Someone recently quoted to me this recent [article][1] that claims to prove that $\zeta(2n+1) \notin (2\pi )^{2n+1} \mathbb{Q}$. 

[Edit: published reference: Musha, Takaaki.
*Negation of the conjecture for odd zeta values*. Int. J. Pure Appl. Math. 91, No. 1, 103-111 (2014). Not referenced by MathSciNet, and referenced by zbMATH ([link](https://zbmath.org/1286.11008)).]

I always assumed this was well known. More precisely I thought this result followed from the fact that the regulator
$$
  K_{2n-1}(\mathbb{Z})\otimes \mathbb{Q} = \operatorname{Ext}^1_{MT(\mathbb{Z})}(\mathbb{Q}(0),\mathbb{Q}(n))    \longrightarrow \operatorname{Ext}^1_{MHS}(\mathbb{Q}(0),\mathbb{Q}(n)) = \mathbb{C}/(2\pi i)^n\mathbb{Q}
$$
is injective (this is usually quoted as a consequence of Borel's computations of K-groups "Stable real cohomology of arithmetic groups", "Cohomologie de $\operatorname{SL}_n$ et valeurs de fonctions zêta aux points entiers")

Am I mistaken? 

  [1]: http://www.ijpam.eu/contents/2014-91-1/11/