Ornaments and icons, symbols of complexity or evil, aesthetically appealing and endlessly useful in everyday ways, knots are also the object of mathematical theory, used to unravel ideas about the topological nature of space. In recent years knot theory has been brought to bear on the study of equations describing weather systems, mathematical models used in physics, and even, with the realization that DNA sometimes is knotted, molecular biology.

This book, written by a mathematician known for his own work on knot theory, is a clear, concise, and engaging introduction to this complicated subject. A guide to the basic ideas and applications of knot theory, Knots takes us from Lord Kelvin’s early—and mistaken—idea of using the knot to model the atom, almost a century and a half ago, to the central problem confronting knot theorists today: distinguishing among various knots, classifying them, and finding a straightforward and general way of determining whether two knots—treated as mathematical objects—are equal.

Communicating the excitement of recent ferment in the field, as well as the joys and frustrations of his own work, Alexei Sossinsky reveals how analogy, speculation, coincidence, mistakes, hard work, aesthetics, and intuition figure far more than plain logic or magical inspiration in the process of discovery. His spirited, timely, and lavishly illustrated work shows us the pleasure of mathematics for its own sake as well as the surprising usefulness of its connections to real-world problems in the sciences. It will instruct and delight the expert, the amateur, and the curious alike.

An interdisciplinary study of hair through the art, philosophy, and science of fifteenth-century Florence.

In this innovative cultural history, hair is the portal through which Emanuele Lugli accesses the cultural production of Lorenzo il Magnifico’s Florence. Lugli reflects on the ways writers, doctors, and artists expressed religious prejudices, health beliefs, and gender and class subjugation through alluring works of art, in medical and political writings, and in poetry. He considers what may have compelled Sandro Botticelli, the young Leonardo da Vinci, and dozens of their contemporaries to obsess over braids, knots, and hairdos by examining their engagement with scientific, philosophical, and theological practices.
 
By studying hundreds of fifteenth-century documents that engage with hair, Lugli foregrounds hair’s association to death and gathers insights about human life at a time when Renaissance thinkers redefined what it meant to be human and to be alive. Lugli uncovers overlooked perceptions of hair when it came to be identified as a potential vector for liberating culture, and he corrects a centuries-old prejudice that sees hair as a trivial subject, relegated to passing fashion or the decorative. He shows hair, instead, to be at the heart of Florentine culture, whose inherent violence Lugli reveals by prompting questions about the entanglement of politics and desire.