JonahSinick comments on The Use of Many Independent Lines of Evidence: The Basel Problem - Less Wrong

22 Post author: JonahSinick 03 June 2013 04:42AM

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Comment author: JonahSinick 04 June 2013 06:07:04PM 2 points [-]

This is a very standard list of evidence, but I am skeptical that it reflects how mathematicians judge the evidence. I think that of the items you mention, the random model is by far the most important. The study of small zeros is also relevant. But I don't think that the theorems about infinitely many zeros have much effect on the judgement.

I agree with this, but would I cite the empirical truth of the RH for other global zeta functions, as well as the proof of the Weil conjectures, as evidence that mathematicians actually think about.

I'd be interested in corresponding a bit — shoot me an email if you'd like

Comment author: Eugine_Nier 06 June 2013 05:35:31AM -1 points [-]

I agree with this, but would I cite the empirical truth of the RH for other global zeta functions

An interesting thing about the GRH is that at oft neglected piece of evidence against it is how the Siegal zero seems to behave like a real object, i.e., having consistent properties.

Comment author: JoshuaZ 08 June 2013 06:05:11PM 1 point [-]

An interesting thing about the GRH is that at oft neglected piece of evidence against it is how the Siegal zero seems to behave like a real object, i.e., having consistent properties.

I'm not sure what you mean here. If it didn't have consistent properties we could show it doesn't exist. Everything looks consistent up until the point you show it isn't real. Do you mean that it has properties that don't look that implausible? That seems like a different argument.

Comment author: Eugine_Nier 09 June 2013 05:51:09AM -1 points [-]

If we can easily prove a conjecture except for some seemingly arbitrary case, that's evidence for the conjecture being false in that case.

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