Chapter 2 Smoke Rings

Knot theory is one of the hottest topics in contemporary mathematics, right there at the interface between a range of exciting research fronts in pure mathematics, with seminal contributions made by leading string theorist Edward Witten. We shall see more of how it fits the higher-dimensional outlook in later chapters. Here, I want to take the time to consider the peculiar constellation of circumstances which brought about knot theory’s early development. Knowledge of the history of a discipline is vital for philosophical reflection. Thoughtful practitioners of a discipline are usually well read in its history. It reminds us that ideas we hold dear had once to start to take a grip on us, and that theories which seemed highly plausible at one time appear now as old curiosities, wrongheaded yet uncannily presaging modern viewpoints. Although the spirit of a time might seem quite foreign to us today, one can only wonder at the way so many contemporary ideas are melded together from earlier fragments.