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Comment by samstave | Hacker News Reader

Can anyone explain in lag terms what the implications of this may be.

Just the phrase "deep connection between prime numbers" sounds really interesting, so, if this were true would there be any practical application of this in the next (N) years that would not be possible without this proof?

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abc conjecture is asymptotic. That is, its statement is of the form "for every positive epsilon there exists a constant". A proof can be constructive, that is, an algorithm that can calculate a constant from an epsilon, or it can be nonconstructive. For any practical application it would seem a constructive proof is needed.

I am not at all qualified to talk about the claimed proof, but I think it would be nonconstructive.

Thanks, but I said in "lay" ("lag" due to stupid iPhone AC) terms...

I dont really get how your response answers my question.

Can you really dumb it down for me; explain like I am 5 how this will result in practical applications in the next (N) years.

thanks

His answer was that he thinks there will be no practical applications from this proof, since it merely states that something exists without giving us an idea of how to find that thing.

Yeah. For the most part non-constructive proofs are only good for proving things about existing algorithms - their convergence properties, their correctness, their running time etc. Formal proof often isn't necessary in practice, though - "seems to work well enough" is ok in many domains.

Of course, this isn't to say that new mathematics based on the result and on the techniques used to prove it won't lead to new algorithms.

Here is the best layman's explanation I could find: http://i.imgur.com/VrjiG.gif

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