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)(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)(HLbL);(P) = 94.3(5.3) x 10(-11), whose uncertainty is well below the one foreseen at future experiments measuring the (g(mu) - 2).