  A recent improved determination of the fine structure constant, $\alpha=
1/137.035999046(27)$, leads to a $\sim 2.4 \sigma$ negative discrepancy between
the measured electron anomalous magnetic moment and the Standard Model
prediction. That situation is to be compared with the muon anomalous magnetic
moment where a positive $\sim 3.7 \sigma$ discrepancy has existed for some
time. A single scalar solution to both anomalies is shown to be possible if the
two-loop electron Barr-Zee diagrams dominate the scalar one-loop electron
anomaly effect and the scalar couplings to the electron and two photons are
relatively large. We also briefly discuss the implications of that scenario.
