Hervé Le Bras examines here how post-modern mathematics, targeting concrete issues, can help us to address a fundamental concern of all human societies, i.e., how space is occupied. Among many topics he examines pastoral nomadism, agricultural sedentariness, territorial conquest, migrations, ancient and modern urban planning, national and regional development, and road traffic. Each of those issues is best understood when it is examined in the light of such new tools as fractals, chaos, computer-generated simulations, and algorithmic methods. It has been observed, for example, that the older one gets the less chances one has of dying! This empirical observation can be explained by a very simple mathematical law that apples to germs, flies, and humans, as well as cars. The phenomenon occurs whenever a population reaches a certain dimension — and this is why, in a few decades, there will be more senior citizens than young people.

Hervé Le Bras, a graduate of the Ecole Polytechnique, is a demographer and course director at the Ecole des Hautes Etudes en Sciences Sociales.