Software affects almost every aspect of our lives in the 21st century. It manages our telephone networks, nuclear power plants, air-traffic control systems, and our banking and financial institutions - to name just a few. Unfortunately many software systems are "fragile" in the sense that they are unreliable, suffer from security and performance lapses, and are difficult to maintain and upgrade to satisfy new demands. Software Engineering, as it is practised today, is an art rather than a science. This talk will discuss research in Software Engineering, the creation and analysis of mathematical models of software systems, and how these ideas promise to provide tools for combatting the fragility of software.