Talk:Mathematics

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Contents 1 Protection 2 Peirce's quotation needs to have the period within the quotation marks. 3 Factual Inaccuracy 4 Looking for the meaning in English 5 algebra 6 Overview look

[edit] Protection

Surely it's time for this article to be unprotected? 86.27.59.185 (talk) 23:42, 30 January 2008 (UTC)

The "protected" tag may have to stay. Large numbers of bored high school students want to add to the article, "My math teecher suks." Now, they can do that during class, using their cell phones.Rick Norwood (talk) 14:16, 31 January 2008 (UTC)

Bored with maths - I can't believe that! Anyway, we should unprotect it and see if this really does happen. By default Wikipedia articles shouldn't be protected. If a big problem emerges then it can soon be re-protected. 86.27.59.185 (talk) 21:38, 2 February 2008 (UTC)

I agree. Last anon edit was back on Nov 2nd. That's long enough. Unprotect it and reprotect only if/when persistent vandalism (re-)occurs. - dcljr (talk) 19:24, 4 February 2008 (UTC)

Could a passing Admin please unprotect. 81.76.82.232 (talk) 17:41, 6 February 2008 (UTC)

[edit] Peirce's quotation needs to have the period within the quotation marks.

—Preceding unsigned heading added by 76.22.155.72 (talk • contribs) 09:28, February 1, 2008 (UTC)

Not really. There are two competing conventions for the placement of punctuation marks – inside or outside – at the end of a quotation: "American style" or typesetter's quotation and "British style" or logical quotation. The Mathematics article is rather inconsistent in this respect, but the Manual of Style prescribes the use of logical quotation, which for the Peirce quote means: outside.  --Lambiam 20:02, 1 February 2008 (UTC)

In the Mathematics article, it makes sense to standardise on the "logical quotation". Do do otherwise would be "odd." Stephen B Streater (talk) 09:40, 5 February 2008 (UTC)

[edit] Factual Inaccuracy

The following is factually inaccurate:

"However, in the 1930s important work in mathematical logic showed that mathematics cannot be reduced to logic, and Karl Popper concluded that "most mathematical theories are, like those of physics and biology, hypothetico-deductive: pure mathematics therefore turns out to be much closer to the natural sciences whose hypotheses are conjectures, than it seemed even recently.""

1. this "work" 1930s is undoubtedly Godel's work on axiomatic systems and the discover of a Godelian assertion. Godels work does not in fact imply that mathematics does not reduce to logic because mathematics is only logic. All mathematics is only logic. This is not a matter of opinion. It is fact. All mathematical study consists of forming a set of axioms and definitions and using logic to connect the definitions using the axioms. All Godel did with the incompleteness theorems is demonstrate that there are statements that are not provable using logic.

2. Popper's quote does not imply that mathematics does not reduce to logic. Popper may be remarking on the fact that the study starts with conjecture and then proceeds to look for proof. This is indeed the case in both mathematics and natural science.

3. If, however, Popper is suggesting that mathematics is not pure logic, he is wrong. Just because he is respected doesn't mean he isn't extremely wrong. Mathematics is only logic. Mathematics is in no way a science that uses observation or measurement in any way in order to provide proof of an assertion.

I will let the author change it so that the flow of the paragraph can be maintained. The point is, Godel's work is celebrated as a breakthrough in logic, not a demonstration that mathematics is not purely logical. Mathematics is defined for all practical purposes as "logical evaluation of what follows from assumptions", so how can that not be logic?--Gtg207u (talk) 06:06, 10 February 2008 (UTC)

Well, the important thing about Gödel's incompleteness theorems is that they show that in any (moderately powerful) formalisation of mathematics there are mathematical statements expressed within that formalisation that are not only not provable starting from the axioms of that formalisation but are also self evidently true. So to see that these statements are true, we must be using reasoning that cannot be captured within our chosen formalisation. I don't think this immediately leads to the conclusion that mathematics is a science - although mathematicians do hold a range of different opinions on that topic as well, some of which are discussed in the Mathematics as science section of the article. I am very dubious about any attempt to define all of mathematics theory and practice within a single phrase or sentence - that is why the article is so long (and this talk page and its archives are much longer).

Anyway, there is no single author of this article - like every article in Wikipedia, it is a piece of collaborative writing - see Wikipedia:About for more information on how Wikipedia works. So you don't have to wait for the "author" to come by and fix things. If you think you can improve on this part of the article then dive in and change it - or, if you prefer, propose a new version here on the talk page first. Gandalf61 (talk) 09:32, 10 February 2008 (UTC)

There are different views on what constitutes mathematics; see Foundations of mathematics and Philosophy of mathematics. The point of view that all mathematics is (reducible to) logic is certainly not universally shared, and some would, rather conversely, maintain that logic (inasmuch as it can be made rigorous) is a form of mathematics. By Gödel's results we know for a fact that there is no single formalization of mathematics that is sound and whose theorems encompass all mathematical statements that are provable. And we definitely have no general method for determining whether a proposed formalization of a fragment of mathematics (like for example ZFC) is sound, nor is there any basis in logic for preferring AC over (for example) AD. Therefore it is too bold to label the contended statement "factually inaccurate". Without looking it up, I don't know if the rendering of Popper's conclusion is adequate, but if it is: this is Popper's conclusion, not Wikipedia's.  --Lambiam 18:40, 10 February 2008 (UTC)

