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Proof: The Art and Science of Certainty
An award-winning mathematician shows how we prove what’s true, and what to do when we can’t
How do we establish what we believe? And how can we be certain that what we believe is true? And how do we convince other people that it is true? For thousands of years, from the ancient Greeks to the Arabic golden age to the modern world, science has used different methods—logical, empirical, intuitive, and more—to separate fact from fiction. But it all had the same goal: find perfect evidence and be rewarded with universal truth.
As mathematician Adam Kucharski shows, however, 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, the weighing up of evidence is far from simple. To discover proof, we must reach into a thicket of errors and biases and embrace uncertainty—and never more so than when existing methods fail.
Spanning mathematics, science, politics, philosophy, and economics, this book offers the ultimate exploration of how we can find our way to proof—and, just as importantly, of how to go forward when supposed facts falter.
How do we establish what we believe? And how can we be certain that what we believe is true? And how do we convince other people that it is true? For thousands of years, from the ancient Greeks to the Arabic golden age to the modern world, science has used different methods—logical, empirical, intuitive, and more—to separate fact from fiction. But it all had the same goal: find perfect evidence and be rewarded with universal truth.
As mathematician Adam Kucharski shows, however, 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, the weighing up of evidence is far from simple. To discover proof, we must reach into a thicket of errors and biases and embrace uncertainty—and never more so than when existing methods fail.
Spanning mathematics, science, politics, philosophy, and economics, this book offers the ultimate exploration of how we can find our way to proof—and, just as importantly, of how to go forward when supposed facts falter.
368 pages, Hardcover
First published May 6, 2025
111 people are currently reading
1445 people want to read
About the author
Adam Kucharski
6 books93 followersAdam Kucharski is a professor at the London School of Hygiene & Tropical Medicine, an award-winning writer, and bestselling author of The Rules of Contagion, which was a Book of the Year in The Times, Guardian and Financial Times.
A mathematician by training, his work on global outbreaks has included Ebola, Zika and COVID. He is in the top 0.1% of cited researchers globally, and he has advised multiple governments and health agencies. He is a TED senior fellow and winner of the University of Cambridge Adams Prize and the Wellcome Trust Science Writing Prize.
His writing has appeared in The Times, Observer, Financial Times, New Statesman and Wired, among others, and he has contributed to several documentaries, including BBC Horizon. He has spoken at venues like TED, Google and the Royal Institution, with his talks viewed over 6 million times online.
A mathematician by training, his work on global outbreaks has included Ebola, Zika and COVID. He is in the top 0.1% of cited researchers globally, and he has advised multiple governments and health agencies. He is a TED senior fellow and winner of the University of Cambridge Adams Prize and the Wellcome Trust Science Writing Prize.
His writing has appeared in The Times, Observer, Financial Times, New Statesman and Wired, among others, and he has contributed to several documentaries, including BBC Horizon. He has spoken at venues like TED, Google and the Royal Institution, with his talks viewed over 6 million times online.
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Displaying 1 - 30 of 39 reviews
June 8, 2025
Every so often I need to dip into philosophy, mix in some math, and sprinkle on some science. Give me that interdisciplinary trip, please and thank you! Proof: The Uncertain Science of Certainty, by Adam Kucharski, seemed like just what Dr. Kara ordered for herself. Indeed, it’s illuminating enough, though it has a few flaws that prevented me from enjoying it more. I received an eARC from NetGalley and publisher Basic Books in exchange for a review.
Beginning with ancient mathematics, Proof is basically a subset of epistemology writ large, seeking to answer not “how do we know what we know?” but “how do we know what we know is what is?” But it doesn’t stop with math: Kucharski takes us from math to law, medicine, and society at large. This is what makes the book so fascinating and relevant, I think. Given the rise of misinformation or junk data, which Proof touches on, it’s more important now than ever to be able to evaluate what we should or should not believe—and to remember we can’t always trust our senses.
While there is plenty in this book I knew already, I also learned a lot. Kucharski has a great talent for diving deep into a subject and then only extracting the parts he wants to show the reader, like a diver who knows exactly how to pluck the best pearl or lobster and bring it up to the surface for onlookers. He doesn’t make you go down the rabbit hole with him, and that’s awesome. Proof is quite readable in that way despite its interdisciplinary nature.
Where it stumbles, in my opinion, is honestly the editing. As a copyeditor (mind you, that’s different from structural, or developmental, editing), I’m loath to criticize my own, but … Kucharski, my guy, someone needed to tell you no more often. Or maybe you needed to listen. See, Proof’s chapters are long. Like, I would hit a new chapter (and this is one of those rare eARCs that were actually formatted as ebooks rather than converted PDFs, woohoo, so my ereader detected chapters), and my ereader would be like, “This chapter will take twenty minutes to read,” and I was like, “Um, what?” because, look, I am no slouch in the speed department, so my ereader knows how fast I read. Sure enough, however … yeah, those chapters are long. Because Kucharski likes to digress, likes to ramble, likes to pack in as much as he can, and it seems like not a single person cared enough to stop him! Moreover, the chapters lack sProof: The Uncertain Science of Certaintytrong organizational structures, such as stories linked to individuals or any sense of narrative.
The result is a paradox of a book: the information is interesting, yet the writing is dull and ponderous. It’s a great example of why science and science communication are two different fields of study, and why being good at one doesn’t make you good at the other. Kucharski clearly knows his stuff, yet his storytelling skills aren’t a match, and it shows.
Proof is fascinating in its own way, and you would probably learn a lot if you picked up this book. But it’s not going to be one that sticks around for me.
Originally posted on Kara.Reviews.
Beginning with ancient mathematics, Proof is basically a subset of epistemology writ large, seeking to answer not “how do we know what we know?” but “how do we know what we know is what is?” But it doesn’t stop with math: Kucharski takes us from math to law, medicine, and society at large. This is what makes the book so fascinating and relevant, I think. Given the rise of misinformation or junk data, which Proof touches on, it’s more important now than ever to be able to evaluate what we should or should not believe—and to remember we can’t always trust our senses.
While there is plenty in this book I knew already, I also learned a lot. Kucharski has a great talent for diving deep into a subject and then only extracting the parts he wants to show the reader, like a diver who knows exactly how to pluck the best pearl or lobster and bring it up to the surface for onlookers. He doesn’t make you go down the rabbit hole with him, and that’s awesome. Proof is quite readable in that way despite its interdisciplinary nature.
