Massive neutrinos suppress the growth of cosmic structure on small, non-linear, scales. It is thus often proposed that using statistics beyond the power spectrum can tighten constraints on the neutrino mass by extracting additional information from these non-linear scales. In this talk, I will first explore the information in the matter field using the Quijote simulations. I will show how the matter power spectrum, halo mass function, and void size function can be combined to break degeneracies between cosmological parameters and give considerably tighter constraints on the neutrino mass compared to the power spectrum alone. I will then explore how much of this information we can realistically expect to find in upcoming cosmological surveys which observe galaxies and weak lensing. Finally, I will motivate an approach to obtain optimal cosmological constraints by reconstructing the initial conditions of the Universe.