CRITICISM OF THE ABOVE ARGUMENT:

When mathematicians say that "math is not reducible to logic" they are alluding to Godel incompleteness. If Godel Incompleteness were not true, then we could aspire to a day when all mathematic truths were deducible from a finite set of axioms. Then mathematics would become essentially a branch of logic and mathematicians could be replaced by computers. But, by Godel incompleteness, such a system will never be constructed and therefore we cannot even aspire to this. This is all we mean when we say "math is not just logic." The comments above have naively interpreted "math is not logic" to mean that mathematics does not employ the tools and methods of logical analysis. In this case the criticism is basically correct. But, by this definition, the creative process of constructing new axioms is "logic" and that is not the usual employment of the term. Creating new axioms is not a purely logical procedure (if by logical procedure we mean step by step deduction), it requires creativity and intuition. Add to this the fact that there will never be a perfect set of axioms, and you have shown that mathematics will never become logical deduction. Imagine if Godel proved arithmetic to be complete. Then Fermat's last theorem probably could have been proven by a computer much sooner then it was. It is a simple arithmetical statement, easily expressible as a logical formula in a first order logic.

-Barry Barrett B.S. in Mathematics University of Rhode Island —Preceding unsigned comment added by 68.226.94.121 (talk) 08:55, 18 May 2008 (UTC)

[edit] Looking for the meaning in English

หาคําแปลภาษาอังกฤษ —Preceding unsigned comment added by 125.26.10.19 (talk) 06:02, 26 April 2008 (UTC)

[edit] algebra

(a+b) —Preceding unsigned comment added by 203.126.166.172 (talk) 08:30, 3 May 2008 (UTC)

Under the entry «Mathematics (disambiguation)» is given the correct definition of the term 'mathematics':

Mathematics is the body of knowledge justified by deductive reasoning about abstract structures, starting from axioms and definitions.

I want to add here that the 'abstract structures' are created by humans and can not be indefinite.

Under the entry «Mathematics» one can read: «...mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects.»

Yes, it evolved from theoretical physics in particular but the modern trend not to separate theoretical physics and mathematics (and call the whole thing mathematics) is an abomination. Mathematicians are studying indefinite objects (which is o.k. in theoretical physics but not in mathematics). Geometry that is taught in schools is not mathematics – it is theoretical physics. —Preceding unsigned comment added by Oldsmobill (talk • contribs) 13:07, 15 May 2008 (UTC)

All of these statements are controversial and could elicit much discussion, but this page is for discussing improvements to the Mathematics article, not for discussing mathematics. If you would like these views to be represented in the article (or in Philosophy of mathematics?) then you should find reputable, verifiable sources that express the views, and cite those sources. Joshua R. Davis (talk) 13:58, 15 May 2008 (UTC)

A little history:

When this article was in its formative stages, there was a big controversy about the definition of mathematics. Is mathematics that body of knowledge that arrises from deductive reasoning, or is mathematics the study of shapes and numbers? Both sides were sure they were right, but the dictionary overruled the pure mathematicians, and the dictionary says shapes and numbers. Further compromises added other subject areas and a nod to the pure mathematicians in the last sentence of the first paragraph. None of us who took part in that long, long battle wants to reopen the question now, since the end result is apt to be the same. Rick Norwood (talk) 12:47, 16 May 2008 (UTC)

[edit] Overview look

Angeliccare (talk) 10:28, 8 June 2008 (UTC): Any ideas how to modify the following text so it could be added to the article?

Mathematics in it's full glory, in limit - is a represenation of human mind: the whole mind: including thinking.

However mathematics does not (even in the full glory) include many things:

• the life: life produces the need of thinking. What is brain and thinking without the need itself for the things to be thought of?

Mathematics is only relevant and pertinent in the context of life.

• the names: how names becomes valuable and meaningful? They represent something more-in-depth than mind, the names are something that can be said via mathematics but is not included into.

Between these 2 - the life and the names lies the whole mathematics.

Personally, I wouldn't put any version of that into the Mathematics article. I don't know where it comes from, but it sounds like a variant on the embodied mind theory of mathematics. Most mathematicians would prefer a more objective and more down-to-earth definition of their subject. I don't think this minority view is sufficiently notable to be mentioned in the subject's top-level article. Gandalf61 (talk) 11:32, 8 June 2008 (UTC)

Angeliccare (talk) 11:50, 8 June 2008 (UTC): Every definition can be described as a projection of the term to it's maximum glory. Such projections, when collected together can in total give the full overview for the subject. Definitions are given when Life demands something strict. But how can you give something strict without completeness? Downed-to-earth is good and practical but loses the fullness.

Sorry, Angeliccare, but I agree with Gandalf61. This does not belong in this article. Rick Norwood (talk) 13:44, 8 June 2008 (UTC)