Where it stumbles, in my opinion, is honestly the editing. As a copyeditor (mind you, that’s different from structural, or developmental, editing), I’m loath to criticize my own, but … Kucharski, my guy, someone needed to tell you no more often. Or maybe you needed to listen. See, Proof’s chapters are long. Like, I would hit a new chapter (and this is one of those rare eARCs that were actually formatted as ebooks rather than converted PDFs, woohoo, so my ereader detected chapters), and my ereader would be like, “This chapter will take twenty minutes to read,” and I was like, “Um, what?” because, look, I am no slouch in the speed department, so my ereader knows how fast I read. Sure enough, however … yeah, those chapters are long. Because Kucharski likes to digress, likes to ramble, likes to pack in as much as he can, and it seems like not a single person cared enough to stop him! Moreover, the chapters lack sProof: The Uncertain Science of Certaintytrong organizational structures, such as stories linked to individuals or any sense of narrative.
The result is a paradox of a book: the information is interesting, yet the writing is dull and ponderous. It’s a great example of why science and science communication are two different fields of study, and why being good at one doesn’t make you good at the other. Kucharski clearly knows his stuff, yet his storytelling skills aren’t a match, and it shows.
Proof is fascinating in its own way, and you would probably learn a lot if you picked up this book. But it’s not going to be one that sticks around for me.
Originally posted on Kara.Reviews.
June 9, 2025
Adam Kucharski’s latest book, Proof: The Uncertain Science of Certainty, offers a compelling exploration of how we define, assess, and communicate truth in an increasingly complex and information-saturated world. Building upon his expertise in mathematics and epidemiology, Kucharski examines the limitations of traditional notions of proof and the challenges of establishing certainty across various domains, including science, law, and public policy.
At the heart of Proof is the assertion that the concept of proof is far more nuanced than often assumed. He traces a lot of these issues back to "axioms" - claims we understand as true and how these can sometimes conflict with each other. Kucharski illustrates this by referencing the Monty Hall problem, a probability puzzle that even confounded renowned mathematician Paul Erdős, to demonstrate how human intuition can falter in the face of statistical reasoning. He further delves into historical shifts in mathematical understanding, such as the development of non-Euclidean geometry and Gödel's incompleteness theorems, to highlight the evolving nature of what constitutes proof. It is an episodic tour through many important moments in math-based epistemology.
The book also scrutinizes the application of algorithms in areas like criminal justice, where tools like the Correctional Offender Management Profiling for Alternative Sanctions (COMPAS) have been shown to exhibit biases, raising questions about fairness and the reliability of algorithmic decision-making. In the realm of medicine, Kucharski challenges the supremacy of randomized controlled trials (RCTs) as the "gold standard" for evidence, arguing that other forms of proof, including experiential knowledge, can be equally valid depending on the context. I'm personally a bit skeptical of this approach, but don't think RCTs are the only source of evidence worth reviewing. I think Kucharski could have handle this discussion with greater care and depth.
Kucharski supports his arguments with an onslaught of historical anecdotes, case studies, and analyses of current events. For instance, he recounts how Abraham Lincoln employed Euclidean logic to argue against slavery, illustrating the intersection of mathematical reasoning and moral philosophy. He also discusses the origins of clinical trial designs, tracing them back to informal discussions at Rothamsted agricultural station, thereby emphasizing the social dimensions of scientific development .
The book's strength lies in its ability to make complex concepts accessible without oversimplification. Kucharski's clear prose and engaging storytelling render intricate ideas in mathematics and science approachable for general readers. His balanced examination of topics, acknowledging both the utility and limitations of various forms of proof, enhances the book's credibility and relevance.
Proof is particularly timely, addressing the pervasive issues of misinformation and the erosion of public trust in expert knowledge, but has a bit of a fatalistic and/or paternalistic perspective about epistemology for the masses. By dissecting the processes through which we arrive at conclusions and the potential pitfalls therein, Kucharski equips readers with a critical framework for evaluating information. His call for humility and transparency in the communication of scientific findings resonates strongly in an era marked by polarized discourse and skepticism toward established institutions. I always respect epistemic humility.
While the book addresses sophisticated topics, its lucid explanations and relatable examples make it accessible to a broad audience. Readers without a background in mathematics or science will find the discussions enlightening rather than daunting, but will likely not be surprised by much of the content. I offer a qualified recommendation of the book.
At the heart of Proof is the assertion that the concept of proof is far more nuanced than often assumed. He traces a lot of these issues back to "axioms" - claims we understand as true and how these can sometimes conflict with each other. Kucharski illustrates this by referencing the Monty Hall problem, a probability puzzle that even confounded renowned mathematician Paul Erdős, to demonstrate how human intuition can falter in the face of statistical reasoning. He further delves into historical shifts in mathematical understanding, such as the development of non-Euclidean geometry and Gödel's incompleteness theorems, to highlight the evolving nature of what constitutes proof. It is an episodic tour through many important moments in math-based epistemology.
The book also scrutinizes the application of algorithms in areas like criminal justice, where tools like the Correctional Offender Management Profiling for Alternative Sanctions (COMPAS) have been shown to exhibit biases, raising questions about fairness and the reliability of algorithmic decision-making. In the realm of medicine, Kucharski challenges the supremacy of randomized controlled trials (RCTs) as the "gold standard" for evidence, arguing that other forms of proof, including experiential knowledge, can be equally valid depending on the context. I'm personally a bit skeptical of this approach, but don't think RCTs are the only source of evidence worth reviewing. I think Kucharski could have handle this discussion with greater care and depth.
Kucharski supports his arguments with an onslaught of historical anecdotes, case studies, and analyses of current events. For instance, he recounts how Abraham Lincoln employed Euclidean logic to argue against slavery, illustrating the intersection of mathematical reasoning and moral philosophy. He also discusses the origins of clinical trial designs, tracing them back to informal discussions at Rothamsted agricultural station, thereby emphasizing the social dimensions of scientific development .
The book's strength lies in its ability to make complex concepts accessible without oversimplification. Kucharski's clear prose and engaging storytelling render intricate ideas in mathematics and science approachable for general readers. His balanced examination of topics, acknowledging both the utility and limitations of various forms of proof, enhances the book's credibility and relevance.
Proof is particularly timely, addressing the pervasive issues of misinformation and the erosion of public trust in expert knowledge, but has a bit of a fatalistic and/or paternalistic perspective about epistemology for the masses. By dissecting the processes through which we arrive at conclusions and the potential pitfalls therein, Kucharski equips readers with a critical framework for evaluating information. His call for humility and transparency in the communication of scientific findings resonates strongly in an era marked by polarized discourse and skepticism toward established institutions. I always respect epistemic humility.
While the book addresses sophisticated topics, its lucid explanations and relatable examples make it accessible to a broad audience. Readers without a background in mathematics or science will find the discussions enlightening rather than daunting, but will likely not be surprised by much of the content. I offer a qualified recommendation of the book.
