Population growth is already slated to top out around 11-12 billion and then decrease.
The figure I keep seeing is just short of 10 billion, by the end of this century.
It could be less if poverty in developing countries is eradicated earlier than expected.
The number of people living in poverty has fallen by 40% in the last 15 years. The poverty rate in Africa is now less than 50%, for the first time since anyone has been keeping track. When I was a kid millions of people were starving in China, now they all have TVs and cellphones. The Vietnamese economy is one of the fastest-growing on Earth.
They have actually redefined "poverty" in South America to "living on less than four dollars per day." In the rest of the world it's one dollar. Well except here of course, where the federal government defines it as $11.64 ($17K per year for a family of four.)
Here's a mind game to ponder: if you were presented with a time machine that would take you back to any year you chose, but you had no control of who you would be or where you would live (think gender, nationality, ethnicity), would you go?
Until the Industrial Revolution, 99% of the people on earth in any era were doomed to "careers" in the "food production and distribution industry." I.e., farmers. In most cases subsistence farmers but also yeomen who earned no real income from their work (which was as much as 100 hours per week), and in many places in many eras, slaves. No thanks!
The most important thing in my life is music, and before the Electronic Revolution people were lucky to hear professionally composed and performed music once or twice a year. The small fraction of the population who lived in cities might be able to hear the mediocre pianist play the same songs every Friday night in the saloon, and the greater number who lived near a church could hear the even more mediocre choir sing the same hymns every Sunday morning. No thanks!
Would you take the 50/50 chance that you would be female in any of the increasingly misogynist societies the further back in the past you look?
During the post-Roman era women had a longer life expectancy than men, who were always off killing each other, and during those long lives they developed knowledge and wisdom that earned them a certain respect. The phallocrats put a stop to that by labeling them "witches."
Infant mortality was as high as 80% before the discovery of vaccines and antibiotics.
Europe underwent an enormous backslide after the collapse of Rome. The public health technologies they invented, such as sewers, atrophied. Their streets were all open sewers and the city fathers' idea of street cleaning was to run a herd of pigs through town once a year to eat it all. The water was so polluted that everyone who could afford it drank beer, which explains the economic and cultural dysfunction we affectionately call the Dark Ages. It wasn't until coffee was brought back from Ethiopia that the working IQ of the continent rose back above 100.
For those who worry about us going backwards, think about where we came from! We crawled down from the trees and made computers out of sand! What do people worry we'll go back to? We came from nothing. Our brains are our salvation; they are the most amazing things we are aware of in the entire universe (so far). Our offspring will continue to have this tool if nothing else. With that, we can hope to one day explore the stars rather than worry the sky is falling.
We rewrote evolultion by creating civilization, a superorganism of which we are the cells. Its advance has not been monotonic, but it has never failed to recover from its temporary reversals and burst forth with new creativity.
For those who think a wonderful future will be one in which we hand-make everything, where we live in poverty, where billions less humans get to live and breathe and enjoy existence, where local is better than an inclusive whole -- to them I say: use the time machine. I dare you.
The Post-Industrial Era may very well allow people who want that kind of life to choose it. There will probably be more individuality and less mass-production. Food production will become even more automated than it is today, and we can already socialize with our friends on other continents without leaving our desks. People who want to pretend it's the Stone Age can do so, without having to actually undergo the rigors of a Paleolithic or Neolithic life.