A Brief History of Time
The predictions of the theory
"break down at the big bang singularity"
"Classical general relativity, by predicting points of infinite density, predicts its own downfall, just as classical mechanics predicted its downfall by suggesting that atoms should collapse to infinite density"
pages 37, 38
pages 184, 185
Ask a Mathematician / Physicist
What are singularities? (link)
"In practice, when you’re calculating something in physics and you find a singularity in your calculation (this happens all the time), which usually looks like “1/x”, then that means that there’s a mistake somewhere, or you’re looking at something that never happens, or there are physical laws or effects that haven’t been taken into account."