The population growth rate peaked in 1962 at 2.2 % per year and is now back to 1.1 % per year. There is no way for a population to grow exponentially for a long time, the growth will hit some resource constraint sooner or later and then the growth stops. Therefore also the human population can not and will not grow exponentially forever. But the important point is that you don't want to get stopped by hitting a resource constraint, that is always going to be an unpleasant experience. And the slowdown of the growth of the human population is not due to hitting a resource constraint as it happens in animal populations, it is because of a conscious decision to have less children and having the means to do that. And that's a good thing.

Sure, the demographic transition is a benefit to humanity, and we've seen enough of it to know that while the timing might vary it will eventually happen everywhere, and certainly by the end of this century. Since we agree, I guess I don't know why the supposedly-but-actually-not exponential nature of human population growth was ever mentioned in the first place.

My first comment was meant as an argument that technological advances can not be a substitute for preventing an unchecked population growth, but the comment did a bad job expressing this. A bit down the thread is another comment making things a bit more clear. I also think it is not a clear-cut issue, in some sense we are actively doing population growth control when we promote birth control. The motivation may primarily come from other reasons like avoiding sexually transmitted diseases and not necessarily to avoid overpopulation, but at least in some regions population growth control is part of the motivation.

And, because you mentioned the end of the century, there is still »The Limits to Growth« and it predictions. I am actually not sure on which side I am here. I can't really imagine a collapse of society as we know it in the second half of the century but I am also aware of the sudden and unexpected behavior of complex systems and how hard it is to counteract a system with a lot of inertia. But if the predications come true, population control may become an issue sooner than we like.