They knew how to teach freshman physics, knew some engineering level E&M without actually writing down Maxwell's equations, and did some research in infrared op

They knew how to teach freshman physics, knew some engineering level E&M without actually writing down Maxwell's equations, and did some research in infrared optics. My guess is that there are a lot of experimental physicists who are not at all clear on Fourier series/transforms, the wave equation, good proofs of Stokes theorem, the actual definition of Hilbert space, Bell's inequality, or the differential geometry for general relativity. Still fewer know the exterior algebra of differential forms.