Math Easy Solutions, I’d tighten it to: “Electromagnetic potentials are not merely convenient mathematical constructs; in classical EM they help generate the fields via ( \mathbf{E} ) and ( \mathbf{B} ), and in quantum mechanics they can have direct observable significance, as shown by the Aharonov–Bohm effect.” That’s more accurate because “arise from physical laws and vector calculus identities” undersells their role, while “may point to physical fields” is too weak given the AB phase shift evidence discussed in the original Aharonov–Bohm paper and a recent 2025 overview. Also, minor fix: it’s Aharonov–Bohm, not “Aharanov-Bohm.”