In 1941, Isaac Asimov defines psychohistory as "that branch of mathematics which deals with the reactions of human conglomerates to fixed economic and social stimuli". His trilogy, Foundation and Empire, describes how this new science steers the Galaxy through difficult times, from the end of the Empire to the emergence of a new and better world. Eighty years later, psychohistory still is a fiction, but mathematical models are ubiquitous in the social sciences, as well as in the natural sciences, and the questions raised by Asimov are still valid : can we use these models to predict the future of mankind ? If so, is it still open, that is, can we steer it away from unpleasant possibilities and towards better ones ? How does one factor in human behavior ? These questions are particularly urgent today, as the planet faces climate change. I will try to describe how mathematical models work, how far into the future they can look, to what extent they can anticipate human behaviour, and what the likely outcomes of the present crisis are.