How do we establish what we believe? And how can we be certain that what we believe is true? And, assuming we are certain that what we believe is true, how do we convince other people that it is true? For over two thousand years, from the Medieval Arabic world to the midst of the covid-19 pandemic, scientific progress has relied on different methods of establishing fact from fiction. Achieve logical perfection and be rewarded with ultimate, universal truth. But there is far more to proof than axioms, theories and laws: when demonstrating that a new medical treatment works, persuading a jury of someone's guilt, or deciding whether you trust a self-driving car or a financial transaction, the weighing up of evidence is far from simple. To navigate proof, we must reach into a thicket of errors and biases, embrace uncertainty, to discern between truth and falsehood - never more so than when previously relied-upon methods fail. In Proof, bestselling author, statistician and epidemiologist Adam Kucharski spans science, politics, philosophy and economics, to explore how truth emerges - and why it falters.