4 ms·

What if there won't be? What if, for many of questions, the only proof is as decipherable as MD5 of question?

bhaak 11y ago
That's probably highly improbable. Look at how many different proofs the are for the pythagorean theorem: http://www.cut-the-knot.org/pythagoras/ http://www.cut-the-knot.org/pythagoras/ I'm not mathematician but I guess if there is really only one possible proof for a given question (Gödel might have proven that this is impossible but I don't know for sure), then the question isn't actually an interesting one. Because this would mean that the question touches only very few topics. But the abc conjecture is interesting because it has lots of links with deep questions in number theory.
- guard-of-terra 11y ago
  Okay. What if there's a lot of proofs, but the shortest of those is still not within reach of human intellect?
  - bhaak 11y ago
    So far, we don't know if there are any proofs that are beyond the human intellect. I don't think that we currently believe such a thing to exist theoretically. Every provable conjecture should be understandable in principle by a generic human mind. Now, there for certain systems that are so complex that proofs within those systems are beyond us. Not because we couldn't understand them but because learning and applying all the rules of that system takes longer than a human mind is able to live (currently). But that's just a practical limitation, not a theoretical one.
    - guard-of-terra 11y ago
      I'm talking about practical limitations. It turns out human exploration becomes impractical :(
      - bhaak 11y ago
        Practical limitations can be overcome. At first it was artificial light sources, then glasses, then machines speeding up calculation and now machines that do calculations themselves. There is certainly a practical limit of what a human mind can grasp but that limit is far away and with tools, it is even much farther. We won't run out on difficult problems to solve anytime soon.
- deleted 11y ago
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bhaak 11y ago

That's probably highly improbable. Look at how many different proofs the are for the pythagorean theorem: http://www.cut-the-knot.org/pythagoras/ http://www.cut-the-knot.org/pythagoras/ I'm not mathematician but I guess if there is really only one possible proof for a given question (Gödel might have proven that this is impossible but I don't know for sure), then the question isn't actually an interesting one. Because this would mean that the question touches only very few topics. But the abc conjecture is interesting because it has lots of links with deep questions in number theory.

guard-of-terra 11y ago
Okay. What if there's a lot of proofs, but the shortest of those is still not within reach of human intellect?
- bhaak 11y ago
  So far, we don't know if there are any proofs that are beyond the human intellect. I don't think that we currently believe such a thing to exist theoretically. Every provable conjecture should be understandable in principle by a generic human mind. Now, there for certain systems that are so complex that proofs within those systems are beyond us. Not because we couldn't understand them but because learning and applying all the rules of that system takes longer than a human mind is able to live (currently). But that's just a practical limitation, not a theoretical one.
  - guard-of-terra 11y ago
    I'm talking about practical limitations. It turns out human exploration becomes impractical :(
    - bhaak 11y ago
      Practical limitations can be overcome. At first it was artificial light sources, then glasses, then machines speeding up calculation and now machines that do calculations themselves. There is certainly a practical limit of what a human mind can grasp but that limit is far away and with tools, it is even much farther. We won't run out on difficult problems to solve anytime soon.
deleted 11y ago
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