We quantify the information content of the non-linear matter power spectrum, the halo mass function, and the void size function, using the Quijote N-body simulations. We find that these three statistics exhibit very different degeneracies amongst the cosmological parameters, and thus the combination of all three probes enables the breaking of degeneracies, in turn yielding remarkably tight constraints. We perform a Fisher analysis using the full covariance matrix, including all auto- and cross-correlations, finding that this increases the information content for neutrino mass compared to a correlation-free analysis. The multiplicative improvement of the constraints on the cosmological parameters obtained by combining all three probes compared to using the power spectrum alone are: 137, 5, 8, 20, 10, and 43, for $Omega_m$, $Omega_b$, $h$, $n_s$, $sigma_8$, and $M_ u$, respectively. The marginalized error on the sum of the neutrino masses is $sigma(M_ u)=0.018,{rm eV}$ for a cosmological volume of $1,(h^{-1}{rm Gpc})^3$, using $k_{max}=0.5,h{rm Mpc}^{-1}$, and without CMB priors. We note that this error is an underestimate insomuch as we do not consider super-sample covariance, baryonic effects, and realistic survey noises and systematics. On the other hand, it is an overestimate insomuch as our cuts and binning are suboptimal due to restrictions imposed by the simulation resolution. Given upcoming galaxy surveys will observe volumes spanning $sim 100,(h^{-1}{rm Gpc})^3$, this presents a promising new avenue to measure neutrino mass without being restricted by the need for accurate knowledge of the optical depth, which is required for CMB-based measurements. Furthermore, the improved constraints on other cosmological parameters, notably $Omega_m$, may also be competitive with CMB-based measurements.
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