  We investigate the effects of strong number fluctuations on traveling waves
in the Fisher-Kolmogorov reaction-diffusion system. Our findings are in stark
contrast to the commonly used deterministic and weak-noise approximations. We
compute the wave velocity in one and two spatial dimensions, for which we find
a linear and a square-root dependence of the speed on the particle density.
Instead of smooth sigmoidal wave profiles, we observe fronts composed of a few
rugged kinks that diffuse, annihilate, and rarely branch; this dynamics leads
to power-law tails in the distribution of the front sizes.
