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The ellipsoid (along with its degenerate forms) is the workhorse in classical models that capture the role of nonspherical particle shapes in multiphase suspensions and composite materials. The utility of these models in many branches of science have forced generations of students to master the mathematics of elliptic integrals and related functions. And yet for over a half-century we have known that one of the most important entities in these models, namely the surface traction (force per area on the particle surface) has a relatively simple form: essentially the same formula as the sphere and no elliptic integrals. The explanation is rooted in the theory of integral operators as applied to single- and double-layer hydrodynamic potentials. These findings open the door to new velocity representations for ellipsoidal microhydrodynamics and potential applications for micro- and nano-particle technologies. The presentation will conclude with a tribute to the memory of Howard Brenner and his remarks on billions of dollars that link to fundamental research in fluid mechanics.