December 6, 2025
Proof is a timely book, both for me and for the world in general. I did begin this year reading about Radical Uncertainty (John Kay and Mervyn A. King's) and, despite predicting Adam Kucharski would go through many concepts I know and actually studied in university or later, still wanted to finish the year with his own foray into certainty. Humanity is going through a crisis of trust, of belief in knowledge and science, of confidence in institutions and academy. There are many explored reasons as to why and when this has come, but some consequences are inarguable. We are losing some of our own progress, losing the benefits of knowledge we've achieved, of organizations we built, letting our distrust of some people turn into distrust of everything and then going back to trusting individuals (be it a confident idiot, be it our own badly informed "research").
Kucharski's Proof proposes an exploration and clarification of how we come up with considering something demonstrated, proven, "true". In my opinion, he succeeds in having both a good exploration - detailed but not in too deep as to lose much audience - and clarification - by the end we have an emerging framework to understand the flaws of our knowledge but also how not to lose the benefits of acting on the level of evidence we can actually achieve and trade it for chaos. As expected from what I know of the author, there is no scientific nihilism here, criticisms are constructive and enhancing for our epistemic evolution.
Proof explains a lot of processes that humanity uses in coming up with "knowing" something to be "a fact", from mathematical demonstrations - and the progressive reframing and reconstructing that brought us to current maths, from calculus to fractals - to the construction of algorithms - exploring the difference between trusting a result and knowing how someone or something got to that result and how hidden biases can have persistent consequences -, from scientific strength of evidence stratifications (with which I was quite familiar from my medicine degree) - and how they both help us understand evidence more deserving of trust and often limit our action on issues we're unable to do the randomized investigations that get us to those highest of evidence levels - to how court judges and juries get to their decisions. The discussions about probability touch on a particular point of interest to my own worries, be it in my professional position or in daily life: probability is constantly publicly butchered, both by genuine mistake and as means to trick or misinform others. Much of these explorations are further enhanced by many historical anecdotes and the author's own memoir of the COVID-19 pandemic and his own part in coming up with evidence and knowledge-based decisions when one cannot wait for time's long-winded eventual help and people's lives are on the line in more ways than you'd like.
By the end, I feel the author is in alignment with the humility I feel to be necessary in both epistemology and public speaking and decision-making if we are to solve our current crisis and build a new paradigm of trust and progress. We can both be more skeptical - less absolute in what we consider proven or unquestionable (what is?) - and still understand that acting on the best evidence of the moment is in our best interest, that having people and institutions dedicated to knowledge or knowledge based decision-making is the best way to live, that the everchanging landscape of truth can be a reflection of constant improvement, as new proof both builds on but also undermines previous proof.
It is telling that I began 2025 reading about understanding and getting used to uncertainty and end it reading about proof and thinking about the need for a framework for actionable evidence.
I wholeheartedly recommend reading Proof.
Kucharski's Proof proposes an exploration and clarification of how we come up with considering something demonstrated, proven, "true". In my opinion, he succeeds in having both a good exploration - detailed but not in too deep as to lose much audience - and clarification - by the end we have an emerging framework to understand the flaws of our knowledge but also how not to lose the benefits of acting on the level of evidence we can actually achieve and trade it for chaos. As expected from what I know of the author, there is no scientific nihilism here, criticisms are constructive and enhancing for our epistemic evolution.
Proof explains a lot of processes that humanity uses in coming up with "knowing" something to be "a fact", from mathematical demonstrations - and the progressive reframing and reconstructing that brought us to current maths, from calculus to fractals - to the construction of algorithms - exploring the difference between trusting a result and knowing how someone or something got to that result and how hidden biases can have persistent consequences -, from scientific strength of evidence stratifications (with which I was quite familiar from my medicine degree) - and how they both help us understand evidence more deserving of trust and often limit our action on issues we're unable to do the randomized investigations that get us to those highest of evidence levels - to how court judges and juries get to their decisions. The discussions about probability touch on a particular point of interest to my own worries, be it in my professional position or in daily life: probability is constantly publicly butchered, both by genuine mistake and as means to trick or misinform others. Much of these explorations are further enhanced by many historical anecdotes and the author's own memoir of the COVID-19 pandemic and his own part in coming up with evidence and knowledge-based decisions when one cannot wait for time's long-winded eventual help and people's lives are on the line in more ways than you'd like.
By the end, I feel the author is in alignment with the humility I feel to be necessary in both epistemology and public speaking and decision-making if we are to solve our current crisis and build a new paradigm of trust and progress. We can both be more skeptical - less absolute in what we consider proven or unquestionable (what is?) - and still understand that acting on the best evidence of the moment is in our best interest, that having people and institutions dedicated to knowledge or knowledge based decision-making is the best way to live, that the everchanging landscape of truth can be a reflection of constant improvement, as new proof both builds on but also undermines previous proof.
It is telling that I began 2025 reading about understanding and getting used to uncertainty and end it reading about proof and thinking about the need for a framework for actionable evidence.
I wholeheartedly recommend reading Proof.
October 2, 2025
This is more of a contemplation of the idea of proof and how that has evolved over time, than a focused approach to establishing how things are proven. It is one of those books where if you don't like the bit you're reading, you can skip ahead and find something likely to engage you. That also means, of course, that when you find a bit you do really love, it annoying stops just when it was getting interesting. For me, those parts were Kucharski's observations about the evolving and urgent nature of proof in COVID, which give thought to how we balance certainty and risk.
August 15, 2025
Excellent. Great introduction to the fundamentals underpinning the evidence base of medicine, and the broader concept of 'proof' in general. Also provides some amazing behind-the-scenes insight into the mix of deduction, guesswork and collaboration that underpinned the madness of the first year or two of COVID.
July 8, 2025
I really enjoyed this book. This book is a bit more philosophical than I expected, but it’s primarily about what’s considered “proof” in the scientific community. Kucharski goes through the history of what “proof” has meant during different times throughout history and how it’s changed as science and our understanding have progressed. Typically, I’m not a big fan of books that have a ton of stories about history, but this topic intrigues me, so it held my attention, and I loved it.
June 6, 2025
This book is an interesting discussion of what counts as proof amongst academics and scientists. The conception is more rigid than in the majority of society, yet still has many issues simply related to humans hubris.
September 18, 2025
It is perfectly possible, indeed very common as all mathematicians know, to agree with and fail to fault the logic of every step in a sequence offered as a mathematical proof without experiencing any sense of conviction. And without such an experience, without a felt sense and a correlative understanding that the reasoning achieves what it is supposed to achieve, a sequence of steps fails to be a proof; it fails to be a means of persuading anybody of anything and instead remains as a formally correct but inert string of logical moves.
