Pion electromagnetic form factor from analyticity and unitarity

I will describe our work that combines analyticity and unitarity and pieces of information from different regions to provide a high precision determination of the pion electromagnetic form factor whose knowledge is crucial for evaluating the hadronic contribution to the muon g-2.   We use information from e+e- collision, tau-decays as well as measurements of the phase of the form factor, and its value at spacelike values of the momentum squared to achieve our objectives.  Our work confirms the central value of the determations of the hadronic contributions at low to intermediate energes but reduces the error.  We use methods of functional analysis and optimization methods which will be presented in an accessible manner. The labour involved, however, is expected to convince the audience that there is no such thing as a free meson.