Richard Feynman was one of the most famous and important physicists of the second half of the twentieth century. Awarded the Nobel Prize for Physics in 1965, celebrated for his spirited and engaging lectures, and briefly a star on the evening news for his presence on the commission investigating the explosion of the space shuttle Challenger, Feynman is best known for his contributions to the field of quantum electrodynamics.

Humans have been trying to understand the physical universe since antiquity. Aristotle had one vision (the realm of the celestial spheres is perfect), and Einstein another (all motion is relativistic). More often than not, these different understandings begin with a simple drawing, a pre-mathematical picture of reality. Such drawings are a humble but effective tool of the physicist’s craft, part of the tradition of thinking, teaching, and learning passed down through the centuries. This book uses drawings to help explain fifty-one key ideas of physics accessibly and engagingly.

Scientists have been trying to confirm the existence of gravitational waves for fifty years. Then, in September 2015, came a “very interesting event” (as the cautious subject line in a physicist’s email read) that proved to be the first detection of gravitational waves.

Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes.

The separateness and connection of individuals is perhaps the central question of human life: What, exactly, is my individuality? To what degree is it unique? To what degree can it be shared, and how? To the many philosophical and literary speculations about these topics over time, modern science has added the curious twist of quantum theory, which requires that the elementary particles of which everything consists have no individuality at all. All aspects of chemistry depend on this lack of individuality, as do many branches of physics.

We now know that there is much more to classical mechanics than previously suspected. Derivations of the equations of motion, the focus of traditional presentations of mechanics, are just the beginning. This innovative textbook, now in its second edition, concentrates on developing general methods for studying the behavior of classical systems, whether or not they have a symbolic solution. It focuses on the phenomenon of motion and makes extensive use of computer simulation in its explorations of the topic.

This introduction to quantum algorithms is concise but comprehensive, covering many key algorithms. It is mathematically rigorous but requires minimal background and assumes no knowledge of quantum theory or quantum mechanics. The book explains quantum computation in terms of elementary linear algebra; it assumes the reader will have some familiarity with vectors, matrices, and their basic properties, but offers a review of all the relevant material from linear algebra.

In this book, Sanjoy Mahajan shows us that the way to master complexity is through insight rather than precision. Precision can overwhelm us with information, whereas insight connects seemingly disparate pieces of information into a simple picture. Unlike computers, humans depend on insight. Based on the author’s fifteen years of teaching at MIT, Cambridge University, and Olin College, The Art of Insight in Science and Engineering shows us how to build insight and find understanding, giving readers tools to help them solve any problem in science and engineering.

Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences.

The combination of two of the twentieth century’s most influential and revolutionary scientific theories, information theory and quantum mechanics, gave rise to a radically new view of computing and information. Quantum information processing explores the implications of using quantum mechanics instead of classical mechanics to model information and its processing. Quantum computing is not about changing the physical substrate on which computation is done from classical to quantum but about changing the notion of computation itself, at the most basic level.