Brian Rotman Ad Infinitum... The Ghost in Turing's Machine: Taking God Out of Mathematics and Putting the Body Back In. An Essay in Corporeal Semiotics
Some will think that a mathematical argument either is a proof or is not a proof. In the context of elementary analysis I disagree, and believe instead that the proper role of a proof is to carry reasonable conviction to one's intended audience. It seems to me that mathematical rigour is like clothing: in its style ought to suit the occasion, and it diminishes comfort and restricts freedom of movement if it is either too loose or too tight.
George F Simmons Differential Equations with Applications and Historical Notes - International Economy Edition
Well, there's two compelling quotes about "proof". Unfortunately, we get nothing so recondite in Kucharski's book, with its vast promise of scope and slightly miserable delivery.
What is there to say about proof? Euclid, non-Euclidean geometry, computer-aided proofs, incompleteness results ... . We get some of that but told in an episodic style and, in my opinion, inadequately handled.
There's so much of interest on the topic we could have heard: some better account of mathematical logic, Gödel and model theory (Gödel, Escher, Bach: An Eternal Golden Braid is the benchmark for popular accounts of this stuff), the tension between truth and proof, Tarski's theorem. What about Shinichi Mochizuki's purported proof of the abc conjecture, condemned as insane by the majority of mathematicians but accepted by a few? Foundational issues around the axiom of choice and the continuum hypothesis, the law of excluded middle, large cardinals ... Logic as an empirical discipline (handled well in Goodbye, Descartes: The End of Logic and the Search for a New Cosmology of the Mind). The situational logics of Jon Barwise. Much here could have been set out for the general reader but the opportunity was missed. What about Steven Shapin's A Social History of Truth: Civility and Science in Seventeenth-Century England? Or Plato's Meno problem (see S.L. Zabell's Symmetry and its Discontents: Essays on the History of Inductive Probability).
But then so much of the book is not about proof in that narrow mathematical sense at all. It's about evidence, inference and uncertainty. Fascinating and worthwhile topics, though hardly the ones held out by the title "Proof". Kucharski starts off, in the introduction, with the Monty Hall problem. Hardly an obvious setting for discussion of proof. The difficulty is that, in my opinion, he doesn't understand the problem at all. He reads data into the problem that aren't there, failing to understand that the riddle is underspecified. Until you realise that, any analysis will be frustratingly ambivalent. The likelihood function is not specified and not obvious. It has itself to be inferred from other data not given. So that's a bad start.
We then get a confused chapter on logic, law and constitutions. There's Euclid and Abraham Lincoln, something about law as algorithm (I think), the old canard about Gödel and his US citizenship interview. It's not clear what is the author's point. And there's so much useful material he could have drawn on here had he wanted to take this seriously: How to Do Things With Rules: A Primer of Interpretation, or Law as Algorithm
The next chapter wants to be about changing fashions in mathematical proof. Bafflingly, the example he puts forward is Dedekind's construction of a function that is everywhere continuous but nowhere differentiable (a fractal to you and me). Odd, because the distinction between continuity and differentiability was always obvious. It's not clear how this affected the principles of proof. Something about infinitesimals, which have alternated between fashion and condemnation over the years, might have made the argument.
Then we're back to law again. Kucharski deals with algorithm-driven bail decisions. He doesn't really take this anywhere. We get the Howland will forgery trial, DNA and the prosecutor's fallacy (very superficially), something about juries, all a bit of a ramble but without a destination. I was surprised we didn't get The People v Collins. There are so many good books on this subject, most importantly the excellent Analysis of Evidence, a survivor from the whole evidence as a multi-disciplinary subject movement. That book deals with probability and statistics much better than Kucharski's.
Then we get to what Kucharski really wants to tell us about, his own work and an account of data analysis during the Covid-19 pandemic. Had I known this was a book about Covid, and it is, I would not have bought it.
There's a depressingly sketchy attempt to address some pivotal points in the development of statistical science. Nothing about exchangeability or the de Finetti representation theorem.
Then we get to his conclusions, to which I am sympathetic but they're so poorly argued here. He speculates that there no rules as to proof. It's just that if you bother a problem for long enough, solutions are born. He castigates philosophers of science for seeking to impose method. Perhaps he should read some Feyerabend Paul K.. More intriguingly, he speculates whether large language models will open up new avenues of proof. It has occurred to me that successful prediction models based on neural networks might identify new species of partial exchangeability. But that's all for another day.
August 10, 2025
A lot of interesting topics in this book, but I didn’t enjoy it much. I think, considering the title, he really doesn’t get that far into explaining what “proof” and “certainty” mean - he seems far more interested in discussing when it makes sense to take action even when you don’t and maybe can’t find proof or certainty, at least not quickly enough to deal with a pressing issue. And the pressing issue he frequently returns to is how governments responded to Covid. That topic could be a good book, but I don’t think that’s what was promised by the title. Also I got tired of his frequent references to his own work in the UK on the COVID situation, I’m sure very meaningful to him, but it gets tedious to the reader, he doesn’t really impart much of interest there.
September 25, 2025
This was quite a sprawling read, that had some great nuggets of information. I enjoyed stories from the author's own work around COVID, a nice case study in realtime science influencing policy. However, the whole book was too diffuse in its aims. It felt like it lacked a rigorous editorial hand, with chapters that would chop and change. A more focused and defined work could probably have been created here. Proof by intimidation!
February 7, 2025
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.
May 16, 2025
A Disappointing Deduction: A Negative Review of Adam Kucharski's "Proof"
While the premise of Adam Kucharski's "Proof: How Logic Can Deceive Us and How to Fight Back" is undoubtedly intriguing – to explore the pitfalls and power of logical reasoning in everyday life – the execution ultimately falls short of its potential. Instead of a sharp and insightful guide, "Proof" often feels like a meandering collection of anecdotes and somewhat superficial explorations that fail to deliver a truly cohesive or deeply insightful understanding of the subject matter.
One of the book's primary weaknesses lies in its lack of focus. Kucharski jumps between various topics, from cognitive biases and statistical fallacies to conspiracy theories and historical examples of flawed reasoning. While each individual section might contain a nugget of interest, the overall effect is disjointed. The connections between these disparate areas often feel tenuous, leaving the reader struggling to grasp a central argument or a unifying framework. It's as if the author had a collection of interesting ideas and decided to string them together under the loose banner of "logic."
Furthermore, the depth of analysis often feels lacking. While Kucharski introduces various logical concepts, he rarely delves into them with the rigor necessary for a truly enriching understanding. The explanations can feel rushed and overly simplistic, leaving the reader with a superficial grasp rather than a profound insight. For those already familiar with basic concepts of critical thinking and cognitive biases, much of the book will feel like a rehash of well-trodden ground without offering significant new perspectives or advanced analysis.
