  In this small note, we provide an elementary proof of the fact that
infinitely many odd zeta values are irrational. For the first time, this
celebrated theorem been proven by Rivoal and Ball--Rivoal. The original proof
uses highly non-elementary methods like the saddle-point method and
Nesterenko's linear independence criterion. Recently, Zudilin has re-proven a
slightly weaker form of his important result that at least one of the odd zeta
values $\zeta(5),\zeta(7),\zeta(9)$ and $\zeta(11)$ is irrational, by
elementary means. His new main ingredient are certain 'twists by half' of
hypergeometric series. Generalizing this to 'higher twists' allows us to give a
purely elementary proof of the result of Rivoal and Ball--Rivoal.
