The title of this column is a phrase that became a catchcry of the 1960s, and although the problem that it encapsulates is still very much with us (indeed even more acute than it was back then), it is less in vogue nowadays. The phrase refers to the unprecedented growth of the human population that is currently taking place. It is particularly apposite to look once again at the issue involved, because as I write (2011) the world population has just topped 7 billion (7000 million).
It will be convenient to begin our account of the underlying mathematics with the work of Thomas Malthus (1766-1834), who in 1798 produced a most influential book, An Essay on the Principle of Population. It ran in all to six editions in Malthus's lifetime and has been much reprinted since. Among other things it is seen as a pioneering contribution to economics.