The field of cognitive neuroscience is weighing evidence about whether to move from the current standard field strength of 3 Tesla (3T) to ultra-high field (UHF) of 7T and above. The present study contributes to the evidence by comparing a computational cognitive neuroscience paradigm at 3T and 7T. The goal was to evaluate the practical effects, i.e. model predictive power, of field strength on a numerosity task using accessible pre-processing and analysis tools. Previously, using 7T functional magnetic resonance imaging and biologically-inspired analyses, i.e. population receptive field modelling, we discovered topographical organization of numerosity-selective neural populations in human parietal cortex. Here we show that these topographic maps are also detectable at 3T. However, averaging of many more functional runs was required at 3T to reliably reconstruct numerosity maps. On average, one 7T run had about four times the model predictive power of one 3T run. We believe that this amount of scanning would have made the initial discovery of the numerosity maps on 3T highly infeasible in practice. Therefore, we suggest that the higher signal-to-noise ratio and signal sensitivity of UHF MRI is necessary to build mechanistic models of the organization and function of our cognitive abilities in individual participants.