Yesterday I posted something about a list of proposed dates for the end of the world, as maintained by a British cosmetics company. Many of the predictions come from religious or mystical sources, but one of them referenced an short article published in the 4 November 1960 issue of the journal Science. The presumably tongue-in-cheek -- but still disturbing -- title of the piece was "Doomsday: Friday, 13 November, A.D. 2026," and the summary read, "At this date the human population will approach infinity if it grows as it has grown in the last two millennia."
Obviously the authors, three members of the electrical engineering department at the University of Illinois in Urbana, did not expect that to be literally true, but it did make clear that the historical pattern can't possibly continue.
Fortunately, as a special section in the 29 July issue of Science points out, since then the large increase in life expectancy (primarily as a result of reduced infant mortality) has been accompanied by a large drop in fertility. Problems remain, of course, but we have at least some breathing room.
There's an overview of current thinking about population growth in a Science podcast you can listen to (or read a transcript of) here. In brief, there is reason both for concern and for cautious optimism.