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# Is Maths considered a science? watch

1. Mathematics is "the Queen of the Sciences". Carl Friedrich Gauss 1777-1855
2. (Original post by Fat-Love)
how i LOL'D. Did you know it was proven by mathematicians around 40-50 years ago (i believe Kurt Godel or someone else) that mathematics is devised on axioms that cannot be proven within it's own rules. therefore if your basic axioms cannot be proven which leads onto to ALL other branches of mathemtics it could be considered your entire subject is based on the much hated "faith". oh and you cannot prove it's axioms using ones from outside the subject as then you'd have to prove them aswell ad infinitum.
The axioms simply define the framework that we're working in. They don't necessarily have to be "true".

For example, if I were working in a Euclidean framework, I would assume that, given any two points in space, it is possible to draw a straight line connecting them.

I'm not really fussed about whether this axiom is actually "true" in reality or not - I'm not putting any "faith" in it at all. Mathematics doesn't have to have anything to do with reality (unlike science). But unless I set it as one of my axioms, I deviate outside the Euclidean framework I'm supposed to be working in.

Look at it this way: In the chessboard example I gave earlier, I used the axiom that the dominoes cannot be broken in half. This axiom isn't true in reality. If you gave me a real life domino, I probably could break it in half if I really wanted to. But if we allowed for the possibility of broken dominoes, we'd be deviating from the rules that have been given in the question. So even if we said that the answer is "yes, you can cover the chessboard if you break dominoes", we'd be answering the wrong question anyway.
3. maths is above science
4. (Original post by tazarooni89)
The axioms simply define the framework that we're working in. They don't necessarily have to be "true".

For example, if I were working in a Euclidean framework, I would assume that, given any two points in space, it is possible to draw a straight line connecting them.

I'm not really fussed about whether this axiom is actually "true" in reality or not - I'm not putting any "faith" in it at all. Mathematics doesn't have to have anything to do with reality (unlike science). But unless I set it as one of my axioms, I deviate outside the Euclidean framework I'm supposed to be working in.
Nonetheless it doesn't change the fact that at the fundamental base of mathematics your working with ideas that essentially cannot be proven. your right to assume that you can connect any two points in space since as so far nothing has come up that can contradict it. oh and just because these fundamentals cannot be proven doesn't mean we're working with false theories. they could be true but we'll just never know how to figure out they're true.
5. (Original post by tazarooni89)

Look at it this way: In the chessboard example I gave earlier, I used the axiom that the dominoes cannot be broken in half. This axiom isn't true in reality. If you gave me a real life domino, I probably could break it in half if I really wanted to. But if we allowed for the possibility of broken dominoes, we'd be deviating from the rules that have been given in the question. So even if we said that the answer is "yes, you can cover the chessboard if you break dominoes", we'd be answering the wrong question anyway.
at no point did the questions say we couldn't break the dominoes. but i get what you're saying. but even if you create rules that say your not allowed to break the domino in half it still doesn't change the fact that you can't prove the axiom which says dominoes can't be broken in half.
6. (Original post by Fat-Love)
Nonetheless it doesn't change the fact that at the fundamental base of mathematics your working with ideas that essentially cannot be proven. your right to assume that you can connect any two points in space since as so far nothing has come up that can contradict it. oh and just because these fundamentals cannot be proven doesn't mean we're working with false theories. they could be true but we'll just never know how to figure out they're true.
They cannot be proven - but they don't need to be proven to be "true" in reality, since they are "true" by construction.

Einstein said (and I agree with him):
"as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."

The nice thing about Mathematics is that the axioms which are taken to be "true" simply specify the framework that we're dealing with. Sometimes this framework may be "reality", in the case of Applied Mathematics - but in Pure Mathematics, we generally don't deal with reality.

