# Why is math proof

1. Jun 25, 2008

### shamrock5585

so first off i will state that math is a human language... whenever an article is published or a paper written and it is said to be true it must be sited for where the info came from and often times the source has to be checked as well because, who says they are right anyway. when a scientist finds mathematical proof that something is correct and others look over the work and see there are no mistakes it becomes accepted as proof and no sources are required... why does math always prove something correct? anybody got some good answers?

2. Jun 25, 2008

### CompuChip

You mean: why do people accept a theorem from a reference once it is generally agreed upon that the proof of that theorem there is correct?

3. Jun 25, 2008

### shamrock5585

well yeah... i mean if someone comes up with a theorem... others check for errors and if the math is correct... it is generally accepted... with most arguements you have to argue sources and language terminology... but if you prove something mathematically it is pretty much correct by default.

4. Jun 25, 2008

### DaveC426913

Math proofs are derived from a very very small set of fundamental axioms. Fundamental, like 1+1=2 and two straight line segments in Cartesian space intersect at, at most, one point. There's not a lot ofpoint in taking up any science unless you grant these first few axoims.

From those first few, all others can be directly created. A new, published math proof consists of showing that your new formula can be derived directly from existing axioms. No math proof is ever accepted until many colleagues have pored over it and concluded that there is no flaw.

In a nutshell, if one accepts the initial underlying axioms, and the rest of the math is done correctly, one has no choice but to accept the new formula.

5. Jun 25, 2008

### DaveC426913

You seem to know the answer to your own question. Are you just having fun?

6. Jun 25, 2008

### shamrock5585

basically just looking for a good explanation of WHY... thanks

7. Jun 25, 2008

### CompuChip

So to summarize, I guess the answer to "why do we accept a theorem once it is proven?" would be: "by definition of a proof".

8. Jun 25, 2008

### maze

What? No. The symbols used in math could, in some sense, be considered a language, but they are not math itself.

If I make up my own symbols but solve the same problem, I would not be doing "different math", I would just be writing it a different way.

9. Jun 25, 2008

### DaveC426913

I believe his point is more like 'math does not exist without humans'.

10. Jun 25, 2008

### shamrock5585

yes but if i make up my own symbols for english and speak them when i see the symbols im still speaking english just not writing english...

11. Jun 25, 2008

### shamrock5585

well i guess... but what i was getting at is that if you are arguing a point you need to site your sources and prove their credibility but in math you just need to prove that YOU didnt make any mistakes.

12. Jun 25, 2008

### matt grime

I think you're under a slight misapprehension. In mathematics it is very important to cite (not 'site') any sources you use - you're never going to prove everything from first principles. Of course many things are sufficiently self evident, or well known, as to require no citation - you wouldn't bother citing Fermat if you invoke Fermat's Little Theorem, for example, nor would you even name Lagrange if you said "since ord(x) divides |G|" these days.

13. Jun 25, 2008

### CompuChip

Yes, in math you are trying to prove that YOU didn't make any mistakes. If you did use work from someone else (which you have to cite, of course!) you already assume that they are correct (because the steps in them were already checked or assumed correct from cited works, etc., all the way back to first principles.)

Why is there a bar through the name?

14. Jun 25, 2008

### DaveC426913

That means he's been banned, at least temporarily.

15. Jun 25, 2008

### Anhar Miah

you know the funny thing is, the very principle axiomatic foundations of maths is based upon "self-evedent truths" i.e. we can't prove it is, we just accept that it is, i.e. there is no rationality or logic to rationality or logic itself;

Is logic and rationality ultimately purposeless?

even that is even more twisted, imagine if you will, that you are asked to make a purposeless machine, can you make it?

(a) Well if you make the machine, even if it does nothing, it was made with a purpose (i.e. to be purposeless) but that then makes it null, becuase in creating purposeless requires a purpose in the first instance

(b) you don't create any machine at all, but then you contradict the initial point, i.e. you can't make it, but at the same time you "can't; can't make it"

eek! :D

16. Jun 25, 2008

### DaveC426913

Well now, I don't know if it follows that it's not rational.

Some of these axioms we actually define to be so.

eg. 1+1=2 (and only 2). While we can't "prove" it, we have defined this to be so.
Same with others.

17. Jun 25, 2008

### Anhar Miah

18. Jun 25, 2008

### CompuChip

Yes, we build math from axioms.
You can take that as an axiom, if you want. I also don't know whether statements like "there is no rationality or logic to rationality or logic itself" are really relevant in this thread. I could argue about making assumptions and using intuition as a basis for science, but I won't :)

19. Jun 25, 2008

### Littlepig

why? because the definition: We assume something, and we start from that assumption(like 1+1=2), and than we make this: if 1+1=2 than 2+1=1+1+1 so, 1+1+1=2+1==3.(and i've defined the 3 number with the premiss 1+1=2). I've just made a definition that, assuming 1+1=2, than 1+1+1=3. Can you disproof my proof? No, because is just a definition.

However, from this definition, one can proof that exists infinite natural numbers, by a logical method called induction. Now, if you imagine that induction is like defining that pi=perimeter/diameter than you can't deny my proof of infinite natural numbers, because that would tell you that: pi≠perimeter/diameter or 1+1≠2. And that is contradicting your definitions. So, It must be true that exists infinite natural numbers.
Now, the whole math is based in this kind of logical concept. Even the most complex idea like derivative, integral, limit, is based on basic axioms like that one, so, it is true because the assumptions you used were all derived from axioms(definitions), if the theorem isn't true, than some definition is contradicting other or itself.