That's why I said I'm not sure. I just heard some other people claiming something, so I simply explained a line of reasoning that assumes their claim. I haven't studied any of the consequences of RH yet, so perhaps their claim was false.
I will clarify the point he is trying to get across.
I'm not sure whether the results of RH actually help you break cryptography, but let's assume that it does somehow. Well then, in practice, you don't actually need a proof of RH to make use of it! Sure, you won't be 100% certain that it will work, but that can't stop you from trying! RH was already very strongly thought to be true, so if assuming RH helps you break cryptography somehow, then just assume it without proof and see if you can do so.
Hopefully that was clearer? That's why it's more like "Math for the sake of Math", because there's no direct application of the proof, aside from more Math. Of course, within Number Theory, RH is huge. There's already a large body of work that assumes RH, and so all that work would be rendered useless if RH turned out to be false.
I love how I understood what you're talking about.:D
I'm double majoring in Computer Science and Math right now, and Set Theory and Number Theory are two of my favorite things. Too bad the proof is probably still a little too complicated for me to understand. I'm definitely going to print it out thought. I'll see if I can read up on anything I don't know yet...
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That's why I said I'm not sure. I just heard some other people claiming something, so I simply explained a line of reasoning that assumes their claim. I haven't studied any of the consequences of RH yet, so perhaps their claim was false.
I will clarify the point he is trying to get across.
I'm not sure whether the results of RH actually help you break cryptography, but let's assume that it does somehow. Well then, in practice, you don't actually need a proof of RH to make use of it! Sure, you won't be 100% certain that it will work, but that can't stop you from trying! RH was already very strongly thought to be true, so if assuming RH helps you break cryptography somehow, then just assume it without proof and see if you can do so.
Hopefully that was clearer? That's why it's more like "Math for the sake of Math", because there's no direct application of the proof, aside from more Math. Of course, within Number Theory, RH is huge. There's already a large body of work that assumes RH, and so all that work would be rendered useless if RH turned out to be false.
I love how I understood what you're talking about. :D
I'm double majoring in Computer Science and Math right now, and Set Theory and Number Theory are two of my favorite things. Too bad the proof is probably still a little too complicated for me to understand. I'm definitely going to print it out thought. I'll see if I can read up on anything I don't know yet...