Math is Understanding, the Continuum hypothesis and computational proof.
Channel: Cool Math
Date: 2013-04-16

Cool Math, Math is Understanding, the Continuum hypothesis and computational proof
http://youtu.be/ekZrJ9jjNXQ

Math is understanding

Math relies on understanding to move forward.

If you don't understand 1+1=2 then how could you get to the point where you understand 2+2=4?

If you did not understand 1+1=2 you simply could not move forward. Unless someone has stated that it is true by way of proof. You should be able to take it as fact and deduce with logic that 1+2 would  = 3. and from there you could move further.

Well, maths has moved a lot further than simple addition. But it is still not totally understood.

Usually, something is either true or false and that is it.

But, there is 1 problem that as far as we can tell has another answer. Undecided.

This is the Continuum hypothesis

without getting into it too deeply, the basic idea is this,

We have a number line, that runs to infinity in either direction 1234 etc

and -1-2-3-4-5 etc. these are natural numbers.

Lets call the infinity that the numbers go to 'Infinity set A'.

Now when we look between 1+2 we see ½ and 1/4 and thirds etc etc these are called real numbers there is also an infinite number of these numbers just between 1 and 2.

so lets call the sets between natural numbers infinity set B.

It is agreed that infinity B is bigger than infinity A.

Now the question.

Is there an infinity set that is smaller than B but bigger than A?

Its a tough question to answer. Infact it is so hard that the only proofs we have are

that it has been proven that we cannot prove it to be false.

and we can not prove it to be true.

Because we cant properly comprehend infinities we just cant get an answer either way.

But, what if a computer could comprehend infinities and actually answer the question for us?

and say Yes. there is an infinity between A and B.

Well, then we would have an answer. But how can we tell if the answer is right or wrong?  Maybe get another computer to tell us, but then, we go down a never ending spiral of 'But how do we know for sure?'

Well, math is heading in this direction. We are looking at computers to solve problems that are so deep and complex that we can hardly understand them. Take the information it spits out and then go on to use it in another equation. for deeper and more complex answers.

But What's the value of an answer without the understanding?

Well, with these answers we will start to be able to do some pretty crazy things.

Who knows, maybe one day we will meet aliens. and the alien will ask us, how the heck did you get all the way out here.

and our answer will be...I dont know.

This video is completely open source