  Recent precision cosmological parameter constraints imply that the spatial
curvature of the Universe is essentially dynamically negligible - but only if
relatively strong assumptions are made about the equation of state of dark
energy (DE). When these assumptions are relaxed, strong degeneracies arise that
make it hard to disentangle DE and curvature, degrading the constraints. We
show that forthcoming 21cm intensity mapping experiments such as HIRAX are
ideally designed to carry out model-independent curvature measurements, as they
can measure the clustering signal at high redshift with sufficient precision to
break many of the degeneracies. We consider two different model-independent
methods, based on `avoiding' the DE-dominated regime and non-parametric
modelling of the DE equation of state respectively. Our forecasts show that
HIRAX will be able to improve upon current model-independent constraints by
around an order of magnitude, reaching percent-level accuracy even when an
arbitrary DE equation of state is assumed. In the same model-independent
analysis, the sample variance limit for a similar survey is another order of
magnitude better.
