Extinctionism is the act of causing every possible monster in a game of NetHack to become extinct. In other words, if you kill enough monsters of one species, then that kind of monster cannot be generated anymore. A creature is extinct when 120 of its kind have been born. Once a species has become extinct, there are very few ways to create new monsters of that species. There are exceptions, however, such as pudding division, the monster spell summon nasties, etc.