Mathematical modelers from different disciplines and regulatory agencies worldwide agree on the importance of a careful sensitivity analysis (SA) of model-based inference. The most popular SA practice seen in the literature is that of ’one-factor-at-a-time’ (OAT). This consists of analyzing the effect of varying one model input factor at a time while keeping all other fixed. While the shortcomings of OAT are known from the statistical literature, its widespread use among modelers raises concern on the quality of the associated sensitivity analyses. The present paper introduces a novel geometric proof of the inefficiency of OAT, with the purpose of providing the modeling community with a convincing and possibly definitive argument against OAT. Alternatives to OAT are indicated which are based on statistical theory, drawing from experimental design, regression analysis and sensitivity analysis proper.