Several uncertainties contribute to the determination of a precise value for critical masses, including (1) detailed knowledge of fission cross sections, (2) calculation of geometric effects. This latter problem provided significant motivation for the development of the "Monte Carlo method" in computational physics by Nicholas Metropolis and Stanislaw Ulam. In fact, even for a homogeneous solid sphere, the exact calculation is by no means trivial. Finally, note that the calculation can also be performed by assuming a continuum approximation for the neutron transport. This reduces it to a diffusion problem. However, as the typical linear dimensions are not significantly larger than the mean free path, such an approximation is only marginally applicable.