The Amur leopard (Panthera pardus orientalis) is one of the world’s rarest wild cat species. The answer to the question in the title can be found on the IUCN Red List website but even they will be slightly imprecise because population measurement of wild cats is not precise. They say that the total population remains at less than 60 individuals cats, which means it is has been at that figure for a while. An astonishingly small number for an entire subspecies of wild cat.
I can remember about 10 years ago the population size being stated as around 400 and stable. If that is true there has been a marked decline. The difference may be due to more accurate measurements.
All of these cats are in the Russian Far East, Korean Peninsula and northeastern China. What more can I say? Perhaps this: such a small population size may be unviable for survival by which I mean they may not be able to breed sufficiently to sustain themselves. They may die out as a species in the wild. There is a lower limit at which point the species becomes effectively extinct in the wild. How many of these 60 cats can breed? Perhaps they only count breeding adults. It is worth mentioning that these 60 or less cats live in fragmented locations. Perhaps there are a series of small groups and if so this makes their survival even more precarious.
The IUCN Red List say that the taxonomy of the leopard is under review. This means the scientists are not convinced that there are nine subspecies as stated. The IUCN Red List is meant to be the premier source for information about the conservation status of all species.