Robustness and evolvability are fundamental characteristics of life whose relationship has intrigued generations of biologists. Studies of several genotype-phenotype maps (GPMs) such as the map between short DNA sequences and their bindings to transcription factors showed that phenotype robustness (PR) promotes phenotype evolvability (PE), but the underlying reason is unclear. Here, we show mathematically that the expected PE is a monotonically increasing function of the expected PR in random GPMs. Population genetic simulations confirm that increasing PR raises the probability that a target phenotype appears in a population within a given time, under empirical as well as randomly rewired GPMs. These and other results demonstrate that the positive correlation between PR and PE is mathematical rather than biological. Hence, it is unsurprising to observe this correlation in every empirical GPM investigated, although the magnitude of the correlation may vary due to influences of various biological factors.