TITLE: Apery's constant
QUESTION [6 upvotes]: I read that it is unknown if $\zeta (3)$ is algebraic but it is known to be irrational. Has anyone proved anything of the form $\zeta (3)$ is not a root of a polynomial of degree $12345$ with integer coefficients, or is it that the degree one case proof won't work for any other degrees?

REPLY [2 votes]: This is a COMMENT and quote I consider of interest for many people. This remarkable result was given in the ICM, 1978, Helsinski, if I remember correctly.