There’s enough people with enough ingenuity and enough people with enough money to pay them to be ingenious that at least an elite core will survive right up until the world ceases to be capable of supporting life. After that they’ll probably spend a rather long time travelling through space looking for somewhere new.
In the meantime wars over religion and resources will probably make the world an unpleasant place for large sectors of the population. Apple and Microsoft may be called upon to hand out huge quantities of free product loaded with ‘Angry Birds’ to act as a pacifier to hostile groups.