Meissel's mathematical interests covered the following fields: number theory (in particular, properties of prime numbers), theta functions, elliptic functions, spherical trigonometry, hydrodynamics, ordinary differential equations, asymptotic expansions, and Bessel functions.
Meissel's matematiko interes sakop ang mga sumusunod na patlang: number theory (sa partikular, ang mga pag-aari ng kalakasan numero), theta function, patambilog function, pabilog trigonometrya, haydrodinamika, karaniwang kaugalian equation, asymptotic expansions, at Bessel function.