The incipient sixth mass extinction that started in the Late Pleistocene has already erased over 300 mammal species and, with them, more than 2.5 billion years of unique evolutionary history. At the global scale, this lost phylogenetic diversity (PD) can only be restored with time as lineages evolve and create new evolutionary history. Given the increasing rate of extinctions however, can mammals evolve fast enough to recover their lost PD on a human time scale? We use a birth–death tree framework to show that even if extinction rates slow to preanthropogenic background levels, recovery of lost PD will likely take millions of years. These findings emphasize the severity of the potential sixth mass extinction and the need to avoid the loss of unique evolutionary history now. This file contains all R code and raw data files necessary to reproduce our analyses.