Thank you to NetGalley, the author, and the publisher for this complementary ARC in exchange for my honest review!

This book is a sort of hybrid math-science-history book, covering all sorts of different topics revolving around how we prove things. Each chapter touches on a different subject and goes in depth about how proof factors in - I found the legal section particularly interesting.

I had hoped that the math portion had gone a bit more in depth but overall I would recommend this to anyone looking for a more broad perspective of how things are proved.

Ideas like evidence and proof are at the heart of so many aspects of modern life. On the surface they seem to be relatively simple and clear concepts, which anyone can use. But the author shows that there are surprising levels of underlying complexity, to both the interpretation of what proof means and to how it is applied in real world situations.

With chapters exploring proof in contexts of politics, mathematics, law, medicine and daily life, the book presents a wealth of examples in each chapter, to illustrate how and why proof is applied in the way that it typically is. Whether it be calculating the numbers of enemy tanks on a battlefield, or matching teeth to bite marks, the author shows that there have been remarkable developments (and failures) in what can be considered to be proof.

The chapter on legal issues was particularly interesting. It referred to cases from a wide range of jurisdictions, which included subtly different legal principles and some very nuanced models of proof. In one country the bar for conviction was ‘high,’ so that there was less risk of accidentally convicting innocent people. In another country the bar was ‘low’ so that it didn’t matter if innocent people were accidentally convicted. The difference between a ‘high’ and a ‘low’ bar often revolved around the principles and methodology of what counted as proof.

One of the issues often in the background of proof, is the question of how key words are interpreted. This was illustrated well with a number of historical examples, such as segregated education. At the beginning of the twentieth century segregated education was understood to be compatible with equality. By the middle of the twentieth century that was no longer the case. Changing social understandings can completely reverse what counts as a proof in different eras.

Where I think that the book could have pressed issues a little harder, was with the factors surrounding proof in the context of public policy. There are some very real contemporary questions about the competing policies of political parties. If the red party argues for policy x, and the blue party argues for policy y, what does it mean for one policy to be proved ‘better’ than another? Is it simply a matter of votes and preferences, or are there other factors which are relevant, and which perhaps drive votes and preferences?

Overall, this was an informative book which should be accessible to readers from any background. In places. the complexities of the issues mean that the book will probably be most appreciated by graduate readers. Around 20% of the text consists of notes, so there are links and follow up references for readers who want to pursue matters further.

I should add that this is a review of a (free) digital Advanced Review Copy (ARC) of the text. It carried a note to reviewers which implied that there may be differences between the text which I saw, and the final published copy. If that is so, then that means that elements of the rating and comments above may not accurately reflect what the final version of the book ends up looking like.