Some of the most spectacularly wrong predictions in history have been made by those who claim that overpopulation is going to swamp the planet. Thomas Malthus, a British economist writing in the late 1700s, is the most famous of these. Extrapolating past trends into the future, he predicted that population growth would inevitably swamp available food resources, leading to mass starvation. That didn't happen -- we continued to develop new technologies that let us stay ahead of the reaper.
In 1968, Stanford biologist Paul Ehrlich wrote "The Population Bomb," warning that unchecked population growth would lead to mass starvation in the 1970s. He was just as wrong as Malthus. Global population did surge, but food production managed to keep up.