Talk:Mathematics/Archive 4

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Complex numbers/imaginary numbers

I am not entirely sure if this is a good place to discuss this but I wanted to conglomerate a discussion into a single location where everyone can find it. I did some reading on complex numbers and it seems to me that we have an awful lot of overkill on:

Or maybe it's because I'm new to the subject. Can someone please advise. --Will2k 17:44, Jan 10, 2005 (UTC)

Well, if you mean, should there be just one article, I don't think so. These articles, while related, are about different things. Imaginary unit is about the number i, the square root of −1. Imaginary number Is about all the so-called "pure" imaginary numbers (including i), of the form: ib where b is a real number. And Complex number is about the "mixed" numbers (including all the "pure" imaginary numbers), of the form: a + bi, where a and b are real numbers. So they are different but related, with the "imaginary unit" being a particular (and most "important") "Imaginary number", while the imaginary numbers are (an "important") subset of the "complex numbers". Consequently there is some overlap, but there's nothing really wrong with that. Paul August ☎ 18:38, Jan 10, 2005 (UTC)
Will2k, something you'll notice when studying math is that a lot of terms overlap, but more importantly that different subjects approach a topic in different manners. In the case of i, there are multiple ways to define it. One is the algebraic definition, the solution to x2 = −1. Another is to imagine complex numbers as the x-y plane, where the real numbers are the x axis and the imaginary numbers are the y axis. These different articles are based on different definitions of the complex numbers. --Sean Kelly 03:13, 11 Jan 2005 (UTC)

"the queen of the sciences"

Einstein may have called math "the queen of the sciences", but Gauss said so first. -- Gruepig 07:46, 6 Mar 2005 (UTC)

Both Gauss and Einstein borrowed the 'queen of the sciences' quote from Thomas Aquinas. The original quote is 'Theologia scientiarum regina est, et philosphia serva suae est' (Theology is the queen of the sciences, and philosophy is her handmaid). It seems that this view was based on Boethius, who used the imagary of being a queen in describing philosophy. Gaus and Einstein were merely extending the metaphor to modern epistemology: classical philosophy, mediaeval theology and modern mathematics. Immanuel Kant described metaphysics as the queen of the sciences. I don't think mathematics can claim this title outright: such would lead to much feuding intra-campum. Gareth Hughes 13:12, 6 Mar 2005 (UTC)
In case there is ever dispute. . .a monarch need not be of the same race as the subjects. Mathematica may be queen of the sciences, but this does not imply that she IS a member of that category. Dpr 03:43, 16 Mar 2005 (UTC)


On the worsening state of this article

I remember when I took biology back in high school, my teacher began by asking the class what biology was. When we all agreed that it was the study of life, he asked us what life was. By the end of the class, after agonizing our brains, we paradoxically knew that we could classify 99.9% of the things in this world as living or not, but could not seem to come up with a consistent definition of life.

If my mathematics professors in college had tried to get us nascent students to come up with a definition of mathematics at the beginning of our studies, there would have been a much smaller graduating class. Trying to define mathematics is as futile and meaningless as trying to define life. Instead, our professors taught us the different techniques and core concepts of mathematics, and left it up to us to figure out what the nature of mathematics was.

This little rant was spurred on by the worsening problem of people waxing philosophic in this article. The following paragraph was recently added:

While higher maths deviate from this definition, for most people math is a language designed to express quantities and the relationships between quantities, as well as a problem solving process designed to determine unknown quantities and quantitative relationships.

At the moment, the introduction to this article takes up the majority of my screen, and contains almost no actual information. I feel that most of it is philosophical babble; I myself have committed this sin by filling this talk page with discussions of whether mathematics is a science or not.

I would like to throw away the current introduction and replace it with something like

Mathematics is most commonly thought of as the study of numbers and equations, though in fact a wide variety of topics are covered by the discipline.

Along with a comment warning editors that anything they add to the introduction will be deleted by me. I was just going to post this and see what the reaction was... I'll wait until I'm in a sour mood to do any real damage. --Sean Kelly 07:19, 15 Mar 2005 (UTC)

Sean - the recently added paragraph that you disliked (and I agree with you on this) has now been removed. By all means try to improve the introduction - but I hope you are not serious about adding "a comment warning editors that anything they add to the introduction will be deleted". For obvious reasons, that is at best un-Wikipedian, and could be construed as an open invitation to an edit war. Gandalf61 08:59, Mar 16, 2005 (UTC)
There is quite a strong case for strengthening the whole article, with a re-write of substantive parts. Charles Matthews 10:19, 17 Mar 2005 (UTC)

Math is Hard

i think math is hard. i think we should talk about how hard math is.

I think that comment applies to everything and is therefore not relevant here (although it would have to be said by different people to make the "I" accurate). Brianjd | Why restrict HTML? | 04:43, 2005 Apr 8 (UTC)


Tautologous definition?

Mathematics, often abbreviated maths (British English) or math (American English), is the investigation of axiomatically defined abstract structures using symbolic logic and mathematical notation.

By definition, "mathematics" uses "mathematical notation".


