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

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

Am I mistaken? 


  [1]: http://www.zentralblatt-math.org/zmath/en/advanced/?q=an%3Apre05770900&format=complete