> -----Original Message-----
> From: Matt Mahoney via AGI [mailto:[email protected]]
> 
> NP-hard means NP-complete or harder. NP-complete means that a solution
> would solve any problem in NP. NP is the class of problems whose answers
> can be verified in time that is a polynomial function of the input size. P is 
> the
> class of problems that can be solved in polynomial time. It is widely believed
> by everyone except Jim Bromer that P != NP. This belief is not because of any
> proof, but because thousands of other people like Jim Bromer who believed
> P = NP failed to find polynomial time solutions to any NP-complete problems
> after years of effort until they were convinced they would be better off if
> they gave up. The time it takes to give up is inversely proportional to the
> person's efforts into studying the math and researching the work of others
> instead of repeating their mistakes.
> 

No, there are others that believe P=NP besides Jim I'm sure some of you have 
been following Bolotin's argument from last year:

https://medium.com/the-physics-arxiv-blog/the-astounding-link-between-the-p-np-problem-and-the-quantum-nature-of-universe-7ef5eea6fd7a

which to me is very interesting and cutting edge IMO.

John




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