Conciseness

I just removed the following which was just added to the intro:

Mathematics, often abbreviated maths in British English or math in American English, by one strict and concise academic definition, Mathematics is a logical methodical process of dealing with quantification, numbers, operators, variables, sets, outcomes, definitions, theorems, and axioms. The field of mathematics started very primitively with counting, addition, subtraction, multiplication, and division. It encompasses those primitive roots and teachings, but has progressed such that now the leading mathematicians are exploring purely hypothetical areas as well as purely mathematical explorations of empirical areas, such as mathematical physics. All areas of mathematics from its roots to its most current and abstract from, are continuing to be taught and explored by budding mathematicians and professionals.

Mathematics is quite often based on empirical, or on hypothetical axioms, and definitions. However, even when in its purest hypothetical form, the axioms must be defined by using very understandable ideas. Those ideas could be described from the world around us, or purely described by hypothetical idea on top of hypothetical idea, on top of hypothetical idea.

Mathematics is scientific because of both its basis on empirical observations, and on the methodical, logical, and especially repeatable, process one uses to research mathematics and all sciences. It is not purely an empirical science nor is it purely an offshoot of logic. It is its own area of study for the pure enjoyment and gain of knowledge. There are many mathematicians practicing the science purely for the artistic value of the equations.

It is, as are all sciences, heavily dependent on logic, and at times empirical observations. Some observations are strictly observations of outcomes based on calculations of hypothetically defined axioms. Often even those calculations rely on primitive mathematical operations derived long ago by the first observations of mathematicians on the world around them.

All science would be useless without mathematics.

Mathematics differs from the strictly empirical sciences by the primitive nature of its axioms. Physics and Mathematics overlap in places. By definition, empirical sciences must rely on observations of empirical means to verify the mathematical models.

Our knowledge in many fields of mathematics is constantly growing, through research and application. Mathematics is usually regarded as an important tool for science, even though the development of mathematics is not necessarily done with science in mind (See pure mathematics and applied mathematics.).

The specific structures that are investigated by mathematicians sometimes do have their origin in natural and social sciences, including particularly physics and economics. Some contemporary mathematics also has its origins in computer science and communication theory.

Not only is it poorly written, but it is the exact kind of overzealousness that one editor spent a long time editing out. If you want to start a discussion of the nature of mathematics, please do it in a forum somewhere or, if you can write it in a concise manner, in the section titled (appropriately), On the nature and scope of mathematics. Anywhere but where you just put it. --Sean κ. ⇔ 22:33, 15 Apr 2005 (UTC)

I would like to add that I'm not trying to start a revert war or be un-Wikipedian. If you put it back, I won't revert it again. --Sean κ. ⇔ 22:35, 15 Apr 2005 (UTC)
However, I will, and so will others, so please take what he said seriously. – Smyth\talk 09:58, 16 Apr 2005 (UTC)

Remove discussion

Okay, honestly I'm getting sick of the "Is math a _______?" discussion. I think we can all agree that we know what Mathematics is, and that this argument is turning out to be fruitless, given the medium we're working in. So can we please remove any discussion of "Is math a _____?" from the article, and instead just link to the appropriate page? I'd be happy to concede my side of the argument if it prevented this page from getting defaced again. --Sean κ. ⇔ 22:49, 15 Apr 2005 (UTC)

What exactly do you object to, in the current form of the article? There is not much point editing on the basis of trying to prevent further edits, so can we instead just discuss any weaknesses remaining? Charles Matthews 11:51, 17 Apr 2005 (UTC)
Well, I guess I was going to say to prevent further edits :(. It seems to be provoking people to contribute, not factual analysis, but their philosophical hot air. Maybe the page is just having a bad week. --16:03, 17 Apr 2005 (UTC)
It's close to the Main Page, and people are going to come and edit. There was one editor with an axe to grind about 'science', very much as I said above. Charles Matthews 16:46, 17 Apr 2005 (UTC)
Well, I think the thing to do is to work on the Misconceptions part, to try to clarify what is said. Also, turn those dull, old-fashioned lists into some better 'themes'. Charles Matthews 17:27, 17 Apr 2005 (UTC)
Agreed. But I'm still going to take the line, Some hold that since mathematical knowledge is not fundamentally empirical, mathematics is not itself one of the sciences, however closely allied out of the intro. --Sean κ. ⇔ 18:00, 17 Apr 2005 (UTC)


Clap clap clap clap. You bozos have managed to define mathematics as "nothing". Clap clap clap. Axiomactic system. Even the definitoin of and axiom is missing any real definitions.

When you figure out what mathematics is. Please provide the definition.

By the way, developing the axioms is what mathematics is as much as the rote calculations. Describe how mathematicians develop axioms. Please. EDN

If you are making the point that the origin of axiomatic systems is not something shallow, then you are making a good point. And probably not one that we have addressed anywhere directly on WP. On the other hand in order to define mathematics one has to deal with tautology, apparently low content of axiomatics, Russell's definition by quantifier structure, all as advances in the overall philosophy, rather than retreats. Charles Matthews 09:37, 21 Apr 2005 (UTC)
Tell you what. We'll provide an uncontended definition of Mathematics for this article if you provide an uncontended definiton of God for that article. —Sean κ. ⇔ 12:26, 21 Apr 2005 (UTC)