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Rajnish Kaushik

Can someone explain the real meaning of Maths???

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I think of it as a language system used for describing the quantitative properties of the world around us.

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Like I said, it's numbers sorted into order.

 

Thus 1,2,3,4,5,6,7,8,9 is maths.

 

But 7,2,5,3,9,1,8,4,6, is only random numbers.

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What do you mean by "the real meaning of mathematics"? Do you want a definition of mathematics or are you looking for some justification of why it is useful?

 

As for a definition, I am not sure what mathematics really is or what would really encompass all of mathematics.

 

Loosely, I would say that mathematics is the study of the structure of given abstract systems. But this does not really get to the heart of the power or beauty of mathematics. Mathematics can look like a mixed bag of methods or a game in which one makes up the rules to suit. Neither of these views, which can be prevalent, are again not representative of what mathematics really can be.

 

Why not give us your opinion on this?

 

Maths is numbers sorted out?

 

There is a lot more to mathematics than just number.

 

I think of it as a language system used for describing the quantitative properties of the world around us.

This is for sure one of the powers of mathematics. In analogy, Shakespeare wrote poetry with the English language, he did more than just describe what was around him!

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Any simple school level yet effective explanations?? sad.png

 

Is this for a homework assignment?

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Oh.

You are lucky to know the topics of your future exams.

The tactic to follow is to find the answer into the stuff your professor told you, or to find out what he (or she) is waiting for, not evidently what members here tell you.

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no it will be an topic in exams sad.png

Wow, that would be a very hard question in an exam to answer well as there is no completely agreed upon definition of mathematics. Your best bet, as already stated, is to see what your teacher expects and/or give a dictionary answer with some further comments.

 

One problem with all the definitions I have seen is that they just shift the problem to defining something else. Even my loose definition as the "study of the structure of abstract systems" requires careful definitions of "structure" and "abstract systems", both of which are not obviously defined.

 

You can find lots of various working definitions of mathematics with a quick google search, but none are completely satisfactory.

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Well I think mathematics is pure logic. I mean like there is no difference between mathematics and logic at all.

 

Just so happens that logic can be used to quantify physical properties, most of the time scientists would call the areas of logic used to quantify things as 'mathematics' but I think it's far more general than just quantifying things.

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Well I think mathematics is pure logic. I mean like there is no difference between mathematics and logic at all.

There was a school of thought along those lines, Whitehead and Russel were supporters of this philosophy. However, we now know that mathematics cannot be formulated in terms of logic alone, though large parts of it can.

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Why not? :S

 

I mean say you need logic for some parts, but there are some parts that need something other than pure logic to derive them. That'd mean you'd need some kind of empirical findings from the physical world to guide you, but isn't mathematics meant to be totally independent on the physical world?

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Why not? :S

Gödel's incompleteness theorems which show that Hilbert's second problem is answered "no". The second problem is to find a complete and consistent set of axioms for all mathematics is impossible. The null result here means that one cannot start from some all encompassing set of axioms and just apply mathematical logic to get all true statements in mathematics.

 

What I will say is that this deep result in foundational mathematics does not worry most practicing mathematicians and for the most part we can apply logic, just it is done rather informally. So, what you said before is mostly true, but not fully true and we cannot equate all mathematics with logic.

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o_o

 

Fair enough hehe, this is one of these times where my ignorance on this particular issue must be submitted to I guess.

 

Kind of boggles the mind when you think that a complete and consistent set of axioms for all mathematics is impossible, its as though mathematics itself has like a built in self-destruct mechanism or something

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Like I said, it's numbers sorted into order.

 

Thus 1,2,3,4,5,6,7,8,9 is maths.

 

But 7,2,5,3,9,1,8,4,6, is only random numbers.

 

This is an excellent example to show the flavor or sense, if not the meaning, of math.

 

One of the things mathematicians study is order. If we have the set {1,2,3,4} we can order it in several ways. [Let me just use a four-element set for simplicity]

 

One way to order them is called the "usual" or "standard" order, 1 < 2 < 3 < 4.

 

Another way to order them would be 2 '<' 4 '<' 3 '<' 1 where I'm putting the < sign in single quotes to indicate that this is not the same as the usual way of ordering these four numbers.

 

Now, this is perfectly legitimate. As an everyday example, suppose you are a schoolteacher in charge of a class of kids and you tell them to line up by height. Then you tell them to line up by weight. Then you tell them to line up alphabetically by last name. Then you tell them to line up alphabetically by first name. Or in reverse order of their score on the math test.

 

You can see that given a set of objects, there are many ways you can impose an order on them. There are many ways you can impose an order on the set {1,2,3,4}. How many ways? Well, you have free choice for the smallest element of the order. Then you only have 3 choices left for the next element, then 2 choices, then 1 choice. So you can order {1,2,3,4} in 4*3*2 = 24 different ways.

 

So we have a theorem: There are exactly 24 ways to line up four objects in some order. It doesn't matter if the objects are school kids, apples, planets, universes. If there are 4 of them, then there are 24 different ways to line them up in some order.

 

Now, what is math? Math is the subject that can say something sensible about all the different ways you can put a set of four objects into an order.

 

In math we don't care that these are four numbers, four school kids, four cows, or four universes. In math all we care about is the number 4.

 

That's math. Math is an organized body of knowledge that cares about numbers, shapes, and relationships among things, without caring about the nature of the things themselves.

Edited by Someguy1

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So we have a theorem: There are exactly 24 ways to line up four objects in some order. It doesn't matter if the objects are school kids, apples, planets, universes. If there are 4 of them, then there are 24 different ways to line them up in some order.

 

We have to be careful not to be too all embracing.

 

What would happen if all the schoolkids were exactly the same height and you told them to line up in order?

 

Or, since I can take any members what if I ask four hydrogen atoms to line up in order?

 

How about a mathematical example, the set of 4 rotations by degrees {0, 360, 720, 1080} ?

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We have to be careful not to be too all embracing.

 

What would happen if all the schoolkids were exactly the same height and you told them to line up in order?

 

Or, since I can take any members what if I ask four hydrogen atoms to line up in order?

 

How about a mathematical example, the set of 4 rotations by degrees {0, 360, 720, 1080} ?

 

Enter the notion of a "partial ordering" :)

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