The reliance on anecdotes, while sometimes engaging, also becomes a point of frustration. While real-world examples can be powerful tools for illustrating abstract concepts, in "Proof," they often feel more like diversions than integral parts of the argument. Some examples are stretched thin to fit the narrative, and the sheer volume of them can feel overwhelming, obscuring the underlying logical principles the book aims to explore.
Moreover, the book's attempts to offer solutions or strategies for "fighting back" against logical deception feel underdeveloped. While Kucharski touches upon the importance of critical thinking and skepticism, the advice provided is often generic and lacks concrete, actionable steps. The reader is left with a better understanding of the problems but little practical guidance on how to effectively navigate them.
Finally, the writing style, while generally accessible, occasionally suffers from a lack of precision. Certain arguments feel vaguely formulated, and the terminology used can sometimes be ambiguous, hindering a clear understanding of the intended message.
In conclusion, while "Proof" promises a fascinating exploration of the intricacies of logic and its potential for deception, it ultimately delivers a somewhat scattered and superficial treatment of the subject. While it might serve as a very introductory read for someone completely unfamiliar with the concepts discussed, those seeking a deeper, more rigorous, and more cohesive analysis of logical pitfalls and effective countermeasures will likely find themselves disappointed. "Proof" ultimately feels like a collection of interesting observations that never quite coalesce into a truly compelling or insightful argument.
While the premise of Adam Kucharski's "Proof: How Logic Can Deceive Us and How to Fight Back" is undoubtedly intriguing – to explore the pitfalls and power of logical reasoning in everyday life – the execution ultimately falls short of its potential. Instead of a sharp and insightful guide, "Proof" often feels like a meandering collection of anecdotes and somewhat superficial explorations that fail to deliver a truly cohesive or deeply insightful understanding of the subject matter.
One of the book's primary weaknesses lies in its lack of focus. Kucharski jumps between various topics, from cognitive biases and statistical fallacies to conspiracy theories and historical examples of flawed reasoning. While each individual section might contain a nugget of interest, the overall effect is disjointed. The connections between these disparate areas often feel tenuous, leaving the reader struggling to grasp a central argument or a unifying framework. It's as if the author had a collection of interesting ideas and decided to string them together under the loose banner of "logic."
Furthermore, the depth of analysis often feels lacking. While Kucharski introduces various logical concepts, he rarely delves into them with the rigor necessary for a truly enriching understanding. The explanations can feel rushed and overly simplistic, leaving the reader with a superficial grasp rather than a profound insight. For those already familiar with basic concepts of critical thinking and cognitive biases, much of the book will feel like a rehash of well-trodden ground without offering significant new perspectives or advanced analysis.
The reliance on anecdotes, while sometimes engaging, also becomes a point of frustration. While real-world examples can be powerful tools for illustrating abstract concepts, in "Proof," they often feel more like diversions than integral parts of the argument. Some examples are stretched thin to fit the narrative, and the sheer volume of them can feel overwhelming, obscuring the underlying logical principles the book aims to explore.
Moreover, the book's attempts to offer solutions or strategies for "fighting back" against logical deception feel underdeveloped. While Kucharski touches upon the importance of critical thinking and skepticism, the advice provided is often generic and lacks concrete, actionable steps. The reader is left with a better understanding of the problems but little practical guidance on how to effectively navigate them.
Finally, the writing style, while generally accessible, occasionally suffers from a lack of precision. Certain arguments feel vaguely formulated, and the terminology used can sometimes be ambiguous, hindering a clear understanding of the intended message.
In conclusion, while "Proof" promises a fascinating exploration of the intricacies of logic and its potential for deception, it ultimately delivers a somewhat scattered and superficial treatment of the subject. While it might serve as a very introductory read for someone completely unfamiliar with the concepts discussed, those seeking a deeper, more rigorous, and more cohesive analysis of logical pitfalls and effective countermeasures will likely find themselves disappointed. "Proof" ultimately feels like a collection of interesting observations that never quite coalesce into a truly compelling or insightful argument.
March 29, 2025
“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.]
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.]
March 20, 2025
This seemed to be a book that had a lot going for it. The topic of 'the science of certainty' appealed to a reader like me who is fascinated by probability and statistics, and I enjoyed the way the introduction made use of the uncertainty of the impact of the Eyjafjallakökull volcano on flight safety, then the delight that is the Monty Hall problem. But although the rest of the book had some highlights, I couldn't get on with much of it.
In a way, the title is highly misleading, because the book isn't really about 'proof' - after all, very little science involves proof. Certainly most of the studies we see misreported in the press don't. We can only prove something with perfect knowledge. This is fine when applying basic logic. We can make deductions, for example, if we are able to make a statement like 'no square is circular'. But such statements are rarely applicable in the real world. Instead we have to rely on induction or abduction, which is usually the case in science - meaning the best we can do is to have currently supported theory given the evidence available that may change in the future. Proofs work for abstract mathematics (also authors to read and for puddings), but not often in the real world.
This was fine (although I would have enjoyed a book on logic too), and it was interesting to cover ground on p values and frequentist statistics (though I would have liked more than the relatively quick dip into Bayes we get). But the problem was that the vast majority of the book didn't really cover this at all, focussing at length on dealing with the COVID pandemic, and to a lesser extent on taking a logical approach to proof in legal argument.
Both these specifics - Adam Kurcharski's personal experience during COVID and Abraham Lincoln's legal work - would have made excellent cases studies for a couple of pages, but they went on and on interminably. There are plenty of books about dealing with the pandemic - if I wanted to read one of these, I would have done so - but this isn't labelled as a such. I would have liked a whole range of scientific proof issues, taking in physics and cosmology and the other sciences as well. I admit I generally avoid reading about medical science, so this was a bit of a personal issue as well - but this wasn't supposed to be a book about medical science.
It didn't help that the book lacks structure, jumping around from topic to topic in a random-feeling fashion. Bottom line: if you want to find out more about the probability-based decisions made by COVID scientists (from an inside source, as Adam Kucharski was one of them), this is one for you. But if you want an engaging, wide ranging book on the nature of proof (or, rather, the lack of it) in science, this doesn't do what it says on the tin.
In a way, the title is highly misleading, because the book isn't really about 'proof' - after all, very little science involves proof. Certainly most of the studies we see misreported in the press don't. We can only prove something with perfect knowledge. This is fine when applying basic logic. We can make deductions, for example, if we are able to make a statement like 'no square is circular'. But such statements are rarely applicable in the real world. Instead we have to rely on induction or abduction, which is usually the case in science - meaning the best we can do is to have currently supported theory given the evidence available that may change in the future. Proofs work for abstract mathematics (also authors to read and for puddings), but not often in the real world.
