I recently had the pleasure of reading Understanding Uncertainty (2013) by Dennis V. Lindley. In this insightful work, Lindley explores how we navigate uncertainty, presenting the rules of probability as three natural extensions of classical logic. True to his philosophical stance, he reaffirms that probability is inherently personal:
it is not the uncertainty but your uncertainty.
He then goes on to introduce several probability distributions, well-known paradoxes, and decision-making problems. Lindley presents probability as the only coherent framework for handling uncertainty and strongly advocates for its broader application in real-world scenarios. In particular, he emphasises that when probabilities are combined with utilities, they offer a principled and practical approach to decision-making. Written for a general audience with no assumed mathematical background, the book is accessible and engaging for all readers. Lindley also thoughtfully examines the position of statistics within the broader scientific landscape, discussing the role of statisticians in the modern world.
If you have some background in probability, you may also enjoy Lindley’s seminal 2000 paper published by the Royal Statistical Society [link], as the book serves as a more accessible exposition of the ideas presented in that paper. Understanding Uncertainty is an excellent example of how mathematicians can effectively communicate complex ideas to a general audience through clear and simple language.