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[NS] Clay Math Offers Bounty of $1 Million For Solving Equation. - Page 3

post #21 of 60
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Quote:
Originally Posted by Psycho Homer;11793420 
It has had a $1,000,000 bounty for 10 years. Still nothing new going on here.

It's been years though, a breakthrough is bound to pop up.
post #22 of 60
Solving this will be massive impact on computing....

For example, is the way we are Folding today the fastest possible method? Folding is a NP problem.
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post #23 of 60
I guess our average forum user has far less experience with complexity of functions and general computer science than I had imagined. The proof of N=NP will be unlikely to have an impact on our actual computation, but merely upon the problems we actually attempt to solve and the ways in which we solve them. In actuality it is a proof that problems whose solutions can be evaluated with polynomial complexity i.e. O(A*n^k) can also be solved with polynomial complexity-- which is to say they vary polynomially with the increase in problem size.


Quote:
Originally Posted by Oupavoc View Post
This?
You can very easily prove that something is impossible or prove that it is untrue, that is the basis for a very large section of mathematics that you may or may not have run into during your lifetime.
For example, let us take the postulate that
X + Y = 5 for all X and Y less than one million.
This is very clearly not true, as we can rearrange to the following:
X -Y- 5 = 0 for all X and Y less than one million
Allow X and Y to be equal, as allowed by the bounding conditions:
if X = Y, X-Y = 0:
0 - 5 ~= 0
therefore, X+Y ~=5

Substitute ~ for ! if you prefer that as the logical 'NOT' operator.

I am no mathematician, merely an engineer
Edited by wcdolphin - 12/27/10 at 11:31am
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post #24 of 60
Quote:
Originally Posted by cdolphin View Post
I guess our average forum user has far less experience with complexity of functions and general computer science than I had imagined. The proof of N=NP will be unlikely to have an impact on our actual computation, but merely upon the problems we actually attempt to solve and the ways in which we solve them. In actuality it is a proof that problems whose solutions can be evaluated with polynomial complexity i.e. O(A*n^k) can also be solved with polynomial complexity-- which is to say they vary polynomially with the increase in problem size.
Would knowing if N=NP affect algorithm/equations as in... this is the most optimized possible and we can't do any better?
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post #25 of 60
Well, yes and no.
In computer science, complexity of a function roughly describes how the runtime of a given funciton/algorithm changes as the problem size changes. This is not equatable to actual runtime, interestingly you just pointed out a mistake I made-- in complexity calculations, we do not use coefficients, we say that a function is O(n)- pronounced Big O of n, as something that grows linearly with an increase in size of problem, for example, the time it takes to look at every element in a list. We drop all of the coefficients, as they are insignificant when compared to the polynomial aspects.
So yes, the proof would affect our alogorithm's and show that some are 'optimal' but it still allows for optimization on sub order levels-- two algorithms can grow at the same rate and still have very different run times

Two examples of the case you just provided are in our 'comparative' search algorithms, which we can prove are the optimal.

But yes, this is a massive piece of computer science that I hope is solved
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post #26 of 60
Quote:
Originally Posted by Not A Good Idea View Post
when no one can prove you wrong... you're right.
This
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post #27 of 60
Quote:
Originally Posted by Not A Good Idea View Post
when no one can prove you wrong... you're right.
Not quite true since it is easy to frame questions that have a "right" yet false answer.
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post #28 of 60

Wasn't this solved in COD:BO?

post #29 of 60
P = 0 or N=1, check please.
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post #30 of 60
People have always tried to solve the P = NP problem but the work never checks out. Doesn't seem like anything new.
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