This was fine (although I would have enjoyed a book on logic too), and it was interesting to cover ground on p values and frequentist statistics (though I would have liked more than the relatively quick dip into Bayes we get). But the problem was that the vast majority of the book didn't really cover this at all, focussing at length on dealing with the COVID pandemic, and to a lesser extent on taking a logical approach to proof in legal argument.
Both these specifics - Adam Kurcharski's personal experience during COVID and Abraham Lincoln's legal work - would have made excellent cases studies for a couple of pages, but they went on and on interminably. There are plenty of books about dealing with the pandemic - if I wanted to read one of these, I would have done so - but this isn't labelled as a such. I would have liked a whole range of scientific proof issues, taking in physics and cosmology and the other sciences as well. I admit I generally avoid reading about medical science, so this was a bit of a personal issue as well - but this wasn't supposed to be a book about medical science.
It didn't help that the book lacks structure, jumping around from topic to topic in a random-feeling fashion. Bottom line: if you want to find out more about the probability-based decisions made by COVID scientists (from an inside source, as Adam Kucharski was one of them), this is one for you. But if you want an engaging, wide ranging book on the nature of proof (or, rather, the lack of it) in science, this doesn't do what it says on the tin.
November 18, 2025
Award-winning mathematician Adam Kucharski shows how we prove what’s true, in a way that convinces ourselves and others. Over the ages, science has used a variety of methods—logical, empirical, intuitive—to separate fact from fiction.
The following 8 numbered chapters are preceded by an introduction in which Kucharski tells us that the book is about methods people have developed to gather evidence, accommodate uncertainty, and get to something that can serve as a basis for making decisions in complex situations. He also notes that a crucial piece of his narrative is about what happens when those methods fail.
Chapter 1: The National Axioms
Chapter 2: Logic Makes Mathematical Monsters
Chapter 3: One Hundred Guilty and One Innocent
Chapter 4: Tasting Statistical Tea and Brewing Scientific Beer
Chapter 5: Paradigm Rifts
Chapter 6: Big Lies
Chapter 7: In Machines We Trust
Chapter 8: How Much Do We Lose?
The word “proof” often implies showing that something is true/correct in a mathematical sense, but we are also interested in establishing the truth in many other contexts, such as in legal proceedings, economic decision-making, and medical evaluations. The author tells us that President Abraham Lincoln, who reportedly studied Euclid’s Elements very intensely, used proof by contradiction that slavery was wrong. There is also some discussion of the famous Monty Hall Problem that led everyone, including a few top mathematicians with impeccable logical reasoning skills, astray.
In the end, there is no fool-proof way to show that something is true. Reasoning alone is insufficient, as cultural and psychological factors also enter into the picture; hence, the prevalence of conspiracy theories, despite ample contrary evidence in most cases. As a mathematician and epidemiologist, Kucharski elaborates at length on the COVID pandemic and what guidance governments should provide to the public, in the face of many unknowns and rapidly-emerging variants.
The following 8 numbered chapters are preceded by an introduction in which Kucharski tells us that the book is about methods people have developed to gather evidence, accommodate uncertainty, and get to something that can serve as a basis for making decisions in complex situations. He also notes that a crucial piece of his narrative is about what happens when those methods fail.
Chapter 1: The National Axioms
Chapter 2: Logic Makes Mathematical Monsters
Chapter 3: One Hundred Guilty and One Innocent
Chapter 4: Tasting Statistical Tea and Brewing Scientific Beer
Chapter 5: Paradigm Rifts
Chapter 6: Big Lies
Chapter 7: In Machines We Trust
Chapter 8: How Much Do We Lose?
The word “proof” often implies showing that something is true/correct in a mathematical sense, but we are also interested in establishing the truth in many other contexts, such as in legal proceedings, economic decision-making, and medical evaluations. The author tells us that President Abraham Lincoln, who reportedly studied Euclid’s Elements very intensely, used proof by contradiction that slavery was wrong. There is also some discussion of the famous Monty Hall Problem that led everyone, including a few top mathematicians with impeccable logical reasoning skills, astray.
In the end, there is no fool-proof way to show that something is true. Reasoning alone is insufficient, as cultural and psychological factors also enter into the picture; hence, the prevalence of conspiracy theories, despite ample contrary evidence in most cases. As a mathematician and epidemiologist, Kucharski elaborates at length on the COVID pandemic and what guidance governments should provide to the public, in the face of many unknowns and rapidly-emerging variants.
May 31, 2025
Originally posted on my blog Nonstop Reader.
Proof is a (mostly) layman accessible monograph on scientific certainty and methods, written by Dr. Adam Kucharski. Released 6th May 2025 by Hachette on their Basic Books imprint, it's 368 pages and is available in hardcover, audio, and ebook formats. It's worth noting that the ebook format has a handy interactive table of contents as well as interactive links and references throughout.
The author has a wide ranging background: from mathematics to infectious diseases/tropical medicine/epidemiology. This book is similarly wide ranging and not always direct - there's a fair bit of meandering involved. That being said, the author writes well and understandably and doesn't rely on obfuscation and jargon to score points.
Although not academically rigorous, the content is meticulously annotated throughout, and the chapter notes are likely worth the price of the book for the extra content alone. As a multidisciplinary work, there are some wide ranging meanders across disciplines and subjects (and time periods), but overall, it's interesting and fairly engaging. The author is clearly bright, and invested in the subject, and it's indisputably important and noble, helping humans understand how to winnow *actual* facts from the chaff we're all bombarded with continually.
Three and a half stars. It would be a good choice for public or post-secondary school library acquisition, or for niche non-fiction readers.
Disclosure: I received an ARC at no cost from the author/publisher for review purposes.
Proof is a (mostly) layman accessible monograph on scientific certainty and methods, written by Dr. Adam Kucharski. Released 6th May 2025 by Hachette on their Basic Books imprint, it's 368 pages and is available in hardcover, audio, and ebook formats. It's worth noting that the ebook format has a handy interactive table of contents as well as interactive links and references throughout.
The author has a wide ranging background: from mathematics to infectious diseases/tropical medicine/epidemiology. This book is similarly wide ranging and not always direct - there's a fair bit of meandering involved. That being said, the author writes well and understandably and doesn't rely on obfuscation and jargon to score points.
Although not academically rigorous, the content is meticulously annotated throughout, and the chapter notes are likely worth the price of the book for the extra content alone. As a multidisciplinary work, there are some wide ranging meanders across disciplines and subjects (and time periods), but overall, it's interesting and fairly engaging. The author is clearly bright, and invested in the subject, and it's indisputably important and noble, helping humans understand how to winnow *actual* facts from the chaff we're all bombarded with continually.
