The fine-structure constant $\alpha$ is ubiquitous in physics, and a comparison among different experiments provides a powerful test of the Standard Model of particle physics. The most precise measurement of $\alpha$ (to date) is our recently published result, $α = 1/137.035\,999\,046(27),$ with an uncertainty of 200 parts per trillion (ppt). A $2.5-\sigma$ tension with the value obtained from the electron gyromagnetic anomaly $g_e-2$ is a potential sign of new physics that mirrors the well-known $3.7-\sigma$ tension observed in the muon $g_\mu-2$. It motivates a deeper investigation at the frontier of precision measurement. $g_\mu-2$ is currently being re-measured by E989 at Fermilab, which expects to reduce the error more than threefold. Gerald Gabrielse (Northwestern University) is currently re-measuring $g_e-2$ and expects an improvement by an order of magnitude to 20 ppt. We will present our result and our project to improve the accuracy in the fine-structure constant to 40 ppt and, eventually, 10 ppt.