Emotions are powerful. In newspaper headlines, on social media and in political debates, they have become the primary way of understanding the world around us. But emotions have a way of obscuring the truth, and of making it more difficult to see the reality behind the rhetoric. In Thinking Better, Eugenia Cheng shows how mathematical logic can help us cut through the emotive yet illogical arguments that companies and politicians use to deceive us. First Cheng explains how mathematicians use black-and-white logic to build clear, irrefutable arguments, and how we can recognise when someone is using false logic to mislead us. Then - using debate-provoking examples from the modern world ranging from the United Airlines passenger fiasco to the question of free public healthcare - she shows how we can learn to apply logic to our messy world, where black and white merge through infinite shades of grey. Clear-sighted, revelatory and filled with useful real-world examples of logic and illogic at work, Beyond Infinity is an essential guide to the mathematician's art of thinking better.