For example, one mathematical axiom may be "any group must have an identity element".
We simply assume that this is true. There's no chance that someone's going to come along and say "no it isn't really true", because the statement has no meaning in reality. It's "true" just because we make it true.
7. (Original post by ziggycj)
Neg rep for a video? Get over it. I answers the question.
don't worry
i've had similar in the past
there are ******** out there
8. (Original post by tazarooni89)
They cannot be proven - but they don't need to be proven to be "true" in reality, since they are "true" by construction.
one counter-example to this are axioms for counting which led to the introduction of infinity which (i think) is the largest cause of contradictions within mathematics in terms of what it does the to the axiom which introduced it -in other words it messes with how you count (i.e different infinites and number sizes etc).
9. maths is a classical science?
10. (Original post by Fat-Love)
at no point did the questions say we couldn't break the dominoes. but i get what you're saying. but even if you create rules that say your not allowed to break the domino in half it still doesn't change the fact that you can't prove the axiom which says dominoes can't be broken in half.
That's really what an axiom is though. An axiom does not really tell us "breaking the dominoes is impossible in reality", it tells us that "in this framework, you're not allowed to break the dominoes" i.e. "You may assume that these dominoes are unbreakable (regardless of whether they actually are or not, in reality.)"

The reason the answer is 100% certainly true, is because in the question I may as well be saying:
Suppose I live in an alternate universe where dominoes are unbreakable, and I have an unbreakable object which looks like a chessboard without the diagonally opposite corners... etc.

The axioms in pure mathematics simply tell you which "alternate universe" I live in, which I've created myself (so the rules are all mine to control). This alternate universe may be very similar to the real universe we live in now, or it may not be. In Mathematics, we often live in frictionless universes, air-resistance-less universes, etc.
11. (Original post by Fat-Love)
one counter-example to this are axioms for counting which led to the introduction of infinity which (i think) is the largest cause of contradictions within mathematics in terms of what it does the to the axiom which introduced it -in other words it messes with how you count (i.e different infinites and number sizes etc).
I'm not really sure what you're talking about - can you be a bit more specific? What should I search for in Google to find out more?
12. (Original post by Fat-Love)
Nonetheless it doesn't change the fact that at the fundamental base of mathematics your working with ideas that essentially cannot be proven. your right to assume that you can connect any two points in space since as so far nothing has come up that can contradict it. oh and just because these fundamentals cannot be proven doesn't mean we're working with false theories. they could be true but we'll just never know how to figure out they're true.
You don't seem to understand what an axiom is. As tazarooni has tried to explain, axioms AREN'T statements about the real world. They aren't theories that can be falsified. They are the assumptions upon which theorems are built. For example, you have Euclidean geometry. All theorems based on Euclidean geometry are true whenever the axioms are true. That's what maths is all about, a logical game where you choose axioms and see what the consequences of them are. Different branches of maths have different sets of axioms. Euclidean geometry does NOT, for example, conform exactly to the real world, because as Einstein found space is in fact bent (non-Euclidean geometry would thus be more fitting). Maths isn't true in terms of the real world, it's true in terms of its axioms. It's therefore nonsensical to say of an axiom that it could be found to be false, or that a proof just hasn't been found yet, because if an axiom COULD be proved, it wouldn't BE an axiom. An axiom has to be the most simple statement necessary for other theorems to be formed.

http://xkcd.com/435/
Yes I know it doesn't quite answer the question but it's good clean fun

For a more boring accurate answer as far as Uni's are concerned yes Maths is a science
14. (Original post by tazarooni89)
What if I were to not take Popper's view of falsifiability but the following view:

Something can only be falsified if it is false.
Mathematical theorems are (most certainly) not false
Therefore Mathematical theorems are not falsifiable.

Scientific theories stand a chance of being false
Therefore scientific theories may be falsifiable.
If we one day found out that the axioms of set theory lead to a contradiction, that would effectively falsify the theorem, would it not? (Technically, it would make all theorems true, but it would show that our method of proof lacked some desirable characteristics.)
15. (Original post by birdsong1)
If we one day found out that the axioms of set theory lead to a contradiction, that would effectively falsify the theorem, would it not? (Technically, it would make all theorems true, but it would show that our method of proof lacked some desirable characteristics.)
It would falsify the theorem - but not to the extent that we can say "the statement is not true". Rather, it would be "both true and false". So any mathematician who claims that his theorem is most definitely true still has that escape clause!

But yes, it would make the theorem quite useless.
16. yeah maths is a science subject
17. Why did they delete my answer when I answered the question fine. Anyway... once again. Sciences can be proven wrong, Arts can't.
18. (Original post by ziggycj)
Why did they delete my answer when I answered the question fine. Anyway... once again. Sciences can be proven wrong, Arts can't.
19. Maths is the queen of the sciences, *****ez.
20. Yep its apperently better than biology depending on what you're going for though .

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