It was recently proposed (Bushdid et al., 2014) that humans can discriminate between at least a trillion olfactory stimuli. Here we show that this claim is the result of a fragile estimation framework capable of producing nearly any result from the reported data, including values tens of orders of magnitude larger or smaller than the one originally reported in (Bushdid et al., 2014). Additionally, the formula used to derive this estimate is well-known to provide an upper bound, not a lower bound as reported. That is to say, the actual claim supported by the calculation is in fact that humans can discriminate at most one trillion olfactory stimuli. We conclude that there is no evidence for the original claim.