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Mathematical proof..
#1
Mathematical proof..
How do they work? I mean what does one have to do in order to come up with a proof?

For example, I think I can show why the four colour theorem only needs four colours.

Firstly, has it been proven already? And also, what proof would I need to give and in what format?

Thanks.
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#2
RE: Mathematical proof..
You take the rules of the system, you plug in variables, and show that by following those rules those variables yield 'x".
When in the course of human events it becomes necessary for a battle to commence then KPLOW, I hit em with the illness of my quill, Im endowed..with certain unalienable skills....  

-ERB


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#3
RE: Mathematical proof..
Four color problem already solved.

IIRC, that one was done by a computer.
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#4
RE: Mathematical proof..
(September 25, 2014 at 5:05 pm)Rhythm Wrote: You take the rules of the system, you plug in variables, and show that by following those rules those variables yield 'x".

So how would that work with the four colour theorem? What proof would you need?
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#5
RE: Mathematical proof..
(September 25, 2014 at 5:05 pm)Rhythm Wrote: You take the rules of the system, you plug in variables, and show that by following those rules those variables yield 'x".

Exactly. In principle you start with

1. Axioms which are defined as true and

2. rules of logic which allow you to generate new true statements from known true statements.

You then try to find a logical chain from the axioms to the theorem youd like to prove. If you find one, it's proven.

In reality, it's often messier cause no mathematician sticks to making all elementary steps explicitely, which would take forever. By using natural Language and shortcuts, it becomes harder to check which steps in a proof are valid.

The art is in formulating the question properly and finding intermediate steps which get you closer to the desired theorem. Sometes, proving seemingly completely unrelated intermediate "lemmas" suddenly open a path to the actual goal because they can be applied to it somehow.
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition

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#6
RE: Mathematical proof..
(September 25, 2014 at 5:13 pm)vorlon13 Wrote: Four color problem already solved.

IIRC, that one was done by a computer.
Any chance of a link? I did my solution in my head in about half an hour
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#7
RE: Mathematical proof..
(September 25, 2014 at 5:21 pm)lifesagift Wrote:
(September 25, 2014 at 5:13 pm)vorlon13 Wrote: Four color problem already solved.

IIRC, that one was done by a computer.
Any chance of a link? I did my solution in my head in about half an hour

Cool, why don't you post it, then we can pick it apart Smile
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition

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#8
RE: Mathematical proof..
Lol.. not giving it away...just need to know how to represent it
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#9
RE: Mathematical proof..
(September 25, 2014 at 5:38 pm)lifesagift Wrote: Lol.. not giving it away...just need to know how to represent it
Too bad.

I'd say -
Start by introducing unambiguous names for the objects you deal with and their relationships and properties. Then formulate the theorem you want to prove in those terms.
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition

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#10
RE: Mathematical proof..
But if I said it was a special paint for example? how would I have to describe that paint?
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