Empires rise and fall, populations and economies boom and bust, world religions spread or wither... What are the mechanisms underlying such dynamical processes in history? Are there 'laws of history'? We do not lack hypotheses to investigate - to take just one instance, more than two hundred explanations have been proposed for why the Roman Empire fell. But we still don't know which of these hypotheses are plausible, and which should be rejected. More importantly, there is no consensus on what general mechanisms explain the collapse of historical empires. What is needed is a systematic application of the scientific method to history: verbal theories should be translated into mathematical models, precise predictions derived, and then rigorously tested on empirical material. In short, history needs to become an analytical, predictive science.