Draft for a paper by Hawking and Penrose, 1969

Working with Roger Penrose, Hawking showed that singularities are not just a mathematical curiosity, but must really exist in the Universe. This is the draft title page for their key 1970 paper on the subject. Singularities are found inside black holes, formed when a massive star runs out of fuel and collapses in on itself. Hawking also applied this model in reverse, arguing that the Universe itself began in a singularity, known as ‘the Big Bang’.

Source: The Hawking Family Archive