Sex differences in the study of the human physiological response to mental stress are often erroneously ignored. To this end, we set out to show that our understanding of the stress response is fundamentally altered once sex differences are taken into account. This is achieved by comparing the heart rate variability (HRV) signals acquired during mental maths tests from ten females and ten males of similar maths ability; all females were in the follicular phase of their menstrual cycle. For rigor, the HRV signals from this pilot study were analyzed using temporal, spectral and nonlinear signal processing techniques, which all revealed significant statistical differences between the sexes, with the stress-induced increases in the heart rates from the males being significantly larger than those from the females (p-value = 4.4 × 10−4). In addition, mental stress produced an overall increase in the power of the low frequency component of HRV in the males, but caused an overall decrease in the females. The stress-induced changes in the power of the high frequency component were even more profound; it greatly decreased in the males, but increased in the females. We also show that mental stress was followed by the expected decrease in sample entropy, a nonlinear measure of signal regularity, computed from the males' HRV signals, while overall, stress manifested in an increase in the sample entropy computed from the females' HRV signals. This finding is significant, since mental stress is commonly understood to be manifested in the decreased entropy of HRV signals. The significant difference (p-value = 2.1 × 10−9) between the changes in the entropies from the males and females highlights the pitfalls in ignoring sex in the formation of a physiological hypothesis. Furthermore, it has been argued that estrogen attenuates the effect of catecholamine stress hormones; the findings from this investigation suggest for the first time that the conventionally cited cardiac changes, attributed to the fight-or-flight stress response, are not universally applicable to females. Instead, this pilot study provides an alternative interpretation of cardiac responses to stress in females, which indicates a closer alignment to the evolutionary tend-and-befriend response.