Three and a half stars. It would be a good choice for public or post-secondary school library acquisition, or for niche non-fiction readers.
Disclosure: I received an ARC at no cost from the author/publisher for review purposes.
June 24, 2025
At its core, this was a popular book on epistemology. Generally a very good book and a topic that many more people should reflect on. Kucharski covers a lot of ground, from the history of non-Euclidean geometry to the use of algorithms in courtrooms to the challenges inherent in predicting the spread of COVID and finally to artificial intelligence. Some of the examples were cliched for this genre (e.g., the Monte Hall problem), but plenty were new to me and interesting if not fun. This breadth was a strength of the book, however I would have preferred to see the book organized differently. For instance, different types (i.e. strategies) of proof were explored throughout the book and italicized for emphasis. However, these were frequently buried in chapters. I would have rather seen chapters organized around these methods of proof. This leads to my second main criticism, which is that though the anecdotes and illustrative examples were generally interesting, they frequently interrupted each other unnecessarily. Breaking the chapters up more could have helped prevent this without ditching good content.
Finally, my last gripe was with Kucharski's discussion of p-values. In particular, on pg. 107 he somewhat botches the explanation, leaving out the crucial conditional clause (p-values are calculated conditionally on some null model). This is one of the most common mistakes in interpreting p-values. Partially this is because the more precise statement is cumbersome; it wouldn't surprise me if the statement that appears now was the result of the copy editing process. But given the book space Kucharski devoted to the topic, he certainly should have taken the care to get (or insisted on keeping, if it was a copy editing suggestion) that right.
Finally, my last gripe was with Kucharski's discussion of p-values. In particular, on pg. 107 he somewhat botches the explanation, leaving out the crucial conditional clause (p-values are calculated conditionally on some null model). This is one of the most common mistakes in interpreting p-values. Partially this is because the more precise statement is cumbersome; it wouldn't surprise me if the statement that appears now was the result of the copy editing process. But given the book space Kucharski devoted to the topic, he certainly should have taken the care to get (or insisted on keeping, if it was a copy editing suggestion) that right.
October 12, 2025
70%
Book Review: Proof by Adam Kucharski
Adam Kucharski’s Proof explores how certainty shapes our understanding of the world through the lens of mathematics, science, law, and human behavior. The book aims to uncover why “proof” — in its many forms — matters, and how it underpins our ability to make sense of uncertainty. Kucharski, who worked on modeling infectious diseases during the coronavirus pandemic, brings academic rigor to the topic, but the book remains accessible to general readers.
While the subject matter is solid and well-presented, the book doesn’t quite land a strong conclusion or call to action. It outlines how proof operates across disciplines but stops short of driving home why certainty is so critical to human progress and decision-making. The argument is left implicit — readers are expected to make the connection themselves.
In practical terms, certainty and proof give us leverage over chaos. The more probable and accurate our models of reality become, the more effectively we can plan, predict, and act. Most people struggle to plan even twelve hours ahead, but proof — in mathematics, science, or daily life — is what allows us to extend our foresight, increase the fidelity of our choices, and coordinate collective action with purpose.
Kucharski’s Proof is informative and thoughtful, though more explanatory than visionary. It’s worth reading for those interested in understanding how evidence, probability, and reasoning shape modern decision-making — but don’t expect it to tell you what to do with that knowledge.
Rating: 70/100
Book Review: Proof by Adam Kucharski
Adam Kucharski’s Proof explores how certainty shapes our understanding of the world through the lens of mathematics, science, law, and human behavior. The book aims to uncover why “proof” — in its many forms — matters, and how it underpins our ability to make sense of uncertainty. Kucharski, who worked on modeling infectious diseases during the coronavirus pandemic, brings academic rigor to the topic, but the book remains accessible to general readers.
While the subject matter is solid and well-presented, the book doesn’t quite land a strong conclusion or call to action. It outlines how proof operates across disciplines but stops short of driving home why certainty is so critical to human progress and decision-making. The argument is left implicit — readers are expected to make the connection themselves.
In practical terms, certainty and proof give us leverage over chaos. The more probable and accurate our models of reality become, the more effectively we can plan, predict, and act. Most people struggle to plan even twelve hours ahead, but proof — in mathematics, science, or daily life — is what allows us to extend our foresight, increase the fidelity of our choices, and coordinate collective action with purpose.
Kucharski’s Proof is informative and thoughtful, though more explanatory than visionary. It’s worth reading for those interested in understanding how evidence, probability, and reasoning shape modern decision-making — but don’t expect it to tell you what to do with that knowledge.
Rating: 70/100
This entire review has been hidden because of spoilers.
May 14, 2025
Thank you, NatGalley for providing an ARC of this book.
If you never read a book about statistics and maths, you will find this one quite amusing. If you have, then there is likely not enough new things for you to render this a definitive buy.
Let me preface my review by the fact that I’m a scientist and have a quantitative background.
This probably meant that I was expecting something different. A book by a mathematician talking about different types of proofs and logical arguments which inevitably lead to the uncertainty of using data to make arguments.
What the book actually was: largely unconnected collections of thoughts and stories about how we sort of proof things. I found the writing unfocused and meandering (sometimes with an unexpected abruptness the author pivots to a different topic).
As a I stated before, because it’s in my line of work and because I read books on statistics, a good chunk of this book was just a repetition and notes on concepts I know probably too much about. I also found the explanations of these statistical concepts not clear enough (especially the p-value). So for anyone looking to learn about these, you are better off with David Spiegelhalter.
If you never read a book about statistics and maths, you will find this one quite amusing. If you have, then there is likely not enough new things for you to render this a definitive buy.
Let me preface my review by the fact that I’m a scientist and have a quantitative background.
This probably meant that I was expecting something different. A book by a mathematician talking about different types of proofs and logical arguments which inevitably lead to the uncertainty of using data to make arguments.
What the book actually was: largely unconnected collections of thoughts and stories about how we sort of proof things. I found the writing unfocused and meandering (sometimes with an unexpected abruptness the author pivots to a different topic).
As a I stated before, because it’s in my line of work and because I read books on statistics, a good chunk of this book was just a repetition and notes on concepts I know probably too much about. I also found the explanations of these statistical concepts not clear enough (especially the p-value). So for anyone looking to learn about these, you are better off with David Spiegelhalter.
August 5, 2025
This book was an interesting read. I felt a little out of my depth for certain aspects of it, but that's part of the appeal. It's one thing to listen to a book about a subject that I already know fairly well; it's quite another to try something new. It required more of my focus and attention than other audiobooks, but the experience was worth it. I appreciate how varied its topics were, including historical figures such as Abraham Lincoln as well as events as recent as the COVID pandemic.
