2009 (UTC)
- Mathematics is certainly not a science in my view. Firstly, mathematics is an axiomatic theory; that is, a mathematican defines truth, and deduces further truth. In science, the "axioms" may change as new theories develop since the axioms must usually be verified by experiment in science. Secondly, mathematics is not done solely for science (lay readers may interpret "mathematics is a science" in this way, as many are already under this misconception). Branches of mathematics such as general topology or number theory are not done for science only. Therefore, I think that we should not make links to science until later in the article. --PST 00:59, 3 November 2009 (UTC)
- This is not really the right forum for discussing whether math is a science, but just to clarify my position: as a mathematical realist I consider mathematics to be about objects that exist independently of our reasoning about them, and therefore the truths about them do not derive from the axioms; rather the axioms must be chosen so that they are true. Figuring out which ones are correct (for example, large cardinal axioms) as opposed to the ones that are wrong (for example, the axiom of constructibility) is a scientific, and partly empirical, endeavor, and is definitely part of mathematics. --Trovatore (talk) 01:13, 3 November 2009 (UTC)
- I think a strong argument could be made that math is an experimental science, but I did not see this in the "Mathematics as science" section. I am not at ease with the purely axiomatic view of math. It would be good to hear more about this, but Trovatore's link to "mathematical realist" does not go anywhere. I am glad for the revert to "study" for now, if only for reasons of style and clarity. But it would be good to understand this further, perhaps with some links to other references? Or is everyone tired of this debate? --seberle (talk) 03:08, 3 November 2009 (UTC)
- Oh, I can argue about it endlessly — this just isn't really the right place. --Trovatore (talk) 03:10, 3 November 2009 (UTC)
The introduction should use a neutral word. I think "Mathematics is the study of..." is fairly neutral. Let's leave it at that unless there is a consensus on some other word. Rick Norwood (talk) 16:15, 3 November 2009 (UTC) - I agree completely. The lower part of the article can discuss the "science" term at length, as it should be. — Carl (CBM · talk) 21:38, 3 November 2009 (UTC)
[edit] "strict synax"? Under "Notation, language, rigor", there's a statement "modern mathematical notation has a strict syntax". I'd like to see a citation to back this up, or indeed a link to a wp page describing "the" strict syntax, especially since there's a link for musical notation. In my experience there are a variety of different notations used in math, often varying within fields, between authors in the same field, and sometimes even on the same page of exposition. Gwideman (talk) 14:42, 11 December 2009 (UTC) I think the idea being expressed here is not that there is one and only one strict syntax for all of mathematics but rather that the syntax, whatever it may be, is strict, and you cannot, for example, write x+1^n when you mean (x+1)^n. It could probably be expressed more clearly. Rick Norwood (talk) 20:09, 11 December 2009 (UTC) - Perhaps "precise" would be a better word than "strict"?Paul August ☎ 20:15, 11 December 2009 (UTC)
-
- I agree that the objective is to convey an idea precisely from author to reader. And agreed that within a subset of notation, the writer has to write it in accordance with that idea, and the reader has to read it the same way. However there are all sorts of ambiguities: Should one write d/dx, or use prime, or a dot? If one reads x', does that mean derivative of x, or a second variable that may or may not be related to an x somewhere else? What does a caret ("hat") mean? Are square brackets an array subscript or an operator of some kind? Does the author's choice of beginning- and end-of-alphabet letters (a, b, c vs x, y, z) distinguish coefficients from variables, or not? What about i, j, k: Variables? Subscript? Sqrt(-1)? Much relies on context and upon the reader being familiar with the author's mathematical "culture". Which is to say, the notation not strict or precise according to some consistent standard, but relies on the reader divining which convention the author is using, or sometimes even what convention the author has invented on the spot.
- Anyhow, I'm certainly not qualified to characterize this -- I was hoping someone would point to a reference or two on the subject! Gwideman (talk) 02:22, 12 December 2009 (UTC)
[edit] Calculations, measurement, arithmetic; not part of mathematics? The following sentence is pasted directly from the lead: "Although incorrectly considered part of mathematics by many, calculations and measurement are features of accountancy and arithmetic." I am not an authority on mathematics, so perhaps I fall under the category of the many who make incorrect assumptions according to that statement, but the arithmetic lead on this same wikipedia mentions that subject specifically as being "the oldest and most elementary branch of mathematics". There is definitely a contradiction here. Measurement too might be argued to be a branch of mathematics (i.e. geometry ("earth-measuring")); Euclid's Elements, which is a treatise on geometry, is specifically mentioned in the lead as an example of mathematics. Zalmoxe (talk) 16:12, 24 December 2009 (UTC) |
