  We employ a mathematical framework based on rational approximants in order to
calculate the pseudoscalar-pole piece of the hadronic light-by-light
contribution to the anomalous magnetic moment of the muon,
$a_{\mu}^{\textrm{HLbL};P}$. The method is systematic and data based, profiting
from over 13 different collaborations, and able to ascribe, for the first time,
a systematic uncertainty which provides for the model independence. As a
result, we obtain $a_{\mu}^{\textrm{HLbL};P}=94.3(5.3) \times10^{-11}$, which
uncertainty is well below the one foreseen at future experiments measuring the
$(g_{\mu}-2)$.