My one complaint is that the audiobook was formatted a little strangely. It listed about ten chapters, but towards the end, they stopped lining up with the narrators reading chapter titles. It seems as though the audiobook was divided into more sections than there were chapters, perhaps because some chapters were more than two hours long. This made things a little confusing as a listener. In an ideal world, the audiobook would list not just chapter numbers but chapter titles as well in its index. This would make navigation within the audiobook much simpler, and it would allow listeners to better keep track of what the audiobook is currently discussing.
My one complaint is that the audiobook was formatted a little strangely. It listed about ten chapters, but towards the end, they stopped lining up with the narrators reading chapter titles. It seems as though the audiobook was divided into more sections than there were chapters, perhaps because some chapters were more than two hours long. This made things a little confusing as a listener. In an ideal world, the audiobook would list not just chapter numbers but chapter titles as well in its index. This would make navigation within the audiobook much simpler, and it would allow listeners to better keep track of what the audiobook is currently discussing.
June 28, 2025
What makes this book truly shine is Kucharski’s gift for making the abstract feel tangible. He effortlessly bridges disciplines—from ancient philosophy to modern cryptography, from courtroom trials to scientific experiments—highlighting how humans have always wrestled with questions of proof, truth, and trust. The result is a narrative that is not only educational but deeply engaging.
Kucharski doesn’t just present facts; he provokes reflection. At a time when misinformation abounds and public trust in expertise is under strain, Proof arrives as both a timely and timeless work. It reminds us that certainty is often less about having all the answers and more about asking the right questions—and understanding the tools we use to find our way toward truth.
Whether you're a science enthusiast, a philosopher at heart, or simply someone who enjoys a good intellectual detective story, Proof offers insight, clarity, and just the right amount of challenge. Adam Kucharski has written a book that is not only readable but re-readable—a true testament to the power of thoughtful inquiry.
Kucharski doesn’t just present facts; he provokes reflection. At a time when misinformation abounds and public trust in expertise is under strain, Proof arrives as both a timely and timeless work. It reminds us that certainty is often less about having all the answers and more about asking the right questions—and understanding the tools we use to find our way toward truth.
Whether you're a science enthusiast, a philosopher at heart, or simply someone who enjoys a good intellectual detective story, Proof offers insight, clarity, and just the right amount of challenge. Adam Kucharski has written a book that is not only readable but re-readable—a true testament to the power of thoughtful inquiry.
May 31, 2025
I thought it was going to be a math book, and, though I put it my math shelf, it really isn't. There is a part about mathematical proof in the beginning, but it only scratches the surface of topics that interest me, and then in the end it circles back to math with a discussion of probabilistic and computer-driven proofs and whether they can ever be given dignity equivalent to logical proofs in axiomatic systems. But the middle of the book is much more about decision making under uncertainty and forms of argument that may sometimes be characterized as forms of proof, but that are fundamentally different from mathematical proof. Of course, you can prove propositions in game theory and probability that can facilitate better decision making under uncertainty, but that skirts around the edge of what I was looking for in this book and didn't get.
July 1, 2025
Waste of time....
From the marketing "teases" about the book, I was expecting an honest and robust deep dive into how our culture accepts proof, and how we should be pursuing proof. The book does not even concern itself with how the "scientific" community erred regarding COVID, or the vaccines. Rather, there is a presumption that the author and his cohorts were correct from the beginning, yet struggled to combat the skeptics with questions. This book could have been written by the World Health Organization, with its !misguided perspective.
A honest retroactive inspection should have been provided. That would be worth the time to read.
From the marketing "teases" about the book, I was expecting an honest and robust deep dive into how our culture accepts proof, and how we should be pursuing proof. The book does not even concern itself with how the "scientific" community erred regarding COVID, or the vaccines. Rather, there is a presumption that the author and his cohorts were correct from the beginning, yet struggled to combat the skeptics with questions. This book could have been written by the World Health Organization, with its !misguided perspective.
A honest retroactive inspection should have been provided. That would be worth the time to read.
October 27, 2025
A wide-ranging book looking at all sorts of ways to decide truth in science, mathematics, medicine, jurisprudence and politics (among other fields).
There is a lot of difference between the kind of proofs in Euclid’s works and in the amount of knowledge you have to have before calling for a lockdown because of an on-coming pandemic. How do we decide if the accused did in fact commit the crime? We need to know things before we act, but to what degree of certainty?
A very interesting audiobook well-structured, clear and thought-provoking, and also read/narrated/performed well. Some very interesting insights into knowledge-gathering and dissemination during the Covid pandemic.
There is a lot of difference between the kind of proofs in Euclid’s works and in the amount of knowledge you have to have before calling for a lockdown because of an on-coming pandemic. How do we decide if the accused did in fact commit the crime? We need to know things before we act, but to what degree of certainty?
A very interesting audiobook well-structured, clear and thought-provoking, and also read/narrated/performed well. Some very interesting insights into knowledge-gathering and dissemination during the Covid pandemic.
February 22, 2025
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.
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.
May 26, 2025
This is a very interesting book about how we have arrived at this point in time where thinking and logic are up for grabs. A historical perspective of truth and how to solve to it takes you from bloodletting and drowning alleged witches to politics and AI. For the most part the book stays out of the deep weeds but is does make you question where we are heading. Reads like a mind game of sorts but worth the introspection.
November 25, 2025
This was an interesting read, well up my alley in terms of topic matter. The author used compelling stories to back up technical points, and the coverage of many disciplines made it a mostly enjoyable read. However, it was sprawling in scope, dragged on at times, and could use some sharpening in structure. At times, I forgot the plot as it ran down side streets and alleyways, especially the COVID examples - which were interesting in substance, but ran on far too long in many cases.
December 6, 2025
Okay book. Strong start with a great clear narrative and connection of Abraham Lincoln and Euler. But it falls apart shortly after - the author is so learned he keeps jumping - he simply knows so much. At first every few paragraphs and then every paragraph. Changing topics and connecting but you start getting lost from the central narrative. In the attempt at breadth we lose the depth and also for me, the reader’s interest.
March 2, 2025
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.
May 20, 2025
Well, the author’s blog is very good.
This book is example after example after example, almost all of which you have probably read before.
The best parts by far are his personal anecdotes from the pandemic, but these are too few and far between. I suppose the publisher didn’t have confidence that a pure memoir would sell. A shame.
This book is example after example after example, almost all of which you have probably read before.
The best parts by far are his personal anecdotes from the pandemic, but these are too few and far between. I suppose the publisher didn’t have confidence that a pure memoir would sell. A shame.
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