“Proof,” by Adam Kucharski, is a thought-provoking read about how we obtain comfort and reach consensus that something is true in the absence of definitive proof. The chapters present situations (e.g., legal verdicts, medical testing, artificial intelligence) where this occurs and cover the mathematical and scientific approaches used to procure ample proof in these situations. The chapters also provide a history of how adequate proof has been attained throughout time, from Euclidean definitions and self-evident axioms (circa 300 BC) to Newtonian physics to modern-day AI models.

The book is nonmathematical in nature. However, the chapters do discuss many statistical terms and methods (at a high-level) to provide context and clarity to the situations considered. Some included terms and methods are: null hypothesis, p-values, confidence intervals, randomized controlled trials (RCTs), Type I and Type II errors, and various proof types (e.g., by exhaustion, by simulation, by contradiction, etc.).

The legal standards of “preponderance of the evidence” (civil cases) and “proof beyond a reasonable doubt” (criminal cases) are also discussed, as well as their inherent problems in balancing wrongful convictions against freeing the guilty. The author, who was an epidemiologist during the COVID-19 pandemic, also shares his experiences and insights throughout the pandemic—including difficulties related to data collection, variants, testing, vaccines, public sentiment, media coverage, politics, and obtaining consensus.

Some lighter proof situations are also discussed. One sets out to establish why tea tastes better when milk is poured into a cup before tea is added vs. afterward. Another involves the transition that Guiness made from traditional beer-making (dependent on human judgment) to industrial brewing, and the science and methods used to do so without diminishing beer quality.

Throughout the book, the author adequately demonstrates why proof is difficult to obtain. Even when sufficient evidence is available to convince ourselves that something is correct, the next step is to convince others—which can be particularly difficult due to factors such as psychology, politics, and prior beliefs. The author suggests that we continually learn to embrace uncertainty, balance our beliefs, and update our tools and approaches to modern problems that cannot be solved using old methods. The author also proposes that we increasingly trust our researchers, institutions, etc., while being cognizant of disinformation and other tactics used to distort the truth in modern society.

“Proof” is an excellent read that opens your mind and allows you to better recognize situations that lack certain truth. It also helps you more fully appreciate the difficulties that researchers and institutions encounter, and the complex decisions that must be made, when definitive proof is unobtainable.

[My special thanks to Basic Books (Hachette Book Group) and NetGalley for an advance reader’s copy of this book.]

I enjoyed the conversational tone of the writing and the good pacing. But I did find the explanations overly complex. I also felt that there was too much on artificial intelligence and was uncertain how this fit with the rest of the book. I think that people with greater background will enjoy the book more than I did. Thank you to Netgalley and Basic Books for the advance reader copy.

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.