[Doctor Stochastic]

The Continuum Hypothesis seems to have been settled by Cohen in 1964 or so. It's consistent with set theory; it's negation is also consistent with set theory. (Zerlemo-Frankel set theory anyway.)

I do not think the Riemann Hypothesis falls into the class of things that can be taken either way.

[Virginia-American]

I do not think the Riemann Hypothesis falls into the class of things that can be taken either way.

Check this guy out: G. J. Chaitin, IBM Research and some of the links from it. The RH may very well be unprovable, depends on the axions.

I don't know enough about foundational stuff, but isn't it logically consistent that it's possible to construct a non-critical-line zero, using the axiom of choice, and to prove that there is no such construction without AC?

[longshadow]

The Continuum Hypothesis seems to have been settled by Cohen in 1964 or so. It's consistent with set theory; it's negation is also consistent with set theory. (Zerlemo-Frankel set theory anyway.)

I understand that that the conjecture, and it's negation, are both consistent with set theory, but I wasn't aware that it had been resolved whether or not it is true.