Is a Proof a Proof If No One Can Check It?

Re:Is a Proof a Proof If No One Can Check It? by J_McQuade on Wednesday June 24, 2009 @08:57PM (#672985)

Well, the proof is perfectly valid, as on some abstract level a computer == Turing machine == something you can reason about. If you can prove that your program works in the required way, then your proof holds.

However, brute force solutions are ugly and shed little (if any) new light on the problem, and in the words of G.H.Hardy - "There is no permanent place in the world for ugly mathematics". With things like this I just can't help but think that an elegant and enlightening proof will unexpectedly pop up some time in the distant future when we're all off researching some sort of new-age hypermaths or something...

... well, I suppose a man's got to dream, right?

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Re:Is a Proof a Proof If No One Can Check It? by andrew1 on Thursday June 25, 2009 @03:56AM (#673326)

I'd agree with your dislike of ugly solutions. I guess the benefit of this being accepted as a proof is that all the conjectures that begin 'Assuming that x is true...' can now be converted to theorems saying 'x is true, therefore...', which might tidy up a lot of loose ends.

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