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Efforts to estimate global species richness often rely on species accumulation curves based on the year of species description. However, this approach assumes that description years accurately reflect discovery times. Many of the recently accepted species (in some groups the majority) are, however, resurrected synonyms or subspecies raised to species level rather than de novo discoveries. Their authority years (i.e. years of first description) are therefore often much older than the year of general acceptance at the species level, meaning that the authority years may provide little information on how many species will eventually be accepted within a clade. Here, we highlight the limitations of relying on authority year, by comparing two taxonomic snapshots taken approximately a decade apart for amphibians, birds, and mammals. We consistently find lower estimates of diversity when relying on older taxonomic snapshots. This occurs because using the authority year on average overestimates how long a species has been accepted, which in turn results in an underestimate of the number of unrecorded species. Based on our analysis, we argue that due to the unreliability of authority year, approaches that rely on it are flawed and may provide misleading support for biogeographic or conservation hypotheses. Therefore, we suggest and advocate for alternative methods to reliably estimate the magnitude of undescribed species. We estimate undescribed species of amphibians, mammals and birds based on two temporally separated global checklists. We show that estimates of undescribed species based on analyses of authority year produce consistent and occasionally large underestimates. The underestimation of undescribed biodiversity arises because raised synonyms or subspecies retain the authority year of their original description, rather than the year they were elevated to species level. The geographic analysis suggests that the underestimate is most severe in the well-studied regions, indicating that although disproportionally many undescribed species likely occur in poorly studied tropical regions, the magnitude of this pattern has been overestimated in previous studies. We advocate for the development of methods for estimating the unknown number of species that do not rely on authority year.