This enjoyable book tells the story of Fourier series and transforms, their role in solving the heat equation, and subsequent applications. Providing a multitude of takeaways, Paul Nahin masterfully moves back and forth between the mathematical advances involved in the development and usage of Fourier analysis and the historical events and characters associated with the field.--Oscar Fernandez, author of Calculus Simplified Introducing readers to some of the most important scientific questions and technological challenges of the nineteenth century, this delightful book shows how they were solved using the heat equation. Reliving this exciting period through letters, stories, and insights, Hot Molecules, Cold Electrons is a triumphant success.--Christopher Tully, author of Elementary Particle Physics in a Nutshell Hot Molecules, Cold Electrons vividly demonstrates the power of mathematical tools for studying the heat equation in connection to the trans-Atlantic cable. This excellent book will be useful to anyone with an interest in mathematics, physics, or engineering.--Yasuyuki Kawahigashi, University of Tokyo