Adam Smith is often thought of as the father of modern economics. In his book "An Inquiry into the Nature and Causes of the Wealth of Nations" Smith decribed the "invisible hand" mechanism by which he felt economic society operated. Modern game theory has much to add to Smith's description.
Over the past one hundred years, mathematics has been used to understand and predict the spread of diseases, relating important public-health questions to basic infection parameters. Matthew Keeling describes some of the mathematical developments that have improved our understanding and predictive ability.